Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index M > Category: Mathematician

Mathematician Quotes (387 quotes)
Mathematicians Quotes

Godfrey Harold Hardy quote “Languages die and mathematical ideas do not.”
background by Tom_Brown 6117, CC by 2.0 (source)

Aux mathématiciens, il appartient de chercher le vrai; les philosophes doivent se contenter du probable
The concern of mathematicians is to seek the truth; philosophers must be content with the probable.
In 'Divers Opuscules' collected in Oeuvres de Vico (1835), Vol. 1, 159. Translation by Webmaster.
Science quotes on:  |  Concern (228)  |  Content (69)  |  Must (1526)  |  Philosopher (258)  |  Probable (20)  |  Seek (213)  |  Truth (1057)

Die Mathematiker sind eine Art Franzosen. Spricht man zu ihnen, so übersetzen sie alles in ihre eigene Sprache, und so wird es alsobald etwas ganz anderes.
Mathematicians are a kind of Frenchmen. Whenever you say anything or talk to them, they translate it into their own language, and right away it is something completely different.
Quoted by Christiane Senn-Fennell, 'Oral and Written Communication', in Ian Westbury et al. (eds.), Teaching as a Reflective Practice (2000), 225.
Science quotes on:  |  Art (657)  |  Completely (135)  |  Different (577)  |  Frenchman (4)  |  Kind (557)  |  Language (293)  |  Man (2251)  |  Right (452)  |  Say (984)  |  Something (719)  |  Talk (100)  |  Translate (19)  |  Whenever (81)

Les mathématiciens parviennent à la solution d’un problême par le simple arrangement des données, & en réduisant le raisonnement à des opérations si simples, à des jugemens si courts, qu’ils ne perdent jamais de vue l’évidence qui leur sert de guide.
Mathematicians come to the solution of a problem by the simple arrangement of the data, and reducing the reasoning to such simple operations, to judgments so brief, that they never lose sight of the evidence that serves as their guide.
From a paper read to the Académie Royales des Sciences (18 Apr 1787), printed in Méthode de Nomenclature Chimique (1787), 12. Translation from the French by Webmaster.
Science quotes on:  |  Arrangement (91)  |  Brief (36)  |  Court (33)  |  Data (156)  |  Evidence (248)  |  Guide (97)  |  Judgment (132)  |  Lose (159)  |  Never (1087)  |  Operation (213)  |  Operations (107)  |  Problem (676)  |  Reasoning (207)  |  Reduction (51)  |  Sight (132)  |  Simple (406)  |  Solution (267)

Nemo mathematicus genium indemnatus habebit.
No mathematician is esteemed a genius until condemned.
Juvenal
“Mathematician” as used here, is in the sense of astrologer, or soothsayer. In Liberii, Satura VI, 562.
Science quotes on:  |  Astrologer (10)  |  Condemn (44)  |  Esteem (15)  |  Genius (284)  |  Soothsayer (4)

Quand les physiciens nous demandent la solution d'un problème, ce n'est pas une corvée qu'ils nous impsent, c'est nous au contraire qui leur doivent des remercîments.
When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 111.
Science quotes on:  |  Ask (411)  |  Contrary (141)  |  Owe (71)  |  Physicist (259)  |  Problem (676)  |  Solution (267)  |  Thank (46)  |  Thanks (26)

The Annotated Alice, of course, does tie in with math, because Lewis Carroll was, as you know, a professional mathematician. So it wasn’t really too far afield from recreational math, because the two books are filled with all kinds of mathematical jokes. I was lucky there in that I really didn’t have anything new to say in The Annotated Alice because I just looked over the literature and pulled together everything in the form of footnotes. But it was a lucky idea because that’s been the best seller of all my books.
In Anthony Barcellos, 'A Conversation with Martin Gardner', The Two-Year College Mathematics Journal (Sep 1979), 10, No. 4, 241.
Science quotes on:  |   (2863)  |  All (4108)  |  Best (459)  |  Book (392)  |  Lewis Carroll (45)  |  Course (409)  |  Everything (476)  |  Footnote (5)  |  Form (959)  |  Idea (843)  |  Joke (83)  |  Kind (557)  |  Know (1518)  |  Literature (103)  |  Look (582)  |  Lucky (13)  |  Mathematics (1328)  |  New (1216)  |  Professional (70)  |  Pull (43)  |  Pull Together (2)  |  Recreation (20)  |  Say (984)  |  Tie (38)  |  Together (387)  |  Two (937)

Ultima se tangunt. How expressive, how nicely characterizing withal is mathematics! As the musician recognizes Mozart, Beethoven, Schubert in the first chords, so the mathematician would distinguish his Cauchy, Gauss, Jacobi, Helmholtz in a few pages.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 29, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 186-187. From the original German, “Ultima se tangunt. Und wie ausdrucksfähig, wie fein charakterisirend ist dabei die Mathematik. Wie der Musiker bei den ersten Tacten Mozart, Beethoven, Schubert erkennt, so würde der Mathematiker nach wenig Seiten, seinen Cauchy, Gauss, Jacobi, Helmholtz unterscheiden.” [The Latin words translate as “the final touch”. —Webmaster]
Science quotes on:  |  Beethoven (13)  |  Baron Augustin-Louis Cauchy (10)  |  Characterize (20)  |  Chord (4)  |  Distinguish (160)  |  Expressive (6)  |  First (1283)  |  Carl Friedrich Gauss (77)  |  Hermann von Helmholtz (28)  |  Karl Jacobi (10)  |  Mathematics (1328)  |  Mathematics And Art (8)  |  Mathematics As A Fine Art (23)  |  Mozart (2)  |  Musician (21)  |  Page (30)  |  Recognize (125)

A mathematician is a blind man in a dark room looking for a black cat that doesn’t exist. [Misattributed to Charles Darwin.]
Anonymous
Traced by quoteinvestigator.com to Tomlinson Fort, 'Mathematics and the Sciences', The American Mathematical Monthly (Nov 1940), 47, No. 9, 606. The article writer skeptically noted that: “I have heard it said that Charles Darwin gave the following. (He probably never did.)” Quote Investigator cites a number of wide variations of the metaphor, from various authors and sources, going back to at least 1846.
Science quotes on:  |  Black (42)  |  Blind (95)  |  Cat (47)  |  Dark (140)  |  Charles Darwin (303)  |  Exist (443)  |  Looking (189)  |  Man (2251)  |  Misattributed (19)  |  Room (40)

A mathematician is a device for turning coffee into theorems.
In D. S. Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology (2008), Preface, ix. Also attributed incorrectly to Paul Erdos, who did often repeat it.
Science quotes on:  |  Coffee (19)  |  Device (70)  |  Theorem (112)

A mathematician may say anything he pleases, but a physicist must be at least partially sane.
Attributed. Cited in R. B. Lindsay, 'On the Relation of Mathematics and Physics', The Scientific Monthly, Dec 1944, 59, 456.
Science quotes on:  |  Must (1526)  |  Partially (8)  |  Physicist (259)  |  Please (65)  |  Say (984)  |  Truth (1057)

A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.
As quoted in E.T. Bell, Men of Mathematics (1937, 1965), 182. Without citation, except, “As it is often quoted as … Napoleon’s famous estimate of Laplace, of which he is reported to have delivered himself while he was a prisoner at St. Helena.” Laplace had a six-week tenure in the Ministry of the Interior.
Science quotes on:  |  Administration (12)  |  Administrator (11)  |  Deceive (26)  |  Doubtful (29)  |  Everywhere (94)  |  First (1283)  |  Himself (461)  |  Idea (843)  |  Infinitely (13)  |  Pierre-Simon Laplace (62)  |  Mediocre (14)  |  Point (580)  |  Point Of View (80)  |  Question (621)  |  Rank (67)  |  Reveal (148)  |  Revealed (60)  |  Saw (160)  |  Seek (213)  |  Small (477)  |  Spirit (265)  |  Subtlety (19)  |  True (212)  |  View (488)  |  Work (1351)

A mathematician thinks that two points are enough to define a straight line, while a physicist wants more data.
Anonymous
Science quotes on:  |  Data (156)  |  Define (49)  |  Difference (337)  |  Enough (340)  |  Line (91)  |  More (2559)  |  Physicist (259)  |  Point (580)  |  Quip (80)  |  Straight (73)  |  Straight Line (30)  |  Think (1086)  |  Two (937)  |  Want (497)

A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditional mathematics is in danger of becoming a down monkey, and a teacher of modern mathematics an up monkey. The down teacher dishing out one routine problem after another may never get off the ground, never attain any general idea. and the up teacher dishing out one definition after the other may never climb down from his verbiage, may never get down to solid ground, to something of tangible interest for his pupils.
From 'A Story With A Moral', Mathematical Gazette (Jun 1973), 57, No. 400, 86-87
Science quotes on:  |  Attain (125)  |  Becoming (96)  |  Climb (35)  |  Creature (233)  |  Danger (115)  |  Definition (221)  |  Down (456)  |  Enemy (82)  |  Escape (80)  |  Fact (1210)  |  Find (998)  |  Food (199)  |  General (511)  |  Generalization (57)  |  Ground (217)  |  Idea (843)  |  Incessant (8)  |  Interest (386)  |  Mathematics (1328)  |  Modern (385)  |  Modern Mathematics (50)  |  Monkey (52)  |  Moral (195)  |  Must (1526)  |  Never (1087)  |  Other (2236)  |  Problem (676)  |  Pupil (61)  |  Real (149)  |  Routine (25)  |  Solid (116)  |  Something (719)  |  Specialization (23)  |  Tangible (15)  |  Teacher (143)  |  Think (1086)  |  Tree (246)  |  Up (5)  |  Verbiage (3)

A mathematician … has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.
In A Mathematician's Apology (1940, 2012), 84.
Science quotes on:  |  Idea (843)  |  Last (426)  |  Lasting (7)  |  Longer (10)  |  Material (353)  |  Pattern (110)  |  Time (1877)  |  Wear (18)  |  Word (619)  |  Work (1351)

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 84.
Science quotes on:  |  Idea (843)  |  Maker (34)  |  Making (300)  |  More (2559)  |  Painter (29)  |  Pattern (110)  |  Permanence (24)  |  Permanent (64)  |  Poet (83)

A mathematician’s reputation rests on the number of bad proofs he has given.
As quoted in John E. Littlewood, A Mathematician’s Miscellany (1953), 41. [His meaning was that an important result is built upon earlier clumsy work. —Webmaster]
Science quotes on:  |   (2863)  |  Bad (180)  |  Number (699)  |  Proof (287)  |  Reputation (33)  |  Rest (280)

A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.
In Rota's 'Introduction' written (1980) to preface Philip J. Davis and Reuben Hersh, The Mathematical Experience (1981, 2012), xxii.
Science quotes on:  |   (2863)  |  Analogy (71)  |  Being (1278)  |  Core (18)  |  Discovery (780)  |  Frustration (12)  |  Guesswork (4)  |  Making (300)  |  Mind (1338)  |  More (2559)  |  Play (112)  |  Playing (42)  |  Proof (287)  |  Tangle (6)  |  Thinking (414)  |  Trick (35)  |  Way (1217)  |  Wishful (6)  |  Work (1351)

A New Arithmetic: “I am not much of a mathematician,” said the cigarette, “but I can add nervous troubles to a boy, I can subtract from his physical energy, I can multiply his aches and pains, I can divide his mental powers, I can take interest from his work and discount his chances for success.”
Anonymous
In Henry Ford, The Case Against the Little White Slaver (1914), Vol. 3, 40.
Science quotes on:  |  Ache (7)  |  Addition (66)  |  Arithmetic (136)  |  Boy (94)  |  Chance (239)  |  Cigarette (24)  |  Divide (75)  |  Energy (344)  |  Interest (386)  |  Mental (177)  |  Mind (1338)  |  Multiply (37)  |  Nerve (79)  |  New (1216)  |  Pain (136)  |  Physical (508)  |  Power (746)  |  Subtraction (4)  |  Success (302)  |  Trouble (107)  |  Work (1351)

A painter makes patterns with shapes and colours, a poet with words. A painting may embody an “idea,” but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, as Housman insisted, the importance of ideas in poetry is habitually exaggerated. … The poverty of ideas seems hardly to affect the beauty of the verbal pattern. A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.
In A Mathematician’s Apology (1940, 2012), 84-85.
Science quotes on:  |  Affect (19)  |  Beauty (299)  |  Color (137)  |  Commonplace (23)  |  Count (105)  |  Deal (188)  |  Embody (16)  |  Exaggerate (6)  |  Good (889)  |  Habitually (2)  |  A. E. Housman (2)  |  Idea (843)  |  Importance (286)  |  Insist (20)  |  Last (426)  |  Less (103)  |  Material (353)  |  More (2559)  |  On The Other Hand (34)  |  Other (2236)  |  Painter (29)  |  Painting (44)  |  Pattern (110)  |  Poet (83)  |  Poetry (143)  |  Poverty (37)  |  Shape (72)  |  Time (1877)  |  Unimportant (6)  |  Usually (176)  |  Verbal (10)  |  Wear (18)  |  Word (619)  |  Work (1351)

A prominent official was asked to deliver an after-dinner speech at the banquet recently held in Cambridge, Mass., for the Mathematicians at the International Congress. “What do you wish me to speak about?" he asked. "About five minutes," was the answer.
Anonymous
Found as a space filler, Pi Mu Epsilon Journal (1949), 1, No. 1, 102.
Science quotes on:  |  Answer (366)  |  Ask (411)  |  Banquet (2)  |  Congress (19)  |  Deliver (29)  |  Do (1908)  |  International (37)  |  Mass (157)  |  Minute (125)  |  Speak (232)  |  Speech (61)  |  Wish (212)

A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same Nature.
…...
Science quotes on:  |  All (4108)  |  Artist (90)  |  Experience (467)  |  Great (1574)  |  Impression (114)  |  Name (333)  |  Nature (1926)  |  Pleasure (178)  |  Same (157)  |  Scientist (820)  |  Work (1351)  |  Worthy (34)

A single axis is harmless, but a murderous mathematician can go on a killing spree with a pair of axes.
Anonymous
Science quotes on:  |  Axe (15)  |  Axis (9)  |  Kill (100)  |  Murder (13)  |  Pair (9)  |  Single (353)

A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?
In 'Introduction' contributed to Donald J. Albers and Gerald L. Alexanderson, More Mathematical People: Contemporary Conversations (1990), xi.
Science quotes on:  |  Accomplishment (93)  |  Beautiful (258)  |  Mathematics (1328)  |  Music (129)  |  Musician (21)  |  Pattern (110)  |  Proportion (136)  |  Share (75)  |  Surprise (86)

A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.
In Scientific American (May 1963). As quoted and cited in The Hutchinson Encyclopedia of Science (1998), 468.
Science quotes on:  |  Advance (280)  |  Beauty (299)  |  Construct (124)  |  Correct (86)  |  Data (156)  |  Experimental (192)  |  Fit (134)  |  God (757)  |  High (362)  |  Likely (34)  |  Mathematics (1328)  |  More (2559)  |  Order (632)  |  Theory (970)  |  Ugly (14)  |  Universe (857)

A thorough advocate in a just cause, a penetrating mathematician facing the starry heavens, both alike bear the semblance of divinity
In Wilhelm Meister, Wanderjahre, Zweites Buch, in 'Sprüche in Prosa' Natur, VI, 947.
Science quotes on:  |  Advocate (18)  |  Alike (60)  |  Bear (159)  |  Both (493)  |  Cause (541)  |  Divinity (23)  |  Face (212)  |  Heaven (258)  |  Heavens (125)  |  Penetrate (67)  |  Semblance (5)  |  Star (427)  |  Thorough (40)

Abel has left mathematicians enough to keep them busy for 500 years.
As quoted, without citation, in Eric Temple Bell, The Queen of the Sciences (1931), 10.
Science quotes on:  |  Busy (28)  |  Enough (340)  |  Leave (130)  |  Legacy (14)  |  Year (933)

Abel has left mathematicians something to keep them busy for five hundred years.
As quoted by Eric Temple Bell in The Queen of the Sciences (1931, 1938), 10.
Science quotes on:  |  Niels Henrik Abel (15)  |  Busy (28)  |  Hundred (229)  |  Something (719)  |  Year (933)

After a tremendous task has been begun in our time, first by Copernicus and then by many very learned mathematicians, and when the assertion that the earth moves can no longer be considered something new, would it not be much better to pull the wagon to its goal by our joint efforts, now that we have got it underway, and gradually, with powerful voices, to shout down the common herd, which really does not weigh arguments very carefully?
Letter to Galileo (13 Oct 1597). In James Bruce Ross (ed.) and Mary Martin (ed., trans.), 'Comrades in the Pursuit of Truth', The Portable Renaissance Reader (1953, 1981), 599. As quoted and cited in Merry E. Wiesner, Early Modern Europe, 1450-1789 (2013), 377.
Science quotes on:  |  Argument (138)  |  Assertion (32)  |  Better (486)  |  Carefully (65)  |  Common (436)  |  Consider (416)  |  Copernicus_Nicolaud (2)  |  Down (456)  |  Earth (996)  |  Effort (227)  |  First (1283)  |  Goal (145)  |  Gradually (102)  |  Herd (15)  |  Joint (31)  |  Learn (629)  |  Learned (235)  |  Move (216)  |  New (1216)  |  Powerful (139)  |  Pull (43)  |  Shout (25)  |  Something (719)  |  Task (147)  |  Time (1877)  |  Tremendous (26)  |  Voice (52)  |  Wagon (8)  |  Weigh (49)

After an honest day’s work a mathematician goes off duty. Mathematics is very hard work, and dons tend to be above average in health and vigor. Below a certain threshold a man cracks up; but above it, hard mental work makes for health and vigor (also—on much historical evidence throughout the ages—for longevity). I have noticed lately that when I am working really hard I wake around 5.30 a.m. ready and eager to start; if I am slack, I sleep till I am called.
In 'The Mathematician’s Art of Work' (1967), collected in Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 195.
Science quotes on:  |   (2863)  |  Age (499)  |  Average (82)  |  Call (769)  |  Certain (550)  |  Duty (68)  |  Eager (15)  |  Evidence (248)  |  Hard (243)  |  Hard Work (20)  |  Health (193)  |  Historical (70)  |  History (673)  |  Honest (50)  |  Longevity (6)  |  Man (2251)  |  Mathematics (1328)  |  Mental (177)  |  Ready (39)  |  Sleep (76)  |  Start (221)  |  Tend (124)  |  Threshold (10)  |  Throughout (98)  |  Vigor (9)  |  Wake (13)  |  Work (1351)

Although my Aachen colleagues and students at first regarded the “pure mathematician” with suspicion, I soon had the satisfaction of being accepted a useful member not merely in teaching but also engineering practice; thus I was requested to render expert opinions and to participate in the Ingenieurverein [engineering association].
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 527. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
Science quotes on:  |  Accept (191)  |  Association (46)  |  Being (1278)  |  Colleague (50)  |  Engineering (175)  |  Expert (65)  |  First (1283)  |  Member (41)  |  Mere (84)  |  Merely (316)  |  Opinion (281)  |  Participate (8)  |  Practice (204)  |  Pure (291)  |  Regard (305)  |  Render (93)  |  Request (7)  |  Satisfaction (74)  |  Soon (186)  |  Student (300)  |  Suspicion (35)  |  Teaching (188)  |  Useful (250)

Among the memoirs of Kirchhoff are some of uncommon beauty. … Can anything be beautiful, where the author has no time for the slightest external embellishment?—But—; it is this very simplicity, the indispensableness of each word, each letter, each little dash, that among all artists raises the mathematician nearest to the World-creator; it establishes a sublimity which is equalled in no other art, something like it exists at most in symphonic music. The Pythagoreans recognized already the similarity between the most subjective and the most objective of the arts.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 28-29, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 186. From the original German, “Gerade unter den zuletzt erwähnten Abhandlungen Kirchhoff’s sind einige von ungewöhnlicher Schönheit. … kann etwas schön sein, wo dem Autor auch zur kleinsten äusseren Ausschmückung die Zeit fehlt?–Doch–; gerade durch diese Einfachheit, durch diese Unentbehrlichkeit jedes Wortes, jedes Buchstaben, jedes Strichelchens kömmt der Mathematiker unter allen Künstlern dem Weltenschöpfer am nächsten; sie begründet eine Erhabenheit, die in keiner Kunst ein Gleiches,–Aehnliches höchstens in der symphonischen Musik hat. Erkannten doch schon die Pythagoräer die Aehnlichkeit der subjectivsten und der objectivsten der Künste.”
Science quotes on:  |  All (4108)  |  Already (222)  |  Art (657)  |  Artist (90)  |  Author (167)  |  Beautiful (258)  |  Beauty (299)  |  Creator (91)  |  Dash (3)  |  Equal (83)  |  Establish (57)  |  Exist (443)  |  Indispensable (28)  |  Gustav Robert Kirchhoff (4)  |  Letter (109)  |  Little (707)  |  Mathematics And Art (8)  |  Mathematics As A Fine Art (23)  |  Memoir (13)  |  Most (1731)  |  Music (129)  |  Objective (91)  |  Other (2236)  |  Pythagoras (38)  |  Raise (35)  |  Recognize (125)  |  Similarity (31)  |  Simplicity (167)  |  Something (719)  |  Subjective (19)  |  Sublimity (5)  |  Symphony (9)  |  Time (1877)  |  Uncommon (14)  |  Word (619)  |  World (1774)

Ampère was a mathematician of various resources & I think might rather be called excentric [sic] than original. He was as it were always mounted upon a hobby horse of a monstrous character pushing the most remote & distant analogies. This hobby horse was sometimes like that of a child ['s] made of heavy wood, at other times it resembled those [?] shapes [?] used in the theatre [?] & at other times it was like a hypogrif in a pantomime de imagie. He had a sort of faith in animal magnetism & has published some refined & ingenious memoirs to prove the identity of electricity & magnetism but even in these views he is rather as I said before excentric than original. He has always appeared to me to possess a very discursive imagination & but little accuracy of observation or acuteness of research.
'Davy’s Sketches of his Contemporaries', Chymia, 1967, 12, 135-6.
Science quotes on:  |   (2863)  |  Accuracy (78)  |  André-Marie Ampère (11)  |  Animal (617)  |  Call (769)  |  Character (243)  |  Child (307)  |  Electricity (159)  |  Faith (203)  |  Horse (74)  |  Identity (19)  |  Imagination (328)  |  Ingenious (55)  |  Little (707)  |  Magnetism (41)  |  Most (1731)  |  Mount (42)  |  Observation (555)  |  Other (2236)  |  Personality (62)  |  Possess (156)  |  Prove (250)  |  Remote (83)  |  Research (664)  |  Think (1086)  |  Time (1877)  |  Various (200)  |  View (488)  |  Wood (92)

An accomplished mathematician, i.e. a most wretched orator.
[Closing remark in an address, referring to himself.]
In 'The Prefactory Oration' (address to the University of Cambridge upon being elected Lucasian Professor of Mathematics, 14 Mar 1664). In Mathematical Lectures (1734), Preface, xxxii.
Science quotes on:  |  Himself (461)  |  Most (1731)  |  Orator (2)  |  Wretched (8)

An applied mathematician loves the theorem. A pure mathematician loves the proof.
Anonymous
Science quotes on:  |  Applied (177)  |  Apply (160)  |  Love (309)  |  Proof (287)  |  Pure (291)  |  Theorem (112)

An engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard.
After some observations and rough calculations the engineer realizes the situation and starts laughing.
A few minutes later the physicist understands too and chuckles to himself happily, as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.
Anonymous
In 'Zero Gravity: The Lighter Side of Science' APS News (Jun 2003), 12 No. 6.
Science quotes on:  |  Alone (311)  |  Already (222)  |  Anecdote (21)  |  Calculation (127)  |  Consider (416)  |  Corollary (5)  |  Doubt (304)  |  Engineer (121)  |  Enough (340)  |  Evidence (248)  |  Experiment (695)  |  Experimental (192)  |  Find (998)  |  Funny (11)  |  Himself (461)  |  Humor (8)  |  Indeed (324)  |  Joke (83)  |  Laugh (47)  |  Minute (125)  |  Observation (555)  |  Observed (149)  |  Paper (182)  |  Perplex (6)  |  Physicist (259)  |  Presence (63)  |  Publish (36)  |  Rapidly (66)  |  Realize (147)  |  Right (452)  |  Significant (74)  |  Situation (113)  |  Start (221)  |  Subject (521)  |  Themselves (433)  |  Trivial (57)  |  Understand (606)

An essential [of an inventor] is a logical mind that sees analogies. No! No! not mathematical. No man of a mathematical habit of mind ever invented anything that amounted to much. He hasn’t the imagination to do it. He sticks too close to the rules, and to the things he is mathematically sure he knows, to create anything new.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
Science quotes on:  |  Amount (151)  |  Analogy (71)  |  Create (235)  |  Do (1908)  |  Essential (199)  |  Habit (168)  |  Imagination (328)  |  Invent (51)  |  Inventor (71)  |  Know (1518)  |  Logical (55)  |  Man (2251)  |  Mathematics (1328)  |  Mind (1338)  |  New (1216)  |  Rule (294)  |  See (1081)  |  Thing (1915)

And how admirable and rare an ornament, O good God, is mildenesse in a divine? And how much is it to be wished in this age, that all divines were mathematicians? that is men gentle and meeke.
Trigonometria (1595), trans. R. Handson (1614), Epistle Dedicatorie.
Science quotes on:  |  Admiration (59)  |  Age (499)  |  All (4108)  |  Divine (112)  |  God (757)  |  Good (889)  |  Mildness (2)  |  Ornament (20)  |  Rare (89)  |  Rarity (11)  |  Wish (212)

Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians’ stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
From 'Mathematics of War and Foreign Politics', in James R. Newman, The World of Mathematics (1956), Vol. 2, 1248.
Science quotes on:  |  Advantage (134)  |  Amendment (2)  |  Choice (110)  |  Corresponding (3)  |  Definite (110)  |  Find (998)  |  Formula (98)  |  Hardly (19)  |  Mathematics (1328)  |  Merit (50)  |  Ready (39)  |  Statement (142)  |  Stock (7)  |  Useless (33)  |  Vague (47)  |  Verbal (10)  |  Wrong (234)

Another great and special excellence of mathematics is that it demands earnest voluntary exertion. It is simply impossible for a person to become a good mathematician by the happy accident of having been sent to a good school; this may give him a preparation and a start, but by his own individual efforts alone can he reach an eminent position.
In Conflict of Studies (1873), 2.
Science quotes on:  |  Accident (88)  |  Alone (311)  |  Become (815)  |  Demand (123)  |  Earnest (2)  |  Effort (227)  |  Eminent (17)  |  Excellence (39)  |  Exertion (15)  |  Give (202)  |  Good (889)  |  Great (1574)  |  Happy (105)  |  Impossible (251)  |  Individual (404)  |  Mathematics (1328)  |  Person (363)  |  Position (77)  |  Preparation (58)  |  Reach (281)  |  School (219)  |  Send (22)  |  Simply (53)  |  Special (184)  |  Start (221)  |  Value Of Mathematics (60)  |  Voluntary (4)

Archimedes was not free from the prevailing notion that geometry was degraded by being employed to produce anything useful. It was with difficulty that he was induced to stoop from speculation to practice. He was half ashamed of those inventions which were the wonder of hostile nations, and always spoke of them slightingly as mere amusements, as trifles in which a mathematician might be suffered to relax his mind after intense application to the higher parts of his science.
In Lord Bacon', Edinburgh Review (Jul 1887), in Critical and Miscellaneous Essays (1879), Vol. 1, 395.
Science quotes on:  |  Amusement (33)  |  Application (242)  |  Archimedes (55)  |  Ashamed (3)  |  Being (1278)  |  Degrade (8)  |  Difficulty (196)  |  Employ (113)  |  Free (232)  |  Geometry (255)  |  Higher (37)  |  Hostile (8)  |  Induce (22)  |  Intense (20)  |  Invention (369)  |  Mathematicians and Anecdotes (141)  |  Mere (84)  |  Mind (1338)  |  Nation (193)  |  Notion (113)  |  Part (222)  |  Practice (204)  |  Prevailing (3)  |  Produce (104)  |  Relax (2)  |  Science (3879)  |  Slight (31)  |  Speak (232)  |  Speculation (126)  |  Stoop (3)  |  Suffer (41)  |  Trifle (15)  |  Useful (250)  |  Wonder (236)

As an undergraduate who believed himself destined to be a mathematician I happened upon “Man and Superman” and as I read it at a library table I felt like Saul of Tarsus when the light broke. “If literature,” I said to myself, “can be like this then literature is the stuff for me.” And to this day I never see a differential equation written out without breathing a prayer of thanks.
In 'An Open Letter to George Bernard Shaw', Saturday Review (21 Jul 1956), 39, 12. ollected in If You Don't Mind My Saying So: Essays on Man and Nature (1964), 391.
Science quotes on:  |  Belief (578)  |  Breathe (45)  |  Breathing (23)  |  Destined (42)  |  Differential Equation (18)  |  Equation (132)  |  Happen (274)  |  Happened (88)  |  Himself (461)  |  Library (48)  |  Light (607)  |  Literature (103)  |  Man (2251)  |  Myself (212)  |  Never (1087)  |  Prayer (28)  |  Read (287)  |  See (1081)  |  Superman (3)  |  Table (104)  |  Thank (46)  |  Thanks (26)  |  Undergraduate (15)

As for the place of mathematics in relation to other sciences, mathematics can be seen as a big warehouse full of shelves. Mathematicians put things on the shelves and guarantee that they are true. They also explain how to use them and how to reconstruct them. Other sciences come and help themselves from the shelves; mathematicians are not concerned with what they do with what they have taken. This metaphor is rather coarse, but it reflects the situation well enough.
From interview with Marc Kirch, 'My First Fifty years at the Collège de France', collected in Helge Holden and Ragni Piene, The Abel Prize: 2003-2007 The First Five Years (2009), 15-29.
Science quotes on:  |  Coarse (4)  |  Concern (228)  |  Do (1908)  |  Enough (340)  |  Explain (322)  |  Guarantee (30)  |  Help (105)  |  Mathematics (1328)  |  Metaphor (33)  |  Other (2236)  |  Reconstruct (5)  |  Reflect (32)  |  Relation (157)  |  Science (3879)  |  Shelf (8)  |  Situation (113)  |  Themselves (433)  |  Thing (1915)  |  True (212)  |  Use (766)

As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.
At age 36.
"Proceedings of the Royal Society of Edinburgh (1939), 59 122. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 109-110. This quote is also on this web page in a longer version that begins, “Pure mathematics and physics are… ”.
Science quotes on:  |  Age (499)  |  Become (815)  |  Chosen (48)  |  Evident (91)  |  Find (998)  |  Interesting (153)  |  Nature (1926)  |  Rule (294)  |  Time (1877)

As we cannot use physician for a cultivator of physics, I have called him a physicist. We need very much a name to describe a cultivator of science in general. I should incline to call him a Scientist. Thus we might say, that as an Artist is a Musician, Painter or Poet, a Scientist is a Mathematician, Physicist, or Naturalist.
The Philosophy of the Inductive Sciences (1840), Vol. I, cxiii.
Science quotes on:  |  Artist (90)  |  Call (769)  |  Describe (128)  |  Description (84)  |  General (511)  |  Musician (21)  |  Name (333)  |  Naturalist (70)  |  Need (290)  |  Nomenclature (146)  |  Painter (29)  |  Physic (517)  |  Physician (273)  |  Physicist (259)  |  Physics (533)  |  Poet (83)  |  Say (984)  |  Science (3879)  |  Scientist (820)  |  Use (766)

At times the mathematician has the passion of a poet or a conqueror, the rigor of his arguments is that of a responsible statesman or, more simply, of a concerned father, and his tolerance and resignation are those of an old sage; he is revolutionary and conservative, skeptical and yet faithfully optimistic.
Max Dehn
Address (18 Jan 1928) at the University of Frankfurt am Main, Germany. Trans. by Abe Schenitzer, and published in 'The Mentality of the Mathematician: A Characterization', The Mathematical Intelligencer (1983), 5, No. 2. As quoted in Michael Fitzgerald and Ioan James, The Mind of the Mathematician (2007), 6.
Science quotes on:  |  Argument (138)  |  Concern (228)  |  Conqueror (8)  |  Conservative (15)  |  Faithfully (3)  |  Father (110)  |  More (2559)  |  Old (481)  |  Passion (114)  |  Poet (83)  |  Resignation (3)  |  Responsible (17)  |  Revolutionary (31)  |  Rigor (27)  |  Sage (23)  |  Skeptical (20)  |  Statesman (19)  |  Time (1877)  |  Tolerance (10)

Bacon himself was very ignorant of all that had been done by mathematics; and, strange to say, he especially objected to astronomy being handed over to the mathematicians. Leverrier and Adams, calculating an unknown planet into a visible existence by enormous heaps of algebra, furnish the last comment of note on this specimen of the goodness of Bacon’s view… . Mathematics was beginning to be the great instrument of exact inquiry: Bacon threw the science aside, from ignorance, just at the time when his enormous sagacity, applied to knowledge, would have made him see the part it was to play. If Newton had taken Bacon for his master, not he, but somebody else, would have been Newton.
In Budget of Paradoxes (1872), 53-54.
Science quotes on:  |   (2863)  |  Algebra (113)  |  All (4108)  |  Applied (177)  |  Apply (160)  |  Astronomy (229)  |  Sir Francis Bacon (184)  |  Begin (260)  |  Beginning (305)  |  Being (1278)  |  Calculate (54)  |  Comment (11)  |  Enormous (41)  |  Exact (68)  |  Existence (456)  |  Furnish (96)  |  Goodness (25)  |  Great (1574)  |  Heap (14)  |  Himself (461)  |  Ignorance (240)  |  Ignorant (90)  |  Inquiry (78)  |  Instrument (144)  |  Knowledge (1529)  |  Last (426)  |  LeVerrier_Urbain (3)  |  Master (178)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Sir Isaac Newton (333)  |  Note (34)  |  Object (422)  |  Part (222)  |  Planet (356)  |  Play (112)  |  Sagacity (10)  |  Say (984)  |  Science (3879)  |  See (1081)  |  Specimen (28)  |  Strange (157)  |  Throw (43)  |  Time (1877)  |  Unknown (182)  |  View (488)  |  Visible (84)

Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.
In Introduction to Mathematics (1911), 59.
Science quotes on:  |  Arabic (3)  |  Astonish (37)  |  Astonished (9)  |  Call (769)  |  Compulsory (7)  |  Decimal (20)  |  Difficult (246)  |  Division (65)  |  Easy (204)  |  Education (378)  |  Europe (43)  |  Fact (1210)  |  Fraction (13)  |  Greek (107)  |  Impossibility (61)  |  Influence (222)  |  Integer (10)  |  Introduction (35)  |  Largest (39)  |  Learn (629)  |  Mathematics (1328)  |  Mathematics As A Language (20)  |  Miraculous (11)  |  Modern (385)  |  Modern World (4)  |  More (2559)  |  Most (1731)  |  Multiplication (43)  |  Notation (27)  |  Nothing (966)  |  Number (699)  |  Operation (213)  |  Perfect (216)  |  Perform (121)  |  Population (110)  |  Power (746)  |  Probably (49)  |  Reckon (31)  |  Reckoning (19)  |  Result (677)  |  Western (45)  |  Whole (738)  |  World (1774)

Behind the artisan is the chemist, behind the chemist a physicist, behind the physicist a mathematician.
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 217.
Science quotes on:  |  Artisan (9)  |  Behind (137)  |  Chemist (156)  |  Physicist (259)

Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
Science quotes on:  |  Accustom (52)  |  Advantage (134)  |  Approximate (25)  |  Attention (190)  |  Benefit (114)  |  Both (493)  |  Careful (24)  |  Character (243)  |  Chemist (156)  |  Chemistry (353)  |  Complete (204)  |  Constantly (27)  |  Course (409)  |  Demand (123)  |  Depend (228)  |  Difference (337)  |  Discipline (77)  |  Education (378)  |  Element (310)  |  Error (321)  |  Essential (199)  |  Exact (68)  |  Excellence (39)  |  Expectation (65)  |  False (100)  |  Form (959)  |  Fundamental (250)  |  Habituate (3)  |  Hardly (19)  |  Immense (86)  |  Importance (286)  |  Influence (222)  |  Know (1518)  |  Loose (14)  |  Mathematics (1328)  |  Mode (41)  |  Most (1731)  |  Nature (1926)  |  Never (1087)  |  Obtain (163)  |  Opinion (281)  |  Overlook (31)  |  Peculiar (113)  |  Practice (204)  |  Precision (68)  |  Produce (104)  |  Produced (187)  |  Proof (287)  |  Proportional (4)  |  Quality (135)  |  Quantity (132)  |  Require (219)  |  Result (677)  |  Satisfied (23)  |  Science (3879)  |  Slight (31)  |  Source Of Error (2)  |  Student (300)  |  Study (653)  |  Teach (277)  |  Thought (953)  |  Truth (1057)  |  Value Of Mathematics (60)  |  Whole (738)

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals—the flotsam and jetsam of historical currents. The men who radically altered history, the great creative scientists and mathematicians, are seldom mentioned if at all.
Opening paragraph of book review, 'Adventures Of a Mathematician: The Man Who Invented the H-Bomb', New York Times (9 May 1976), 201.
Science quotes on:  |  All (4108)  |  Alter (62)  |  Altered (32)  |  Altering (3)  |  Biography (240)  |  Compulsive (3)  |  Creative (137)  |  Current (118)  |  Flotsam (2)  |  General (511)  |  Great (1574)  |  Historical (70)  |  History (673)  |  Ignorance (240)  |  Ignorant (90)  |  Jetsam (2)  |  King (35)  |  Leader (43)  |  Mention (82)  |  Mentioned (3)  |  Paranoid (3)  |  Political (121)  |  Public School (3)  |  Queen (14)  |  Radically (5)  |  Ridiculous (24)  |  School (219)  |  Scientist (820)  |  Seldom (65)  |  Still (613)  |  Teaching (188)  |  Voyager (3)

Boltzmann was both a wizard of a mathematician and a physicist of international renown. The magnitude of his output of scientific papers was positively unnerving. He would publish two, three, sometimes four monographs a year; each one was forbiddingly dense, festooned with mathematics, and as much as a hundred pages in length.
In 'The Bulldog: A Profile of Ludwig Boltzmann', The American Scholar (1 Jan 1999), 99.
Science quotes on:  |  Ludwig Eduard Boltzmann (17)  |  Both (493)  |  Dense (5)  |  Festoon (3)  |  Hundred (229)  |  International (37)  |  Magnitude (83)  |  Mathematics (1328)  |  Monograph (5)  |  Output (10)  |  Paper (182)  |  Physicist (259)  |  Publish (36)  |  Renown (2)  |  Scientific (941)  |  Two (937)  |  Wizard (4)  |  Year (933)

Büchsel in his reminiscences from the life of a country parson relates that he sought his recreation in Lacroix’s Differential Calculus and thus found intellectual refreshment for his calling. Instances like this make manifest the great advantage which occupation with mathematics affords to one who lives remote from the city and is compelled to forego the pleasures of art. The entrancing charm of mathematics, which captivates every one who devotes himself to it, and which is comparable to the fine frenzy under whose ban the poet completes his work, has ever been incomprehensible to the spectator and has often caused the enthusiastic mathematician to be held in derision. A classic illustration is the example of Archimedes….
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 22. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 186. From the original German, “Wenn Büchsel in seinen Erinnerungen aus dem Leben eines Landgeistlichen erzählt, dass er in der Differentialrechnung von Lacroix Erholung gesucht und geistige Erfrischung ftir seinen Beruf gefunden habe, so erkennen wir darin den grossen Vorzug, den die Beschaftigung mit der Mathematik für jemanden hat, der fern von einer Stadt lebt und auf ihre Kunstgenüsse verzichten muss. Der berückende Zauber der Mathematik, dem jeder unterliegt, der sich ihr ergiebt, und der dem holden Wahnsinn vergleichbar ist, unter dessen Bann der Dichter sein Work vollendet, ist dem betrachtenden Mitmenschen immer unbegreiflich gewesen und hat den begeisterten Mathematiker oft zum Gespött werden lassen. Als klassisches Beispiel wird jedem Schüler Archimedes…”
Science quotes on:  |   (2863)  |  Advantage (134)  |  Archimedes (55)  |  Art (657)  |  Calculus (65)  |  Captivate (4)  |  Cause (541)  |  Charm (51)  |  City (78)  |  Classic (11)  |  Compel (30)  |  Complete (204)  |  Country (251)  |  Derision (8)  |  Devote (35)  |  Differential Calculus (10)  |  Enthusiastic (6)  |  Entrance (15)  |  Example (94)  |  Forego (4)  |  Frenzy (6)  |  Great (1574)  |  Himself (461)  |  Hold (95)  |  Illustration (48)  |  Incomprehensible (29)  |  Intellect (233)  |  Intellectual (255)  |  Life (1795)  |  Live (628)  |  Mathematics (1328)  |  Occupation (48)  |  Parson (3)  |  Pleasure (178)  |  Poet (83)  |  Recreation (20)  |  Refreshment (3)  |  Reminiscence (4)  |  Remote (83)  |  Spectator (10)  |  Work (1351)

Concentrate only on the achievements, and ignore the mistakes. When judging a mathematician you should only integrate f+ (the positive part of his function) and ignore the negative part. Perhaps this should apply more generally to all evaluations of your fellow men.
On his philosophy of writing letters of recommendation. As given in essay, Ronald Coifman and Robert S. Strichartz, 'The School of Antoni Zygmund', collected in Peter Duren (ed.), A Century of Mathematics in America (1989), 348. The authors acknowledge students of Zygmund provided personal recollections to them for the essay in general. Webmaster speculates the quote is from a student recollection, and not necessarily verbatim.
Science quotes on:  |  Achievement (179)  |  All (4108)  |  Apply (160)  |  Concentrate (26)  |  Evaluation (10)  |  Fellow (88)  |  Function (228)  |  General (511)  |  Ignore (45)  |  Integrate (7)  |  Judge (108)  |  Mistake (169)  |  More (2559)  |  Negative (63)  |  Positive (94)

Considering that, among all those who up to this time made discoveries in the sciences, it was the mathematicians alone who had been able to arrive at demonstrations—that is to say, at proofs certain and evident—I did not doubt that I should begin with the same truths that they have investigated, although I had looked for no other advantage from them than to accustom my mind to nourish itself upon truths and not to be satisfied with false reasons.
In Discourse upon Method, Part 2, in Henry A. Torrey (ed., trans. )Philosophy of Descartes in Extracts from His Writings , (1892), 47-48.
Science quotes on:  |  Accustom (52)  |  Advantage (134)  |  All (4108)  |  Alone (311)  |  Arrive (35)  |  Begin (260)  |  Certain (550)  |  Consider (416)  |  Demonstration (113)  |  Discovery (780)  |  Doubt (304)  |  Evident (91)  |  False (100)  |  Investigate (103)  |  Look (582)  |  Mind (1338)  |  Nourish (16)  |  Other (2236)  |  Proof (287)  |  Reason (744)  |  Same (157)  |  Satisfied (23)  |  Say (984)  |  Science (3879)  |  Time (1877)  |  Truth (1057)

Daniel Bernoulli used to tell two little adventures, which he said had given him more pleasure than all the other honours he had received. Travelling with a learned stranger, who, being pleased with his conversation, asked his name; “I am Daniel Bernoulli,” answered he with great modesty; “and I,” said the stranger (who thought he meant to laugh at him) “am Isaac Newton.” Another time, having to dine with the celebrated Koenig, the mathematician, who boasted, with some degree of self-complacency, of a difficult problem he had solved with much trouble, Bernoulli went on doing the honours of his table, and when they went to drink coffee he presented Koenig with a solution of the problem more elegant than his own.
In A Philosophical and Mathematical Dictionary (1815), 1, 226.
Science quotes on:  |  Adventure (56)  |  All (4108)  |  Answer (366)  |  Ask (411)  |  Being (1278)  |  Daniel Bernoulli (5)  |  Boast (22)  |  Celebrate (19)  |  Coffee (19)  |  Complacent (6)  |  Conversation (43)  |  Degree (276)  |  Difficult (246)  |  Dine (5)  |  Doing (280)  |  Drink (53)  |  Elegant (36)  |  Great (1574)  |  Honour (56)  |  Laugh (47)  |  Learn (629)  |  Learned (235)  |  Little (707)  |  Mathematicians and Anecdotes (141)  |  Modesty (17)  |  More (2559)  |  Name (333)  |  Sir Isaac Newton (333)  |  Other (2236)  |  Pleased (3)  |  Pleasure (178)  |  Present (619)  |  Problem (676)  |  Self (267)  |  Solution (267)  |  Solve (130)  |  Stranger (15)  |  Table (104)  |  Tell (340)  |  Thought (953)  |  Time (1877)  |  Travel (114)  |  Travelling (17)  |  Trouble (107)  |  Two (937)

Dr. Wallace, in his Darwinism, declares that he can find no ground for the existence of pure scientists, especially mathematicians, on the hypothesis of natural selection. If we put aside the fact that great power in theoretical science is correlated with other developments of increasing brain-activity, we may, I think, still account for the existence of pure scientists as Dr. Wallace would himself account for that of worker-bees. Their function may not fit them individually to survive in the struggle for existence, but they are a source of strength and efficiency to the society which produces them.
In Grammar of Science (1911), Part, 1, 221.
Science quotes on:  |  Account (192)  |  Activity (210)  |  Bee (40)  |  Brain (270)  |  Correlate (6)  |  Darwinism (3)  |  Declare (45)  |  Development (422)  |  Efficiency (44)  |  Especially (31)  |  Existence (456)  |  Fact (1210)  |  Find (998)  |  Fit (134)  |  Function (228)  |  Great (1574)  |  Ground (217)  |  Himself (461)  |  Hypothesis (296)  |  Increase (210)  |  Individually (2)  |  Natural (796)  |  Natural Selection (96)  |  Other (2236)  |  Power (746)  |  Produce (104)  |  Pure (291)  |  Science (3879)  |  Scientist (820)  |  Selection (128)  |  Society (326)  |  Source (93)  |  Still (613)  |  Strength (126)  |  Struggle (105)  |  Survive (79)  |  Theoretical Science (4)  |  Think (1086)  |  Alfred Russel Wallace (40)

Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.
Reflections: Mathematics and Creativity', New Yorker (1972), 47, No. 53, 39-45. In Douglas M. Campbell, John C. Higgins (eds.), Mathematics: People, Problems, Results (1984), Vol. 2, 3.
Science quotes on:  |  All (4108)  |  Generation (242)  |  Great (1574)  |  Harm (39)  |  Importance (286)  |  Mathematics (1328)  |  Nothing (966)  |  Notice (77)  |  Other (2236)  |  Research (664)  |  Teacher (143)  |  Useful (250)

Engineers think that equations approximate the real world.
Physicists think that the real world approximates equations.
Mathematicians are unable to make the connection.
Anonymous
In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 41.
Science quotes on:  |  Approximate (25)  |  Connection (162)  |  Engineer (121)  |  Equation (132)  |  Physicist (259)  |  Real World (14)  |  Think (1086)  |  Unable (24)  |  World (1774)

Enlist a great mathematician and a distinguished Grecian; your problem will be solved. Such men can teach in a dwelling-house as well as in a palace. Part of the apparatus they will bring; part we will furnish.
Advice given to the Trustees of Johns Hopkins University on the choice of a professorial staff. In Report of the President of Johns Hopkins University (1888), 29. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 122.
Science quotes on:  |  Advice (55)  |  Apparatus (68)  |  Bring (90)  |  Distinguish (160)  |  Distinguished (83)  |  Dwelling (11)  |  Enlist (2)  |  Faculty (72)  |  Furnish (96)  |  Great (1574)  |  Grecian (2)  |  House (140)  |  Johns Hopkins (7)  |  Palace (8)  |  Part (222)  |  Problem (676)  |  Professor (128)  |  Solve (130)  |  Teach (277)  |  University (121)  |  Will (2355)

Euclid and Archimedes are allowed to be knowing, and to have demonstrated what they say: and yet whosoever shall read over their writings without perceiving the connection of their proofs, and seeing what they show, though he may understand all their words, yet he is not the more knowing. He may believe, indeed, but does not know what they say, and so is not advanced one jot in mathematical knowledge by all his reading of those approved mathematicians.
In Conduct of the Understanding, sect. 24.
Science quotes on:  |  Advance (280)  |  All (4108)  |  Allow (45)  |  Approve (3)  |  Archimedes (55)  |  Belief (578)  |  Connection (162)  |  Demonstrate (76)  |  Euclid (54)  |  Indeed (324)  |  Jot (3)  |  Know (1518)  |  Knowing (137)  |  Knowledge (1529)  |  Mathematics (1328)  |  More (2559)  |  Perceive (40)  |  Proof (287)  |  Read (287)  |  Reading (133)  |  Say (984)  |  See (1081)  |  Seeing (142)  |  Show (346)  |  Study And Research In Mathematics (61)  |  Understand (606)  |  Word (619)  |  Writing (189)

Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
Science quotes on:  |   (2863)  |  Advance (280)  |  Algebra (113)  |  All (4108)  |  Amused (3)  |  Ask (411)  |  Atheism (9)  |  Belief (578)  |  Believer (25)  |  Check (24)  |  Circle (110)  |  Consent (14)  |  Contrive (10)  |  Converse (8)  |  Conviction (97)  |  Court (33)  |  Deal (188)  |  Demonstration (113)  |  Desirable (33)  |  Desire (204)  |  Denis Diderot (6)  |  Direct (225)  |  Doctrine (75)  |  Leonhard Euler (35)  |  Europe (43)  |  Existence (456)  |  Exposition (15)  |  Follow (378)  |  France (27)  |  Freely (13)  |  Gladly (2)  |  God (757)  |  Good (889)  |  Grant (73)  |  Gravely (2)  |  Guest (5)  |  Hear (139)  |  Hebrew (10)  |  Inform (47)  |  Invitation (11)  |  Knowledge (1529)  |  Laughter (31)  |  Learn (629)  |  Learned (235)  |  Lively (17)  |  Mathematicians and Anecdotes (141)  |  Member (41)  |  Name (333)  |  North (11)  |  Peal (2)  |  Perfect (216)  |  Permission (7)  |  Personal (67)  |  Plot (11)  |  Possession (65)  |  Return (124)  |  Rose (34)  |  Russia (13)  |  Say (984)  |  Side (233)  |  Story (118)  |  Straightforward (10)  |  Suggest (34)  |  Tell (340)  |  Throughout (98)  |  Tone (22)  |  Tongue (43)  |  Toward (45)  |  Truth (1057)  |  Visit (26)  |  Whole (738)  |  Young (227)  |  Younger (21)

Every common mechanic has something to say in his craft about good and evil, useful and useless, but these practical considerations never enter into the purview of the mathematician.
Quoted in Robert Drew Hicks, Stoic and Epicurean (1910), 210.
Science quotes on:  |  Common (436)  |  Consideration (139)  |  Craft (10)  |  Enter (141)  |  Evil (116)  |  Good (889)  |  Mechanic (119)  |  Never (1087)  |  Practical (200)  |  Say (984)  |  Something (719)  |  Something To Say (4)  |  Useful (250)  |  Usefulness (86)  |  Uselessness (22)

Every good mathematician is at least half a philosopher, and every good philosopher at least half a mathematician.
Quoted, without citation, in 'Gottlob Frege', The New Encyclopedia Britannica (1992), Vol. 4, 968. If you know a primary source, please contact Webmaster.
Science quotes on:  |  Good (889)  |  Half (56)  |  Least (75)  |  Philosopher (258)

Every good mathematician should also be a good chess player and vice versa.
Science and Method (1914, 2003), 48.
Science quotes on:  |  Chess (25)  |  Good (889)  |  Vice (40)  |  Vice Versa (6)

Every man is ready to join in the approval or condemnation of a philosopher or a statesman, a poet or an orator, an artist or an architect. But who can judge of a mathematician? Who will write a review of Hamilton’s Quaternions, and show us wherein it is superior to Newton’s Fluxions?
In 'Imagination in Mathematics', North American Review, 85, 224.
Science quotes on:  |   (2863)  |  Approval (10)  |  Architect (29)  |  Artist (90)  |  Condemnation (15)  |  Fluxion (7)  |  Fluxions (2)  |  Sir William Rowan Hamilton (10)  |  Join (26)  |  Judge (108)  |  Man (2251)  |  Sir Isaac Newton (333)  |  Orator (2)  |  Philosopher (258)  |  Poet (83)  |  Quaternion (9)  |  Ready (39)  |  Review (26)  |  Show (346)  |  Statesman (19)  |  Superior (81)  |  Will (2355)  |  Write (230)

Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously… this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work….
In The Apprenticeship of a Mathematician (1992), 91.
Science quotes on:  |  Do (1908)  |  Eager (15)  |  Exaltation (5)  |  Experience (467)  |  Feel (367)  |  Feeling (250)  |  Hour (186)  |  Last (426)  |  Lucid (8)  |  Miraculous (11)  |  Name (333)  |  Repeat (42)  |  State (491)  |  Succeed (109)  |  Thought (953)  |  Time (1877)  |  Unable (24)  |  Will (2355)  |  Work (1351)  |  Worthy (34)

Everybody firmly believes in it [Nomal Law of Errors] because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
…...
Science quotes on:  |  Belief (578)  |  Error (321)  |  Everybody (70)  |  Fact (1210)  |  Firmly (6)  |  Imagine (164)  |  Law (894)  |  Mathematics (1328)  |  Observation (555)  |  Observer (43)  |  Theory (970)

Everyone believes in the law of errors, the experimenters because they think it is a mathematical theorem, and the mathematicians because they think it is an experimental fact.
Remark to Henri Poincaré about the Gaussian curve. From the original French, “Les expérimentateurs s’imaginent que c’est un théorème de mathématique, et les mathématiciens d’être un fait expérimental”, in Henri Poincaré, Calcul des Probabilités (1896), 149. Poincaré introduces it as, “me disait un jour M. Lippmann” (Mr. Lippman told me one day). Quote above as translated in F. Downton, 'Review: Nonparametric Methods in Statistics', The Mathematical Gazette (Feb 1959), 43, No. 343, 67.
Science quotes on:  |  Error (321)  |  Experimental (192)  |  Experimenter (40)  |  Fact (1210)  |  Law (894)  |  Normal (28)  |  Theorem (112)  |  Think (1086)

Exact science and its practical movements are no checks on the greatest poet, but always his encouragement and support … The sailor and traveller, the anatomist, chemist, astronomer, geologist, phrenologist, spiritualist, mathematician, historian and lexicographer are not poets, but they are the lawgivers of poets and their construction underlies the structure of every perfect poem.
In Walt Whitman and William Michael Rossetti (ed.), 'Preface to the First Edition of Leaves of Grass', Poems By Walt Whitman (1868), 46.
Science quotes on:  |  Anatomist (23)  |  Astronomer (93)  |  Check (24)  |  Chemist (156)  |  Construction (112)  |  Encouragement (23)  |  Geologist (75)  |  Greatest (328)  |  Historian (54)  |  Love (309)  |  Movement (155)  |  Perfect (216)  |  Perfection (129)  |  Phrenologist (2)  |  Poem (96)  |  Poet (83)  |  Practical (200)  |  Sailor (16)  |  Science (3879)  |  Science And Art (184)  |  Structure (344)  |  Support (147)  |  Traveler (30)  |  Underlie (18)

For other great mathematicians or philosophers, he [Gauss] used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.
In History of Mathematics (3rd Ed., 1901), 362.
Science quotes on:  |  Alone (311)  |  Anecdote (21)  |  Epithet (3)  |  Carl Friedrich Gauss (77)  |  Great (1574)  |  Mathematicians and Anecdotes (141)  |  Sir Isaac Newton (333)  |  Other (2236)  |  Philosopher (258)

For the saving the long progression of the thoughts to remote and first principles in every case, the mind should provide itself several stages; that is to say, intermediate principles, which it might have recourse to in the examining those positions that come in its way. These, though they are not self-evident principles, yet, if they have been made out from them by a wary and unquestionable deduction, may be depended on as certain and infallible truths, and serve as unquestionable truths to prove other points depending upon them, by a nearer and shorter view than remote and general maxims. … And thus mathematicians do, who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions. Certain theorems that they have settled to themselves upon sure demonstration, serve to resolve to them multitudes of propositions which depend on them, and are as firmly made out from thence as if the mind went afresh over every link of the whole chain that tie them to first self-evident principles.
In The Conduct of the Understanding, Sect. 21.
Science quotes on:  |  Afresh (4)  |  All (4108)  |  Axiom (63)  |  Back (390)  |  Case (99)  |  Certain (550)  |  Chain (50)  |  Deduction (82)  |  Demonstration (113)  |  Depend (228)  |  Do (1908)  |  Evident (91)  |  Examine (78)  |  Firmly (6)  |  First (1283)  |  General (511)  |  Infallible (15)  |  Intermediate (37)  |  Link (43)  |  Long (790)  |  Maxim (17)  |  Mind (1338)  |  Multitude (47)  |  Nature Of Mathematics (80)  |  Nearer (45)  |  New (1216)  |  Other (2236)  |  Point (580)  |  Position (77)  |  Principle (507)  |  Problem (676)  |  Progression (23)  |  Proposition (123)  |  Prove (250)  |  Provide (69)  |  Recourse (12)  |  Remote (83)  |  Resolve (40)  |  Run (174)  |  Save (118)  |  Say (984)  |  Self (267)  |  Self-Evident (21)  |  Serve (59)  |  Settle (19)  |  Settled (34)  |  Several (32)  |  Short (197)  |  Stage (143)  |  Themselves (433)  |  Theorem (112)  |  Thought (953)  |  Through (849)  |  Tie (38)  |  Train (114)  |  Truth (1057)  |  Unquestionable (9)  |  View (488)  |  Wary (3)  |  Way (1217)  |  Whole (738)

Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played] … an historical role … in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded … as “pathological,” .… as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out, … Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
From 'Characterizing Irregularity', Science (12 May 1978), 200, No. 4342, 677-678. Quoted in Benoit Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 3-4.
Science quotes on:  |   (2863)  |  19th Century (33)  |  All (4108)  |  Art (657)  |  Belief (578)  |  Beyond (308)  |  Break (99)  |  Century (310)  |  Class (164)  |  Classical (45)  |  Completely (135)  |  Curve (49)  |  Development (422)  |  Discovery (780)  |  Euclid (54)  |  Fit (134)  |  Flower (106)  |  Fractal (9)  |  Gallery (7)  |  Great (1574)  |  Historical (70)  |  Idea (843)  |  Imagination (328)  |  Inherent (42)  |  Joke (83)  |  Large (394)  |  Limitation (47)  |  Benoit Mandelbrot (13)  |  Mathematics (1328)  |  Modern (385)  |  Modern Mathematics (50)  |  Monster (31)  |  Music (129)  |  Natural (796)  |  Nature (1926)  |  New (1216)  |  Sir Isaac Newton (333)  |  Nomenclature (146)  |  Object (422)  |  Origin (239)  |  Painting (44)  |  Pathological (21)  |  Pattern (110)  |  Point (580)  |  Pure (291)  |  Pure Mathematics (67)  |  Regard (305)  |  Regular (46)  |  Revolution (129)  |  Role (86)  |  Root (120)  |  Saw (160)  |  Separate (143)  |  Set (394)  |  Set Theory (6)  |  Simple (406)  |  Space (500)  |  Structure (344)  |  Taste (90)  |  Theory (970)  |  Time (1877)  |  Together (387)  |  Transcend (26)  |  Turn (447)  |  Word (619)  |  World (1774)

Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.
In J.R. Newman (ed.), 'Commentary on Games and Puzzles', The World of Mathematics (1956), Vol. 4, 2414.
Science quotes on:  |  Adventure (56)  |  Analysis (233)  |  Blanket (10)  |  Creation (327)  |  Delectable (2)  |  Dish (3)  |  Game (101)  |  Human (1468)  |  Human Mind (128)  |  Ingredient (15)  |  Interesting (153)  |  Job (82)  |  Lack (119)  |  Mind (1338)  |  Most (1731)  |  Never (1087)  |  Structure (344)  |  Surprise (86)  |  Taste (90)  |  Transform (73)  |  Unfortunately (38)

Gauss was not the son of a mathematician; Handel’s father was a surgeon, of whose musical powers nothing is known; Titian was the son and also the nephew of a lawyer, while he and his brother, Francesco Vecellio, were the first painters in a family which produced a succession of seven other artists with diminishing talents. These facts do not, however, prove that the condition of the nerve-tracts and centres of the brain, which determine the specific talent, appeared for the first time in these men: the appropriate condition surely existed previously in their parents, although it did not achieve expression. They prove, as it seems to me, that a high degree of endowment in a special direction, which we call talent, cannot have arisen from the experience of previous generations, that is, by the exercise of the brain in the same specific direction.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 96.
Science quotes on:  |   (2863)  |  Achieve (66)  |  Appear (118)  |  Appropriate (61)  |  Artist (90)  |  Brain (270)  |  Brother (43)  |  Call (769)  |  Centre (28)  |  Condition (356)  |  Degree (276)  |  Determine (144)  |  Diminish (17)  |  Direction (175)  |  Do (1908)  |  Endowment (16)  |  Exercise (110)  |  Exist (443)  |  Experience (467)  |  Expression (175)  |  Fact (1210)  |  Facts (553)  |  Family (94)  |  Father (110)  |  First (1283)  |  Carl Friedrich Gauss (77)  |  Generation (242)  |  High (362)  |  Known (454)  |  Lawyer (27)  |  Music (129)  |  Nephew (2)  |  Nerve (79)  |  Nothing (966)  |  Other (2236)  |  Painter (29)  |  Parent (76)  |  Power (746)  |  Previous (12)  |  Produced (187)  |  Prove (250)  |  Son (24)  |  Special (184)  |  Specific (95)  |  Succession (77)  |  Surely (101)  |  Surgeon (63)  |  Talent (94)  |  Time (1877)

Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
Science quotes on:  |  Abstruse (10)  |  All (4108)  |  Applicable (31)  |  Apply (160)  |  Article (22)  |  Become (815)  |  Both (493)  |  Brevity (8)  |  Claim (146)  |  Common (436)  |  Condition (356)  |  Criterion (27)  |  Degenerate (14)  |  Development (422)  |  Difficult (246)  |  Elegance (37)  |  Expense (16)  |  Fail (185)  |  Form (959)  |  Formulate (15)  |  General (511)  |  Generality (45)  |  Importance (286)  |  Intrinsic (18)  |  Intuition (75)  |  Count Joseph-Louis de Lagrange (26)  |  Lead (384)  |  Limit (280)  |  Material (353)  |  Mathematics (1328)  |  Method (505)  |  Methods (204)  |  Modern Mathematics (50)  |  More (2559)  |  Necessary (363)  |  Point (580)  |  Point Of View (80)  |  Precision (68)  |  Presentation (23)  |  Profusion (3)  |  Property (168)  |  Proposition (123)  |  Rank (67)  |  Read (287)  |  Scientific (941)  |  Single (353)  |  Smother (3)  |  Special (184)  |  Special Case (9)  |  Spend (95)  |  Study (653)  |  Theorem (112)  |  Time (1877)  |  Triviality (2)  |  View (488)  |  Wholesome (12)  |  Worth (169)  |  Worthless (21)  |  Write (230)

Genetics is the first biological science which got in the position in which physics has been in for many years. One can justifiably speak about such a thing as theoretical mathematical genetics, and experimental genetics, just as in physics. There are some mathematical geniuses who work out what to an ordinary person seems a fantastic kind of theory. This fantastic kind of theory nevertheless leads to experimentally verifiable prediction, which an experimental physicist then has to test the validity of. Since the times of Wright, Haldane, and Fisher, evolutionary genetics has been in a similar position.
Oral history memoir. Columbia University, Oral History Research Office, New York, 1962. Quoted in William B. Provine, Sewall Wright and Evolutionary Biology (1989), 277.
Science quotes on:  |  Biological (137)  |  Biology (216)  |  Experiment (695)  |  Experimental (192)  |  Experimental Physicist (10)  |  Fantastic (20)  |  First (1283)  |  Fischer_Ronald (2)  |  Genetic (108)  |  Genetics (101)  |  J.B.S. Haldane (50)  |  Kind (557)  |  Lead (384)  |  Mathematics (1328)  |  Nevertheless (90)  |  Ordinary (160)  |  Person (363)  |  Physic (517)  |  Physicist (259)  |  Physics (533)  |  Prediction (82)  |  Science (3879)  |  Speak (232)  |  Test (211)  |  Theory (970)  |  Thing (1915)  |  Time (1877)  |  Validity (47)  |  Work (1351)  |  Sewall Wright (9)  |  Year (933)

Get into any taxi and tell the driver you are a mathematician and the response is predictable … you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.”
In paper, 'A Mathematician’s Survival Guide', pdf document linked from his homepage at math.missouri.edu (undated, but 2011 or earlier, indicated by an “accessed on” date elsewhere.) Collected in Peter Casazza, Steven G. Krantz and Randi D. Ruden (eds.) I, Mathematician (2005), 31.
Science quotes on:  |  Being (1278)  |  Driver (5)  |  Good (889)  |  Hear (139)  |  Immortal (35)  |  Mathematics (1328)  |  Never (1087)  |  Response (53)  |  Taxi (4)  |  Tell (340)  |  Will (2355)  |  Word (619)

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand… So Greek mathematics is ‘permanent’, more permanent even than Greek literature.
In A Mathematician’s Apology (1940, 1967), 81.
Science quotes on:  |  First (1283)  |  Greek (107)  |  Language (293)  |  Literature (103)  |  Mathematics (1328)  |  Modern (385)  |  More (2559)  |  Permanent (64)  |  Real (149)  |  Thing (1915)  |  Understand (606)  |  Understanding (513)

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
In The Queen of the Sciences (1938), 2.
Science quotes on:  |  Art (657)  |  Creative (137)  |  Feeling (250)  |  Fitness (9)  |  Generality (45)  |  Guide (97)  |  Indefinable (5)  |  Inspire (52)  |  Mathematics (1328)  |  Past (337)  |  Prospect (30)  |  Sense (770)  |  Simplicity (167)  |  Symmetry (43)  |  Thing (1915)  |  Ultimate (144)  |  Usefulness (86)

Had you or I been born at the Bay of Soldania, possibly our Thoughts, and Notions, had not exceeded those brutish ones of the Hotentots that inhabit there: And had the Virginia King Apochancana, been educated in England, he had, perhaps been as knowing a Divine, and as good a Mathematician as any in it. The difference between him, and a more improved English-man, lying barely in this, That the exercise of his Facilities was bounded within the Ways, Modes, and Notions of his own Country, and never directed to any other or farther Enquiries.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book I, Chapter 4, Section 12, 92.
Science quotes on:  |  Bound (119)  |  Country (251)  |  Difference (337)  |  Direct (225)  |  Divine (112)  |  Englishman (3)  |  Enquiry (87)  |  Exercise (110)  |  Facility (11)  |  Farther (51)  |  Good (889)  |  Knowing (137)  |  Lying (55)  |  Man (2251)  |  More (2559)  |  Never (1087)  |  Notion (113)  |  Other (2236)  |  Possibly (111)  |  Thought (953)  |  Way (1217)

Haldane could have made a success of any one of half a dozen careers—as mathematician, classical scholar, philosopher, scientist, journalist or imaginative writer. On his life’s showing he could not have been a politician, administrator (heavens, no!), jurist or, I think, a critic of any kind. In the outcome he became one of the three or four most influential biologists of his generation.
Essay, 'J.B.S.', in Pluto’s Republic: Incorporating The Art of the Soluble and Induction and Intuition in Scientific Thought (1982), collected in The Strange Case of the Spotted Mice and Other Classic Essays on Science (1996), 87.
Science quotes on:  |   (2863)  |  Administrator (11)  |  Biography (240)  |  Biologist (69)  |  Career (75)  |  Classical (45)  |  Critic (20)  |  Generation (242)  |  J.B.S. Haldane (50)  |  Heaven (258)  |  Heavens (125)  |  Imagination (328)  |  Influential (4)  |  Journalist (8)  |  Jurist (4)  |  Kind (557)  |  Life (1795)  |  Most (1731)  |  Philosopher (258)  |  Politician (38)  |  Scholar (48)  |  Scientist (820)  |  Success (302)  |  Think (1086)  |  Writer (86)

He was not a mathematician–he never even took a maths class after high school–yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century.
In 'Martin Gardner Obituary', The Guardian (27 May 2010)
Science quotes on:  |  Age (499)  |  Century (310)  |  Class (164)  |  Die (86)  |  Figure (160)  |  Martin Gardner (50)  |  High (362)  |  High School (11)  |  Influence (222)  |  Inspiration (75)  |  Last (426)  |  Mathematics (1328)  |  Most (1731)  |  Never (1087)  |  School (219)

How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasture nothing but years of effort can extract it. You can’t hurry the process. Or pass from arithmetic to algebra; you can’t shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon. So died, for each of us, still bravely fighting, our mathematical training; except for a set of people called “mathematicians”—born so, like crooks.
In Too Much College: Or, Education Eating up Life, with Kindred Essays in Education and Humour (1939), 8.
Science quotes on:  |  Algebra (113)  |  Arithmetic (136)  |  Binomial (6)  |  Binomial Theorem (5)  |  Brave (12)  |  Calculus (65)  |  Call (769)  |  Crook (2)  |  Die (86)  |  Effort (227)  |  End (590)  |  Equation (132)  |  Extract (40)  |  Fall (230)  |  Fight (44)  |  Foot (60)  |  Growth (187)  |  Horizon (45)  |  Hurry (15)  |  Impede (4)  |  Mathematics (1328)  |  Multiplication (43)  |  Multiplication Table (16)  |  Nothing (966)  |  Other (2236)  |  Pace (14)  |  Pass (238)  |  Past (337)  |  Pasture (13)  |  People (1005)  |  Process (423)  |  Ripple (9)  |  Root (120)  |  Set (394)  |  Shorten (5)  |  Shoulder (33)  |  Sight (132)  |  Sink (37)  |  Square (70)  |  Square Root (12)  |  Stern (3)  |  Still (613)  |  Struggle (105)  |  Stump (3)  |  Subject (521)  |  Table (104)  |  Tangle (6)  |  Theorem (112)  |  Through (849)  |  Training (80)  |  Victory (39)  |  Way (1217)  |  Year (933)

How did Biot arrive at the partial differential equation? [the heat conduction equation] … Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.
The Tragicomical History of Thermodynamics, 1822-1854 (1980), 51.
Science quotes on:  |  Beginning (305)  |  Biot_Jean (2)  |  Conduction (8)  |  Derive (65)  |  Differential Equation (18)  |  Differentiation (25)  |  Equation (132)  |  Great (1574)  |  Heat (174)  |  Pierre-Simon Laplace (62)  |  Maintain (105)  |  Merely (316)  |  Mortal (54)  |  Ordinary (160)  |  Research (664)  |  Sink (37)  |  Superiority (19)  |  Swim (30)  |  Thermodynamics (40)  |  Trying (144)  |  Way (1217)  |  Year (933)

How do we convince people that in programming simplicity and clarity–in short: what mathematicians call ‘elegance’–are not a dispensable luxury, but a crucial matter that decides between success and failure?
…...
Science quotes on:  |  Call (769)  |  Clarity (47)  |  Convince (41)  |  Crucial (9)  |  Decide (41)  |  Dispense (9)  |  Do (1908)  |  Elegance (37)  |  Failure (161)  |  Luxury (21)  |  Matter (798)  |  People (1005)  |  Program (52)  |  Short (197)  |  Simplicity (167)  |  Success (302)

How happy the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve.
The Dyer’s Hand and Other Essays (1965), Prologue, 'Writing', 15.
Science quotes on:  |  Colleague (50)  |  Deserve (65)  |  Happy (105)  |  High (362)  |  Lot (151)  |  Reputation (33)  |  Rival (19)  |  Win (52)

However far the calculating reason of the mathematician may seem separated from the bold flight of the artist’s phantasy, it must be remembered that these expressions are but momentary images snatched arbitrarily from among the activities of both. In the projection of new theories the mathematician needs as bold and creative a phantasy as the productive artist, and in the execution of the details of a composition the artist too must calculate dispassionately the means which are necessary for the successful consummation of the parts. Common to both is the creation, the generation, of forms out of mind.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 185. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
Science quotes on:  |   (2863)  |  Activity (210)  |  Artist (90)  |  Bold (22)  |  Both (493)  |  Calculate (54)  |  Common (436)  |  Composition (84)  |  Consummation (7)  |  Creation (327)  |  Creative (137)  |  Detail (146)  |  Dispassionate (8)  |  Execution (25)  |  Expression (175)  |  Fantasy (14)  |  Flight (98)  |  Form (959)  |  Generation (242)  |  Image (96)  |  Mathematics As A Fine Art (23)  |  Mean (809)  |  Means (579)  |  Mind (1338)  |  Momentary (4)  |  Must (1526)  |  Necessary (363)  |  Need (290)  |  New (1216)  |  Productive (32)  |  Projection (5)  |  Reason (744)  |  Remember (179)  |  Separate (143)  |  Snatch (13)  |  Successful (123)  |  Theory (970)

However far the mathematician’s calculating senses seem to be separated from the audacious flight of the artist’s imagination, these manifestations refer to mere instantaneous images, which have been arbitrarily torn from the operation of both. In designing new theories, the mathematician needs an equally bold and inspired imagination as creative as the artist, and in carrying out the details of a work the artist must unemotionally reckon all the resources necessary for the success of the parts. Common to both is the fabrication, the creation of the structure from the intellect.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. Translated by Webmaster using online resources. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
Science quotes on:  |   (2863)  |  All (4108)  |  Arbitrary (26)  |  Artist (90)  |  Audacious (4)  |  Bold (22)  |  Both (493)  |  Calculate (54)  |  Carrying Out (13)  |  Common (436)  |  Creation (327)  |  Creative (137)  |  Design (195)  |  Detail (146)  |  Equally (130)  |  Fabrication (2)  |  Flight (98)  |  Image (96)  |  Imagination (328)  |  Inspire (52)  |  Instantaneous (3)  |  Intellect (233)  |  Manifestation (58)  |  Mathematics As A Fine Art (23)  |  Mere (84)  |  Must (1526)  |  Necessary (363)  |  Need (290)  |  New (1216)  |  Operation (213)  |  Part (222)  |  Reckon (31)  |  Refer (14)  |  Resource (63)  |  Sense (770)  |  Separate (143)  |  Structure (344)  |  Success (302)  |  Tear (42)  |  Theory (970)  |  Torn (17)  |  Work (1351)

I am a Christian which means that I believe in the deity of Christ, like Tycho de Brahe, Copernicus, Descartes, Newton, Leibnitz, Pascal ... like all great astronomers mathematicians of the past.
…...
Science quotes on:  |  All (4108)  |  Astronomer (93)  |  Belief (578)  |  Christ (17)  |  Christian (43)  |  De (3)  |  Deity (22)  |  René Descartes (81)  |  Great (1574)  |  Gottfried Wilhelm Leibniz (49)  |  Mean (809)  |  Means (579)  |  Newton (10)  |  Pascal (2)  |  Past (337)

I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.
As quoted, without citation, in Peter G. Casazza 'A Mathematician’s Survival Guide', pdf document linked from his homepage at math.missouri.edu (undated, but 2011 or earlier, indicated by an “accessed on” date elsewhere.) Collected in Peter Casazza, Steven G. Krantz and Randi D. Ruden (eds.) I, Mathematician (2005), 31.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Declare (45)  |  Illiterate (6)  |  Living (491)  |  Odd (13)  |  People (1005)  |  Pride (78)  |  Professional (70)  |  Surrounded (2)  |  Vacuum (39)

I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
Science quotes on:  |  According (237)  |  Analysis (233)  |  Application (242)  |  Approximation (31)  |  Attention (190)  |  Benefit (114)  |  Cause (541)  |  Chance (239)  |  Chosen (48)  |  Civil (26)  |  Complication (29)  |  Concern (228)  |  Consideration (139)  |  Constant (144)  |  Data (156)  |  Decision (91)  |  Depend (228)  |  Deserve (65)  |  Determine (144)  |  Difficulty (196)  |  Error (321)  |  Event (216)  |  Final (118)  |  Formula (98)  |  Function (228)  |  General (511)  |  Government (110)  |  Importance (286)  |  Inoculation (9)  |  Institution (69)  |  Insurance (9)  |  Investigate (103)  |  Investigation (230)  |  Large (394)  |  Law (894)  |  Life (1795)  |  Light (607)  |  Limit (280)  |  Mean (809)  |  Moral (195)  |  Morality (52)  |  Most (1731)  |  Myself (212)  |  Number (699)  |  Observation (555)  |  Occur (150)  |  Outcome (13)  |  Philosopher (258)  |  Present (619)  |  Presuppose (15)  |  Probability (130)  |  Proportion (136)  |  Question (621)  |  Regularity (40)  |  Repetition (28)  |  Require (219)  |  Required (108)  |  Result (677)  |  Separate (143)  |  Still (613)  |  Subject (521)  |  Theory (970)  |  Thing (1915)  |  Underlying (30)  |  Vaccine (9)  |  Various (200)  |  Will (2355)  |  Work (1351)

I can testify that she [Emmy Noether] is a great mathematician, but that she is a woman, I cannot swear.
As recalled by John Edensor Littlewood in his A Mathematician’s Miscellany (1953), reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 125. Littlewood identified this as Landau’s response, when “asked for a testimony to the effect that Emmy Noether was a great woman mathematician.” Littlewood also notes for context, “(She was very plain)”.
Science quotes on:  |  Great (1574)  |  Emmy Noether (7)  |  Swear (6)  |  Testify (5)  |  Woman (151)

I can’t think of any definition of the words mathematician or scientist that would apply to me. I think of myself as a journalist who knows just enough about mathematics to be able to take low-level math and make it clear and interesting to nonmathematicians. Let me say that I think not knowing too much about a subject is an asset for a journalist, not a liability. The great secret of my column is that I know so little about mathematics that I have to work hard to understand the subject myself. Maybe I can explain things more clearly than a professional mathematician can.
In Scot Morris, 'Interview: Martin Gardner', Omni, 4, No. 4 (Jan 1982), 68.
Science quotes on:  |  Apply (160)  |  Asset (6)  |  Clearly (41)  |  Column (15)  |  Definition (221)  |  Enough (340)  |  Explain (322)  |  Great (1574)  |  Hard (243)  |  Interest (386)  |  Interesting (153)  |  Journalist (8)  |  Know (1518)  |  Knowing (137)  |  Liability (6)  |  Little (707)  |  Low (80)  |  Mathematics (1328)  |  More (2559)  |  Myself (212)  |  Professional (70)  |  Say (984)  |  Scientist (820)  |  Secret (194)  |  Subject (521)  |  Thing (1915)  |  Think (1086)  |  Understand (606)  |  Word (619)  |  Work (1351)  |  Work Hard (12)

I count Maxwell and Einstein, Eddington and Dirac, among “real” mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as “useless” as the theory of numbers.
In A Mathematician's Apology (1940, 2012), 131.
Science quotes on:  |  Achievement (179)  |  Applied (177)  |  Applied Mathematics (15)  |  Count (105)  |  Paul A. M. Dirac (44)  |  Sir Arthur Stanley Eddington (130)  |  Einstein (101)  |  Albert Einstein (605)  |  Great (1574)  |  Mathematics (1328)  |  Maxwell (42)  |  James Clerk Maxwell (87)  |  Mechanic (119)  |  Mechanics (131)  |  Modern (385)  |  Number (699)  |  Number Theory (6)  |  Present (619)  |  Quantum (117)  |  Quantum Mechanics (46)  |  Real (149)  |  Relativity (88)  |  Subject (521)  |  Theory (970)  |  Theory Of Numbers (7)  |  Uselessness (22)

I do not know if God is a mathematician, but mathematics is the loom on which God weaves the universe.
In The Loom of God: Tapestries of Mathematics and Mysticism (1997, 2009), Introduction, 10.
Science quotes on:  |  Do (1908)  |  God (757)  |  Know (1518)  |  Loom (20)  |  Mathematics (1328)  |  Universe (857)  |  Weave (19)

I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 144.
Science quotes on:  |  Beat (41)  |  Boy (94)  |  Career (75)  |  Do (1908)  |  Examination (98)  |  Mathematics (1328)  |  Most (1731)  |  Noble (90)  |  Notion (113)  |  Other (2236)  |  Passion (114)  |  Remember (179)  |  Scholarship (20)  |  Term (349)  |  Terms (184)  |  Thought (953)  |  Want (497)  |  Way (1217)

I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him. The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.
'Reply to Lewis Edwin Hahn', The Philosophy of Brand Blanshard (1980), 901.
Science quotes on:  |   (2863)  |  Degree (276)  |  Discovery (780)  |  Do (1908)  |  Eternal (110)  |  Follow (378)  |  God (757)  |  G. H. Hardy (71)  |  Johannes Kepler (91)  |  Necessary (363)  |  Nonsense (48)  |  Sense (770)  |  Surrender (20)  |  System (537)  |  Talking (76)  |  Think (1086)  |  Thinker (39)  |  Thinking (414)  |  Thought (953)  |  Timeless (8)  |  Wholly (88)  |  World (1774)

I don’t know anything about mathematics; can’t even do proportion. But I can hire all the good mathematicians I need for fifteen dollars a week.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
Science quotes on:  |  All (4108)  |  Do (1908)  |  Dollar (22)  |  Good (889)  |  Hire (7)  |  Know (1518)  |  Mathematics (1328)  |  Need (290)  |  Proportion (136)  |  Week (70)

I have before mentioned mathematics, wherein algebra gives new helps and views to the understanding. If I propose these it is not to make every man a thorough mathematician or deep algebraist; but yet I think the study of them is of infinite use even to grown men; first by experimentally convincing them, that to make anyone reason well, it is not enough to have parts wherewith he is satisfied, and that serve him well enough in his ordinary course. A man in those studies will see, that however good he may think his understanding, yet in many things, and those very visible, it may fail him. This would take off that presumption that most men have of themselves in this part; and they would not be so apt to think their minds wanted no helps to enlarge them, that there could be nothing added to the acuteness and penetration of their understanding.
In The Conduct of the Understanding, Sect. 7.
Science quotes on:  |  Acuteness (3)  |  Add (40)  |  Algebra (113)  |  Anyone (35)  |  Apt (9)  |  Convince (41)  |  Course (409)  |  Deep (233)  |  Enlarge (35)  |  Enough (340)  |  Experimental (192)  |  Fail (185)  |  First (1283)  |  Good (889)  |  Grow (238)  |  Help (105)  |  Infinite (231)  |  Man (2251)  |  Mathematics (1328)  |  Mention (82)  |  Mind (1338)  |  Most (1731)  |  New (1216)  |  Nothing (966)  |  Ordinary (160)  |  Part (222)  |  Penetration (18)  |  Presumption (15)  |  Propose (23)  |  Reason (744)  |  Satisfied (23)  |  See (1081)  |  Serve (59)  |  Study (653)  |  Themselves (433)  |  Thing (1915)  |  Think (1086)  |  Thorough (40)  |  Understand (606)  |  Understanding (513)  |  Use (766)  |  Value Of Mathematics (60)  |  View (488)  |  Visible (84)  |  Want (497)  |  Will (2355)

I have hardly known a mathematician who was capable of reasoning.
Plato
The Republic. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 159.
Science quotes on:  |  Capable (168)  |  Known (454)  |  Reasoning (207)

I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
In The Conduct of the Understanding, Sect. 7.
Science quotes on:  |  All (4108)  |  Argument (138)  |  Bottom (33)  |  Bring (90)  |  Closely (12)  |  Coherence (13)  |  Connection (162)  |  Deep (233)  |  Demonstration (113)  |  Dependence (45)  |  Follow (378)  |  Habit (168)  |  Idea (843)  |  Knowledge (1529)  |  Manage (23)  |  Mathematics (1328)  |  Mention (82)  |  Mind (1338)  |  Necessarily (135)  |  Necessary (363)  |  Observe (168)  |  Occasion (85)  |  Other (2236)  |  Part (222)  |  Reason (744)  |  Reasoning (207)  |  Settle (19)  |  Single (353)  |  Sort (49)  |  Source (93)  |  Study (653)  |  Think (1086)  |  Train (114)  |  Transfer (20)  |  Value Of Mathematics (60)  |  Way (1217)

Srinivasa Ramanujan quote: I have not trodden through a conventional university course, but I am striking out a new path for mys
I have not trodden through a conventional university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling.”
First letter to G.H. Hardy (16 Jan 1913). In Collected Papers of Srinivasa Ramanujan (1927), xxiii. Hardy notes he did “seem to remember his telling me that his friends had given him some assistance” in writing the letter because Ramanujan's “knowledge of English, at that stage of his life, could scarcely have been sufficient.”
Science quotes on:  |  Conventional (30)  |  Course (409)  |  Divergent (6)  |  General (511)  |  Investigation (230)  |  Local (19)  |  Myself (212)  |  New (1216)  |  Path (144)  |  Result (677)  |  Series (149)  |  Special (184)  |  Startling (15)  |  Striking (48)  |  Term (349)  |  Termed (2)  |  Through (849)  |  Tread (17)  |  University (121)

I have said that mathematics is the oldest of the sciences; a glance at its more recent history will show that it has the energy of perpetual youth. The output of contributions to the advance of the science during the last century and more has been so enormous that it is difficult to say whether pride in the greatness of achievement in this subject, or despair at his inability to cope with the multiplicity of its detailed developments, should be the dominant feeling of the mathematician. Few people outside of the small circle of mathematical specialists have any idea of the vast growth of mathematical literature. The Royal Society Catalogue contains a list of nearly thirty- nine thousand papers on subjects of Pure Mathematics alone, which have appeared in seven hundred serials during the nineteenth century. This represents only a portion of the total output, the very large number of treatises, dissertations, and monographs published during the century being omitted.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 285.
Science quotes on:  |  Achievement (179)  |  Advance (280)  |  Alone (311)  |  Appear (118)  |  Being (1278)  |  Catalogue (5)  |  Century (310)  |  Circle (110)  |  Contain (68)  |  Contribution (89)  |  Cope (6)  |  Despair (40)  |  Detail (146)  |  Development (422)  |  Difficult (246)  |  Dissertation (2)  |  Dominant (26)  |  Energy (344)  |  Enormous (41)  |  Feel (367)  |  Feeling (250)  |  Glance (34)  |  Greatness (54)  |  Growth (187)  |  History (673)  |  Hundred (229)  |  Idea (843)  |  Inability (10)  |  Large (394)  |  Last (426)  |  List (10)  |  Literature (103)  |  Mathematics (1328)  |  Modern Mathematics (50)  |  Monograph (5)  |  More (2559)  |  Multiplicity (14)  |  Nearly (137)  |  Nineteenth (6)  |  Number (699)  |  Oldest (8)  |  Omit (11)  |  Output (10)  |  Outside (141)  |  Paper (182)  |  People (1005)  |  Perpetual (57)  |  Portion (84)  |  Pride (78)  |  Publish (36)  |  Pure (291)  |  Pure Mathematics (67)  |  Recent (77)  |  Represent (155)  |  Royal (57)  |  Royal Society (16)  |  Say (984)  |  Science (3879)  |  Serial (4)  |  Show (346)  |  Small (477)  |  Society (326)  |  Specialist (28)  |  Subject (521)  |  Thirty (6)  |  Thousand (331)  |  Total (94)  |  Treatise (44)  |  Vast (177)  |  Will (2355)  |  Youth (101)

I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty … as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.
In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 72. https://books.google.com/books?id=wgVbAAAAQAAJ James Joseph Sylvester - 1877
Science quotes on:  |  Antagonistic (3)  |  Certain (550)  |  Conceive (98)  |  Cultivation (35)  |  Effect (393)  |  Eloquent (2)  |  Faculty (72)  |  Find (998)  |  Fish (120)  |  Fit (134)  |  Himself (461)  |  Indeed (324)  |  Know (1518)  |  Less (103)  |  Mathematics (1328)  |  More (2559)  |  Must (1526)  |  Nature (1926)  |  Nature Of Things (29)  |  Oration (2)  |  Phenomenon (318)  |  Pursuit (121)  |  Rare (89)  |  Remain (349)  |  State (491)  |  Study (653)  |  Talk (100)  |  Talking (76)  |  Thing (1915)  |  Will (2355)

I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or good mathematician.
From 'Fundamental Conceptions and Methods in Mathematics', Bulletin American Mathematical Society (1904), 9, 133. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 182.
Science quotes on:  |  Activity (210)  |  Amount (151)  |  Art (657)  |  Artist (90)  |  Bear (159)  |  Become (815)  |  Both (493)  |  Certain (550)  |  Chief (97)  |  Control (167)  |  Create (235)  |  Deductive (11)  |  Do (1908)  |  Drawing (56)  |  External (57)  |  Factor (46)  |  Fundamental (250)  |  Good (889)  |  Guide (97)  |  Imagination (328)  |  Important (209)  |  Indeed (324)  |  Look (582)  |  Making (300)  |  Mathematics (1328)  |  Mathematics As A Fine Art (23)  |  More (2559)  |  Most (1731)  |  Name (333)  |  Other (2236)  |  Painter (29)  |  Point (580)  |  Power (746)  |  Reason (744)  |  Reasoning (207)  |  Resemblance (38)  |  Rigorous (48)  |  Say (984)  |  Science (3879)  |  Sense (770)  |  Skill (109)  |  Subtle (35)  |  Technical (43)  |  World (1774)  |  Worth (169)

I must not pass by Dr. Young called Phaenomenon Young at Cambridge. A man of universal erudition, & almost universal accomplishments. Had he limited himself to anyone department of knowledge, he must have been first in that department. But as a mathematician, a scholar, a hieroglyphist, he was eminent; & he knew so much that it is difficult to say what he did not know. He was a most amiable & good-tempered man; too fond, perhaps, of the society of persons of rank for a true philosopher.
J. Z. Fullmer, 'Davy's Sketches of his Contemporaries', Chymia (1967), 12, 135.
Science quotes on:  |  Accomplishment (93)  |  Amiable (10)  |  Call (769)  |  Cambridge (16)  |  Department (92)  |  Difficult (246)  |  Erudition (6)  |  First (1283)  |  Fond (12)  |  Good (889)  |  Himself (461)  |  Know (1518)  |  Knowledge (1529)  |  Limit (280)  |  Limited (101)  |  Man (2251)  |  Most (1731)  |  Must (1526)  |  Pass (238)  |  Person (363)  |  Phenomenon (318)  |  Philosopher (258)  |  Rank (67)  |  Say (984)  |  Scholar (48)  |  Society (326)  |  Universal (189)  |  Young (227)  |  Thomas Young (14)

I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
Astronomia Nova, New Astronomy, (1609), Introduction, second paragraph.
Science quotes on:  |  Attempt (251)  |  Becoming (96)  |  Demonstration (113)  |  Fault (54)  |  Figure (160)  |  Find (998)  |  Material (353)  |  Meaning (233)  |  Mental (177)  |  Mind (1338)  |  Myself (212)  |  Opposite (104)  |  Power (746)  |  Professional (70)  |  Publication (101)  |  Reading (133)  |  Remedy (62)  |  See (1081)  |  Something (719)  |  Word (619)  |  Work (1351)

I spent most of a lifetime trying to be a mathematician—and what did I learn. What does it take to be one? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.
In I Want to be a Mathematician: an Automathography (1985), 400.
Science quotes on:  |  Answer (366)  |  Become (815)  |  Biography (240)  |  Born (33)  |  Give Up (7)  |  Hard (243)  |  Know (1518)  |  Learn (629)  |  Lifetime (31)  |  Love (309)  |  Mathematics (1328)  |  More (2559)  |  Most (1731)  |  Must (1526)  |  Never (1087)  |  Perfect (216)  |  Right (452)  |  Spent (85)  |  Stop (80)  |  Strive (46)  |  Think (1086)  |  Trying (144)  |  Work (1351)

If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.
In A Mathematician's Apology (1940, 2012), 70.
Science quotes on:  |  Age (499)  |  Better (486)  |  Decent (10)  |  Do (1908)  |  Economic (81)  |  Economics (37)  |  Field (364)  |  Hundred (229)  |  Justification (48)  |  Man (2251)  |  Mathematics (1328)  |  Necessity (191)  |  Opportunity (87)  |  Order (632)  |  Other (2236)  |  Real (149)  |  Sacrifice (50)  |  Sense (770)  |  Silly (17)  |  Surrender (20)  |  Talent (94)  |  Undistinguished (3)  |  Will (2355)  |  Work (1351)

If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
Science quotes on:  |  Analytic (10)  |  Apparent (84)  |  Archimedes (55)  |  Class (164)  |  Compare (69)  |  Concreteness (5)  |  Condition (356)  |  René Descartes (81)  |  Diagram (20)  |  Due (141)  |  Feature (44)  |  Field (364)  |  First (1283)  |  Geometric (5)  |  Geometry (255)  |  Impress (64)  |  Instrument (144)  |  Intuition (75)  |  Investigation (230)  |  Lack (119)  |  Main (28)  |  Model (102)  |  Modern Mathematics (50)  |  Past (337)  |  Power (746)  |  Present (619)  |  Proceed (129)  |  Purely (109)  |  Slight (31)  |  Spatial (8)  |  Theory (970)  |  Use (766)  |  View (488)  |  Whole (738)

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
From final remarks in 'The Semantic Conception of Truth and the Foundations of Semantics' (1944), collected in Leonard Linsky (ed.), Semantics and the Philosophy of Language: A Collection of Readings (1952), 41.
Science quotes on:  |  Against (332)  |  Application (242)  |  Applied (177)  |  Ask (411)  |  Back (390)  |  Chain (50)  |  Colleague (50)  |  Disparage (5)  |  Doing (280)  |  Effective (59)  |  Find (998)  |  Hard (243)  |  Kind (557)  |  Locus (5)  |  Man (2251)  |  Method (505)  |  Most (1731)  |  Next (236)  |  Ourselves (245)  |  Question (621)  |  Research (664)  |  Result (677)  |  Say (984)  |  Step (231)  |  Wall (67)  |  Way (1217)  |  Will (2355)  |  Work (1351)

If in Germany the goddess Justitia had not the unfortunate habit of depositing the ministerial portfolios only in the cradles of her own progeny, who knows how many a German mathematician might not also have made an excellent minister.
In Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 13 (1904), 372.
Science quotes on:  |  Cradle (19)  |  Deposit (12)  |  Excellent (28)  |  German (36)  |  Goddess (7)  |  Habit (168)  |  Know (1518)  |  Minister (9)  |  Progeny (15)  |  Unfortunate (19)

If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.
In A Mathematician’s Apology (1940, 1967), 80.
Science quotes on:  |  Ambition (43)  |  Chance (239)  |  Curiosity (128)  |  Dominant (26)  |  Gratification (20)  |  Incentive (9)  |  Intellect (233)  |  Intellectual (255)  |  Pride (78)  |  Profession (99)  |  Professional (70)  |  Research (664)

If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
In Gottfried Wilhelm Leibnitz and Alfred Gideon Langley (trans.), New Essays Concerning Human Understanding (1896), 413-414.
Science quotes on:  |  Aid (97)  |  All (4108)  |  Appear (118)  |  Art (657)  |  Assign (13)  |  Axiom (63)  |  Being (1278)  |  Call (769)  |  Choose (112)  |  Chosen (48)  |  Cleverness (15)  |  Demonstrate (76)  |  Demonstration (113)  |  Difficulty (196)  |  Digression (3)  |  Divide (75)  |  Easy (204)  |  Everything (476)  |  Geometry (255)  |  Insufferable (2)  |  Intervene (8)  |  Intuitive (14)  |  Knowledge (1529)  |  Lemma (2)  |  Mediate (4)  |  Memorable (4)  |  Memory (134)  |  Nature Of Mathematics (80)  |  Necessary (363)  |  Obstacle (42)  |  Often (106)  |  Order (632)  |  Process (423)  |  Prolix (2)  |  Proposition (123)  |  Reduce (94)  |  Science (3879)  |  Separate (143)  |  Shorten (5)  |  Themselves (433)  |  Truth (1057)  |  Understand (606)  |  Understanding (513)  |  Wait (58)  |  Way (1217)  |  Wholly (88)  |  Why (491)  |  Worthy (34)

If the entire Mandelbrot set were placed on an ordinary sheet of paper, the tiny sections of boundary we examine would not fill the width of a hydrogen atom. Physicists think about such tiny objects; only mathematicians have microscopes fine enough to actually observe them.
In 'Can We See the Mandelbrot Set?', The College Mathematics Journal (Mar 1995), 26, No. 2, 90.
Science quotes on:  |  Actual (117)  |  Atom (355)  |  Boundary (51)  |  Enough (340)  |  Entire (47)  |  Examine (78)  |  Fill (61)  |  Fine (33)  |  Hydrogen (75)  |  Mandelbrot Set (2)  |  Microscope (80)  |  Object (422)  |  Observe (168)  |  Ordinary (160)  |  Paper (182)  |  Physicist (259)  |  Section (11)  |  Set (394)  |  Think (1086)  |  Tiny (72)  |  Width (5)

If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.
From interview (1981) with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 3.
Science quotes on:  |  Exist (443)  |  Fund (18)  |  Funding (19)  |  Government (110)  |  Mathematics (1328)  |  Never (1087)  |  See (1081)  |  Wrong (234)

If we compare a mathematical problem with an immense rock, whose interior we wish to penetrate, then the work of the Greek mathematicians appears to us like that of a robust stonecutter, who, with indefatigable perseverance, attempts to demolish the rock gradually from the outside by means of hammer and chisel; but the modern mathematician resembles an expert miner, who first constructs a few passages through the rock and then explodes it with a single blast, bringing to light its inner treasures.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 9. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 114. From the original German, “Vergleichen wir ein mathematisches Problem mit einem gewaltigen Felsen, in dessen Inneres wir eindringen wollen, so erscheint die Arbeit der griechischen Mathematiker uns als die eines rüstigen Steinhauers, der mit Hammer und Meissel in unermüdlicher Ausdauer den Felsen langsam von aussen her zu zerbröckeln beginnt; der moderne Mathematiker aber als ein trefflicher Minirer, der diesen Felsen zunächst mit wenigen Gängen durchzieht, von denen aus er dann den Felsblock mit einem gewaltigem Schlage zersprengt und die Schätze des Inneren zu Tage fördert.”
Science quotes on:  |  Appear (118)  |  Attempt (251)  |  Blast (13)  |  Bring (90)  |  Chisel (2)  |  Compare (69)  |  Construct (124)  |  Demolish (8)  |  Expert (65)  |  Explode (11)  |  First (1283)  |  Gradual (27)  |  Gradually (102)  |  Greek (107)  |  Hammer (25)  |  Immense (86)  |  Inner (71)  |  Interior (32)  |  Light (607)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Miner (9)  |  Modern (385)  |  Modern Mathematics (50)  |  Outside (141)  |  Passage (50)  |  Penetrate (67)  |  Perseverance (23)  |  Problem (676)  |  Resemble (63)  |  Robust (7)  |  Rock (161)  |  Single (353)  |  Through (849)  |  Treasure (57)  |  Wish (212)  |  Work (1351)

If you ask mathematicians what they do, you always get the same answer. They think. They think about difficult and unusual problems. (They never think about ordinary problems—they just write down the answers.)
As translated from Russian in 'A byl li brak?', Literaturnaya Gazeta (5 Dec 1979), 49, 12, as quoted and cited in The American Mathematical Monthly (Nov 1980), 87, No. 97, 696.
Science quotes on:  |  Answer (366)  |  Ask (411)  |  Difficult (246)  |  Do (1908)  |  Down (456)  |  Never (1087)  |  Ordinary (160)  |  Problem (676)  |  Think (1086)  |  Unusual (37)  |  Write (230)

In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded several months’ time, was achieved in three days by Euler with aid of improved methods of his own. … With still superior methods this same problem was solved by the illustrious Gauss in one hour.
In History of Mathematics (1897), 248.
Science quotes on:  |  Academy (35)  |  Achieve (66)  |  Aid (97)  |  Astronomy (229)  |  Demand (123)  |  Eminent (17)  |  Leonhard Euler (35)  |  Carl Friedrich Gauss (77)  |  Hour (186)  |  Illustrious (10)  |  Improve (58)  |  Mathematicians and Anecdotes (141)  |  Method (505)  |  Methods (204)  |  Month (88)  |  Problem (676)  |  Propose (23)  |  Same (157)  |  Several (32)  |  Solve (130)  |  Still (613)  |  Superior (81)  |  Time (1877)

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.
Science quotes on:  |  Amazing (35)  |  Beautiful (258)  |  Beauty (299)  |  Both (493)  |  Concept (221)  |  Connection (162)  |  Develop (268)  |  Dream (208)  |  Dreamed Up (2)  |  Fiber (16)  |  Field (364)  |  Immediately (114)  |  Learn (629)  |  Learned (235)  |  Natural (796)  |  Nowhere (28)  |  Physical (508)  |  Physical World (28)  |  Profound (104)  |  Protest (9)  |  Puzzling (8)  |  Real (149)  |  Speaking (119)  |  Theorem (112)  |  Theory (970)  |  Thrill (22)  |  World (1774)

In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics. (Some have engaged in it for this reason alone.)
In Adventures of a Mathematician (1976), 120.
Science quotes on:  |  Affair (29)  |  Alone (311)  |  Chess (25)  |  Disconnect (3)  |  Drug (57)  |  Escape (80)  |  Event (216)  |  External (57)  |  Find (998)  |  Happiness (115)  |  Immerse (4)  |  Kind (557)  |  Mathematics (1328)  |  Niche (9)  |  Practice (204)  |  Pursuit (121)  |  Reality (261)  |  Reason (744)  |  Role (86)  |  Self (267)  |  Self-Sufficient (2)  |  Sufficiency (16)  |  Themselves (433)  |  Unhappiness (9)  |  World (1774)

In mathematics it [sophistry] had no place from the beginning: Mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly we find no parties among mathematicians, and hardly any disputes.
In Essays on the Intellectual Powers of Man, Essay 1, chap. 1.
Science quotes on:  |  Accordingly (5)  |  Accurately (7)  |  Axiom (63)  |  Begin (260)  |  Beginning (305)  |  Define (49)  |  Dispute (32)  |  Down (456)  |  Find (998)  |  First (1283)  |  Ground (217)  |  Hardly (19)  |  Lie (364)  |  Mathematics (1328)  |  Nature Of Mathematics (80)  |  Party (18)  |  Place (177)  |  Principle (507)  |  Reason (744)  |  Reasoning (207)  |  Sophistry (3)  |  Term (349)  |  Terms (184)  |  Use (766)  |  Wisdom (221)

In mathematics, which is but a mirror of the society in which it thrives or suffers, the pre-Athenian period is one of colorful men and important discoveries. Sparta, like most militaristic states before and after it, produced nothing. Athens, and the allied Ionians, produced a number of works by philosophers and mathematicians; some good, some controversial, some grossly overrated.
In A History of Pi (1970), 34.
Science quotes on:  |  Colorful (2)  |  Discovery (780)  |  Good (889)  |  Important (209)  |  Ionian (2)  |  Mathematics (1328)  |  Military (40)  |  Mirror (41)  |  Most (1731)  |  Nothing (966)  |  Number (699)  |  Period (198)  |  Philosopher (258)  |  Produce (104)  |  Produced (187)  |  Society (326)  |  State (491)  |  Suffer (41)  |  Thrive (18)  |  Work (1351)

In my experience most mathematicians are intellectually lazy and especially dislike reading experimental papers. He (René Thom) seemed to have very strong biological intuitions but unfortunately of negative sign.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 136.
Science quotes on:  |  Biological (137)  |  Dislike (15)  |  Especially (31)  |  Experience (467)  |  Experiment (695)  |  Experimental (192)  |  Intellect (233)  |  Intuition (75)  |  Lazy (9)  |  Most (1731)  |  Negative (63)  |  Paper (182)  |  Read (287)  |  Reading (133)  |  Strong (174)  |  René Frédéric Thom (2)  |  Unfortunate (19)  |  Unfortunately (38)

In my opinion a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy—an opinion, moreover, which has been expressed by many philosophers.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 19.
Science quotes on:  |  Express (186)  |  Himself (461)  |  Opinion (281)  |  Philosopher (258)  |  Philosophy (380)  |  Preoccupy (4)

In other branches of science, where quick publication seems to be so much desired, there may possibly be some excuse for giving to the world slovenly or ill-digested work, but there is no such excuse in mathematics. The form ought to be as perfect as the substance, and the demonstrations as rigorous as those of Euclid. The mathematician has to deal with the most exact facts of Nature, and he should spare no effort to render his interpretation worthy of his subject, and to give to his work its highest degree of perfection. “Pauca sed matura” was Gauss’s motto.
In Presidential Address British Association for the Advancement of Science, Section A, (1890), Nature, 42, 467. [The Latin motto translates as “Few, but ripe”. —Webmaster]
Science quotes on:  |   (2863)  |  Branch (150)  |  Deal (188)  |  Degree (276)  |  Demonstration (113)  |  Desire (204)  |  Effort (227)  |  Euclid (54)  |  Exact (68)  |  Excuse (25)  |  Fact (1210)  |  Facts (553)  |  Form (959)  |  Carl Friedrich Gauss (77)  |  Give (202)  |  High (362)  |  Interpretation (85)  |  Mathematics (1328)  |  Most (1731)  |  Motto (28)  |  Nature (1926)  |  Other (2236)  |  Perfect (216)  |  Perfection (129)  |  Possibly (111)  |  Publication (101)  |  Quick (13)  |  Render (93)  |  Rigorous (48)  |  Science (3879)  |  Seem (145)  |  Slovenly (2)  |  Spare (9)  |  Study And Research In Mathematics (61)  |  Subject (521)  |  Substance (248)  |  Work (1351)  |  World (1774)  |  Worthy (34)

In reality the origin of the notion of derivatives is in the vague feeling of the mobility of things, and of the greater or less speed with which phenomena take place; this is well expressed by the terms fluent and fluxion, which were used by Newton and which we may believe were borrowed from the ancient mathematician Heraclitus.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 407.
Science quotes on:  |  Ancient (189)  |  Borrow (30)  |  Derivative (6)  |  Express (186)  |  Feeling (250)  |  Fluent (2)  |  Fluxion (7)  |  Greater (288)  |  Heraclitus (15)  |  Mobility (11)  |  Sir Isaac Newton (333)  |  Nomenclature (146)  |  Notion (113)  |  Origin (239)  |  Phenomenon (318)  |  Reality (261)  |  Speed (65)  |  Term (349)  |  Terms (184)  |  Thing (1915)  |  Vague (47)

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.
Reflections: Mathematics and Creativity', New Yorker (1972), 47, No. 53, 39-45. In Douglas M. Campbell, John C. Higgins (eds.), Mathematics: People, Problems, Results (1984), Vol. 2, 7.
Science quotes on:  |  Acquisition (45)  |  All (4108)  |  Author (167)  |  Book (392)  |  Businessman (4)  |  Company (59)  |  Discussion (72)  |  Economist (17)  |  Friend (168)  |  Lawyer (27)  |  Mathematics (1328)  |  More (2559)  |  Profound (104)  |  State (491)  |  Understandable (12)  |  Understanding (513)  |  Work (1351)  |  Writer (86)

In the summer of 1937, … I told Banach about an expression Johnny [von Neumann] had once used in conversation with me in Princeton before stating some non-Jewish mathematician’s result, “Die Goim haben den folgendenSatzbewiesen” (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.
In Adventures of a Mathematician (1976, 1991), 107. Von Neumann, who was raised in Budapest by a Jewish family, knew the Yiddish word “goy” was equivalent to “gentile” or a non-Jew. Stefan Banach, a Polish mathematician, was raised in a Catholic family, hence “pure goy”. Ulam thus gives us the saying so often elsewhere seen attributed to von Neumann without the context: “The goys have proved the following theorem.” It is seen anecdotally as stated by von Neumann to begin a classroom lecture.
Science quotes on:  |   (2863)  |  Better (486)  |  Conversation (43)  |  Do (1908)  |  Enchanted (2)  |  Expression (175)  |  Funny (11)  |  Implication (23)  |  Invent (51)  |  Jewish (15)  |  Joke (83)  |  Originate (36)  |  Princeton (4)  |  Prove (250)  |  Pure (291)  |  Result (677)  |  Sayings (2)  |  Start (221)  |  State (491)  |  Summer (54)  |  Theorem (112)  |  Thought (953)  |  John von Neumann (28)

In the world of science different levels of esteem are accorded to different kinds of specialist. Mathematicians have always been eminently respectable, and so are those who deal with hard lifeless theories about what constitutes the physical world: the astronomers, the physicists, the theoretical chemists. But the more closely the scientist interests himself in matters which are of direct human relevance, the lower his social status. The real scum of the scientific world are the engineers and the sociologists and the psychologists. Indeed, if a psychologist wants to rate as a scientist he must study rats, not human beings. In zoology the same rules apply. It is much more respectable to dissect muscle tissues in a laboratory than to observe the behaviour of a living animal in its natural habitat.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
Science quotes on:  |  Animal (617)  |  Apply (160)  |  Astronomer (93)  |  Behaviour (41)  |  Being (1278)  |  Chemist (156)  |  Close (69)  |  Constitute (97)  |  Deal (188)  |  Different (577)  |  Direct (225)  |  Dissection (32)  |  Engineer (121)  |  Esteem (15)  |  Habitat (16)  |  Hard (243)  |  Himself (461)  |  Human (1468)  |  Human Being (175)  |  Human Beings (117)  |  Indeed (324)  |  Interest (386)  |  Kind (557)  |  Laboratory (196)  |  Level (67)  |  Lifeless (14)  |  Live (628)  |  Living (491)  |  Low (80)  |  Matter (798)  |  More (2559)  |  Muscle (45)  |  Must (1526)  |  Natural (796)  |  Observe (168)  |  Physical (508)  |  Physical World (28)  |  Physicist (259)  |  Psychologist (15)  |  Rat (37)  |  Rate (29)  |  Real (149)  |  Relevance (16)  |  Respectable (6)  |  Rule (294)  |  Science (3879)  |  Scientific (941)  |  Scientist (820)  |  Social (252)  |  Sociologist (3)  |  Specialist (28)  |  Status (35)  |  Study (653)  |  Theoretical (22)  |  Theory (970)  |  Tissue (45)  |  Want (497)  |  World (1774)  |  Zoology (36)

Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
Science quotes on:  |   (2863)  |  Art (657)  |  Artist (90)  |  Attain (125)  |  Basic (138)  |  Both (493)  |  Calculating Machine (3)  |  Childish (20)  |  Desk (13)  |  Differ (85)  |  Differently (4)  |  Do (1908)  |  Frenzy (6)  |  Imagination (328)  |  Inspiration (75)  |  Machine (257)  |  Mania (3)  |  Mathematics (1328)  |  Mean (809)  |  Meaning (233)  |  Means (579)  |  Mechanical (140)  |  Naturally (11)  |  Notion (113)  |  Other (2236)  |  Plato (76)  |  Process (423)  |  Psychological (42)  |  Psychology (154)  |  Quality (135)  |  Realm (85)  |  Result (677)  |  Role (86)  |  Ruler (21)  |  Science (3879)  |  Science And Art (184)  |  Sense (770)  |  Sitting (44)  |  Think (1086)  |  Value (365)  |  Karl Weierstrass (9)

Isolated, so-called “pretty theorems” have even less value in the eyes of a modern mathematician than the discovery of a new “pretty flower” has to the scientific botanist, though the layman finds in these the chief charm of the respective Sciences.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 19. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 92. From the original German, “Einzelne, sogenannte „hübsche Sätze“ haben an und für sich in den Augen eines modernen Mathematikers noch weniger Werth, als für den wissenschaftlichen Botaniker die Entdeckung einer neuen „hübschen Blume“, obgleich dem Laien gerade hierin der Hauptreiz der betreffenden Wissenschaft zu liegen pflegt.”
Science quotes on:  |  Botanist (23)  |  Call (769)  |  Charm (51)  |  Chief (97)  |  Discovery (780)  |  Eye (419)  |  Find (998)  |  Flower (106)  |  Isolate (22)  |  Layman (21)  |  Modern (385)  |  New (1216)  |  Pretty (20)  |  Respective (2)  |  Science (3879)  |  Scientific (941)  |  So-Called (71)  |  Study And Research In Mathematics (61)  |  Theorem (112)  |  Value (365)

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.
Collected in Paul Arthur Schilpp (ed.), Albert Einstein: Philosopher-Scientist (1959), Vol. 1, 307. Also, in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 71.
Science quotes on:  |  Einstein (101)  |  Albert Einstein (605)  |  Gottfried Wilhelm Leibniz (49)  |  Philosopher (258)  |  Problem (676)  |  Solution (267)  |  Space (500)  |  Time (1877)  |  Time And Space (39)

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.
In 'Mathematics in the Modern World', Scientific American (Sep 1964) 211, No. 3, 42. Collected in Ronald J. Comer and Morris Kline, Mathematics in the Modern World: Readings from Scientific American (1988), 20.
Science quotes on:  |  Become (815)  |  Binding (9)  |  Divergence (6)  |  Divergent (6)  |  Duty (68)  |  Essence (82)  |  Goal (145)  |  Idea (843)  |  Interest (386)  |  Mathematics (1328)  |  Mediation (4)  |  Motivation (27)  |  Must (1526)  |  Together (387)  |  Urgency (12)  |  Urgent (13)

It has been proposed (in despair) to define mathematics as “what mathematicians do.” Only such a broad definition, it was felt, would cover all the things that might become embodied in mathematics; for mathematicians today attack many problems not regarded as mathematics in the past, and what they will do in the future there is no saying.
In 'The Extent of Mathematics', Prelude to Mathematics (1955), 11.
Science quotes on:  |  All (4108)  |  Attack (84)  |  Become (815)  |  Broad (27)  |  Cover (37)  |  Define (49)  |  Definition (221)  |  Despair (40)  |  Do (1908)  |  Embody (16)  |  Future (429)  |  Mathematics (1328)  |  Past (337)  |  Problem (676)  |  Propose (23)  |  Regard (305)  |  Thing (1915)  |  Today (314)  |  Will (2355)

It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have “collected data” that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler.
In Higher Mathematics for Students of Chemistry and Physics (1902), 3.
Science quotes on:  |  Assist (9)  |  Basis (173)  |  Collect (16)  |  Complete (204)  |  Completed (30)  |  Data (156)  |  Deduce (25)  |  Different (577)  |  Discern (33)  |  Discerning (16)  |  Establish (57)  |  Experiment (695)  |  Experimental (192)  |  Express (186)  |  Michael Faraday (85)  |  Firm (47)  |  Follow (378)  |  Generalization (57)  |  Investigator (67)  |  Johannes Kepler (91)  |  Little (707)  |  Mathematics (1328)  |  Maxwell (42)  |  James Clerk Maxwell (87)  |  Sir Isaac Newton (333)  |  Number (699)  |  Numerical (39)  |  Observation (555)  |  Observational (15)  |  Phenomenon (318)  |  Province (35)  |  Relation (157)  |  Required (108)  |  Science (3879)  |  Scope (45)  |  Special (184)  |  Stage (143)  |  Term (349)  |  Terms (184)  |  Worker (31)

It has long been a complaint against mathematicians that they are hard to convince: but it is a far greater disqualification both for philosophy, and for the affairs of life, to be too easily convinced; to have too low a standard of proof. The only sound intellects are those which, in the first instance, set their standards of proof high. Practice in concrete affairs soon teaches them to make the necessary abatement: but they retain the consciousness, without which there is no sound practical reasoning, that in accepting inferior evidence because there is no better to be had, they do not by that acceptance raise it to completeness.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611.
Science quotes on:  |  Accept (191)  |  Acceptance (52)  |  Accepting (22)  |  Affair (29)  |  Against (332)  |  Better (486)  |  Both (493)  |  Complaint (11)  |  Completeness (19)  |  Concrete (51)  |  Consciousness (123)  |  Convince (41)  |  Convinced (23)  |  Disqualification (2)  |  Do (1908)  |  Easily (35)  |  Evidence (248)  |  Far (154)  |  First (1283)  |  Great (1574)  |  Greater (288)  |  Hard (243)  |  High (362)  |  Inferior (37)  |  Instance (33)  |  Intellect (233)  |  Life (1795)  |  Long (790)  |  Low (80)  |  Necessary (363)  |  Philosophy (380)  |  Practical (200)  |  Practice (204)  |  Proof (287)  |  Raise (35)  |  Reason (744)  |  Reasoning (207)  |  Retain (56)  |  Set (394)  |  Soon (186)  |  Sound (183)  |  Standard (57)  |  Teach (277)

It is a melancholy experience for a professional mathematician to find him writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings; there is no scorn more profound, or on the whole more justifiable, than that of men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 61 (Hardy's opening lines after Snow's foreward).
Science quotes on:  |  Appreciation (34)  |  Art (657)  |  Criticism (78)  |  Do (1908)  |  Experience (467)  |  Explain (322)  |  Feeling (250)  |  Feelings (52)  |  Find (998)  |  Function (228)  |  Mathematics (1328)  |  Melancholy (17)  |  Mind (1338)  |  More (2559)  |  New (1216)  |  Other (2236)  |  Painter (29)  |  Physicist (259)  |  Physiologist (29)  |  Professional (70)  |  Profound (104)  |  Prove (250)  |  Scorn (12)  |  Something (719)  |  Theorem (112)  |  Usually (176)  |  Whole (738)  |  Work (1351)  |  Writing (189)

It is easier to square the circle than to get round a mathematician.
In Budget of Paradoxes (1872), 90.
Science quotes on:  |  Circle (110)  |  Easier (53)  |  Square (70)

It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.
Aristotle
Nicomachean Ethics, 1094b, 25-7. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1730.
Science quotes on:  |  Accept (191)  |  Demand (123)  |  Demonstrative (14)  |  Equally (130)  |  Evidently (26)  |  Foolish (40)  |  Logic (287)  |  Proof (287)  |  Reasoning (207)

It is impossible to be a mathematician without being a poet in soul.
In a letter to Madame Schabelskoy, quoted in Sónya Kovalévsky: Her Recollections of Childhood, translated by Isabel F. Hapgood (1895), 316.
Science quotes on:  |  Being (1278)  |  Impossible (251)  |  Poet (83)  |  Soul (226)

It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.
In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.
Science quotes on:  |   (2863)  |  Abstract (124)  |  Acquired (78)  |  Analyze (10)  |  Arthur Cayley (17)  |  Combine (57)  |  Comprehensive (29)  |  Compute (18)  |  Concept (221)  |  Data (156)  |  Devote (35)  |  Devoted (59)  |  Element (310)  |  Empirical (54)  |  Form (959)  |  General (511)  |  Generalize (19)  |  Idea (843)  |  Labor (107)  |  Master (178)  |  Material (353)  |  Mathematicians and Anecdotes (141)  |  Natural (796)  |  Natural Philosopher (4)  |  Numerical (39)  |  Philosopher (258)  |  Single (353)  |  Stroke (18)  |  Subject (521)  |  Subsequent (33)  |  Test (211)  |  Ultimate (144)  |  Utilization (15)  |  Verification (31)  |  Way (1217)  |  Year (933)  |  Yield (81)

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
Science quotes on:  |   (2863)  |  A Priori (26)  |  Achievement (179)  |  Administrator (11)  |  Admit (45)  |  Affair (29)  |  Aid (97)  |  Alike (60)  |  Alone (311)  |  Analogous (5)  |  Analysis (233)  |  Anatomist (23)  |  Application (242)  |  François Arago (14)  |  Army (33)  |  Attain (125)  |  Author (167)  |  Balance (77)  |  Behold (18)  |  Bernhard Bolzano (2)  |  Calculation (127)  |  Calculus (65)  |  Call (769)  |  Lazare-Nicolas-Marguerite Carnot (4)  |  Celebrated (2)  |  Central (80)  |  Certainty (174)  |  Chair (24)  |  Civil (26)  |  Classic (11)  |  William Kingdon Clifford (21)  |  Commercial (26)  |  Comparative (13)  |  Compare (69)  |  Constantly (27)  |  Constitution (76)  |  Contemplate (18)  |  Creation (327)  |  Creator (91)  |  Current (118)  |  Baron Georges Cuvier (30)  |  Charles Darwin (303)  |  Deal (188)  |  Degree (276)  |  René Descartes (81)  |  Descriptive (17)  |  Descriptive Geometry (3)  |  Devotee (5)  |  Devotion (34)  |  Direct (225)  |  Dissimilar (6)  |  Distinction (72)  |  Diverse (17)  |  Division (65)  |  Doctrine (75)  |  Due (141)  |  Eminent (17)  |  Empire (14)  |  Endless (56)  |  Engage (39)  |  Enough (340)  |  Exercise (110)  |  Eye (419)  |  Fact (1210)  |  False (100)  |  Fauna (13)  |  Field (364)  |  Finally (26)  |  Find (998)  |  Flora (9)  |  Flourish (34)  |  Baron Jean-Baptiste-Joseph Fourier (17)  |  Function (228)  |  Carl Friedrich Gauss (77)  |  General (511)  |  Genuinely (4)  |  Geometry (255)  |  Great (1574)  |  Greatest (328)  |  Ground (217)  |  Group (78)  |  Hero (42)  |  Hide (69)  |  High (362)  |  Histology (3)  |  Host (16)  |  Idea (843)  |  Illuminate (24)  |  Illuminating (12)  |  Immortal (35)  |  Industry (137)  |  Infinitesimal (29)  |  Inheritor (2)  |  Interest (386)  |  Intimate (15)  |  Invoke (6)  |  Judgment (132)  |  Kingdom (78)  |  Felix Klein (15)  |  Know (1518)  |  Known (454)  |  Land (115)  |  Large (394)  |  Gottfried Wilhelm Leibniz (49)  |  Letter (109)  |  Logical (55)  |  Major (84)  |  Master (178)  |  Mathematics (1328)  |  Matter (798)  |  Microscopic (26)  |  Mind (1338)  |  Minute (125)  |  Monarch (4)  |  Gaspard Monge (2)  |  Most (1731)  |  Sir Isaac Newton (333)  |  Office (71)  |  Operation (213)  |  Operations (107)  |  Opinion (281)  |  Organize (29)  |  Other (2236)  |  Part (222)  |  Blaise Pascal (80)  |  Peace (108)  |  Peer (12)  |  Philosophy (380)  |  Henri Poincaré (96)  |  Jean-Victor Poncelet (2)  |  Position (77)  |  Practical (200)  |  Prepare (37)  |  Probability (130)  |  Projective Geometry (3)  |  Public Service (5)  |  Pure (291)  |  Range (99)  |  Reality (261)  |  Recess (8)  |  Reduce (94)  |  Reducible (2)  |  Reflect (32)  |  Relate (21)  |  Render (93)  |  Require (219)  |  Required (108)  |  Bernhard Riemann (7)  |  Rightful (3)  |  Sagacious (7)  |  Salmon (7)  |  Say (984)  |  Scatter (6)  |  Science (3879)  |  Seldom (65)  |  Service (110)  |  Similarity (31)  |  Single (353)  |  Statesman (19)  |  Structure (344)  |  Surprise (86)  |  Survey (33)  |  Theory (970)  |  Thing (1915)  |  Tune (19)  |  Unfit (12)  |  Variety (132)  |  View (488)  |  Vision (123)  |  War (225)  |  Karl Weierstrass (9)  |  Wield (10)  |  Work (1351)  |  World (1774)

It is possible for a mathematician to be “too strong” for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)
In A Mathematician's Miscellany (1953). Reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 144.
Science quotes on:  |  Approach (108)  |  Climber (7)  |  Crack (15)  |  Delicate (43)  |  Different (577)  |  Dreadful (14)  |  Find (998)  |  Force (487)  |  Fruitful (58)  |  More (2559)  |  Occasion (85)  |  Possible (552)  |  Rock (161)  |  Route (15)  |  Strong (174)  |  Subtle (35)  |  Through (849)

It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
Science quotes on:  |   (2863)  |  Accord (36)  |  According (237)  |  All (4108)  |  Appear (118)  |  Approach (108)  |  Arrangement (91)  |  Ascendant (2)  |  Ascertain (38)  |  Astrologer (10)  |  Author (167)  |  Beyond (308)  |  Birth (147)  |  Book (392)  |  Bring (90)  |  Chance (239)  |  Child (307)  |  Children (200)  |  Circumstance (136)  |  Coming (114)  |  Compose (17)  |  Concern (228)  |  Connect (125)  |  Contract (11)  |  Course (409)  |  Cup (7)  |  Curiosity (128)  |  Daughter (29)  |  Delay (20)  |  Destined (42)  |  Destiny (50)  |  Disappoint (14)  |  Disappointed (6)  |  Down (456)  |  Dress (9)  |  Eternal (110)  |  Examine (78)  |  Existence (456)  |  Expect (200)  |  Expectation (65)  |  Fall (230)  |  Father (110)  |  Find (998)  |  Firmly (6)  |  Follow (378)  |  Girl (37)  |  Good (889)  |  Ground (217)  |  Happen (274)  |  Happened (88)  |  Hole (16)  |  Hour (186)  |  Indian (27)  |  Influx (2)  |  Intend (16)  |  Jewel (10)  |  Keep (101)  |  Knowing (137)  |  Late (118)  |  Leave (130)  |  Life (1795)  |  Long (790)  |  Look (582)  |  Lucky (13)  |  Marriage (39)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Moderate (6)  |  Name (333)  |  Natural (796)  |  Observe (168)  |  Occasion (85)  |  Operation (213)  |  Order (632)  |  Pass (238)  |  Pearl (6)  |  Precious (41)  |  Promise (67)  |  Quality (135)  |  Remain (349)  |  Roll (40)  |  Say (984)  |  Second (62)  |  Separate (143)  |  Short (197)  |  Small (477)  |  Son (24)  |  Stop (80)  |  Subside (5)  |  Time (1877)  |  Treatise (44)  |  Two (937)  |  Unfortunate (19)  |  United (14)  |  Unmarried (3)  |  Vessel (63)  |  Wait (58)  |  Water (481)  |  Will (2355)  |  Work (1351)  |  Write (230)

It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.
In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 72-73.
Science quotes on:  |  Aim (165)  |  All (4108)  |  Condense (13)  |  Constant (144)  |  Expression (175)  |  Language (293)  |  Lowest (10)  |  Maximum (12)  |  Meaning (233)  |  Minimum (12)  |  Phrase (61)  |  Reduce (94)  |  Retrench (2)  |  Superfluous (21)  |  Term (349)  |  Terms (184)  |  Word (619)

It is the invaluable merit of the great Basle mathematician Leonhard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1884), 12. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 153. Seen incorrectly attributed to Thomas Reid in N. Rose, Mathematical and Maxims and Minims (1988).
Science quotes on:  |  All (4108)  |  Analysis (233)  |  Bound (119)  |  Bounds (7)  |  Calculus (65)  |  Establish (57)  |  Leonhard Euler (35)  |  Field (364)  |  Free (232)  |  Geometry (255)  |  Great (1574)  |  Independent (67)  |  Invaluable (11)  |  Leadership (9)  |  Maintain (105)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Merit (50)  |  Science (3879)  |  Time (1877)

It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
From letter to Sofia Kovalevskaya (27 Aug 1883), as quoted by Mittag-Leffler in Compte Rendu du Deuxième Congrès International des Mathématiciens Tenu à Paris du 6 au 12 Août 1900 (1902), 149. In Robert Edoward Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 121. From the original German, “Es ist wahr, ein Mathematiker, der nicht etwas Poet ist, wird nimmer ein vollkommener Mathematiker sein.” Also seen translated as, “No mathematician can be a complete mathematician unless he is also something of a poet”, in, for example, E.T. Bell, Men of Mathematics (1937), 432.
Science quotes on:  |  Never (1087)  |  Perfect (216)  |  Poet (83)  |  Will (2355)

It is with mathematics not otherwise than it is with music, painting or poetry. Anyone can become a lawyer, doctor or chemist, and as such may succeed well, provided he is clever and industrious, but not every one can become a painter, or a musician, or a mathematician: general cleverness and industry alone count here for nothing.
In Ueber die Anlage zur Mathematik (1900), 5. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 184.
Science quotes on:  |  Alone (311)  |  Become (815)  |  Chemist (156)  |  Clever (38)  |  Cleverness (15)  |  Count (105)  |  Doctor (187)  |  General (511)  |  Industrious (12)  |  Industry (137)  |  Lawyer (27)  |  Mathematics (1328)  |  Mathematics And Art (8)  |  Mathematics As A Fine Art (23)  |  Music (129)  |  Musician (21)  |  Nothing (966)  |  Painter (29)  |  Painting (44)  |  Poetry (143)  |  Provide (69)  |  Succeed (109)

It is, so to speak, a scientific tact, which must guide mathematicians in their investigations, and guard them from spending their forces on scientifically worthless problems and abstruse realms, a tact which is closely related to esthetic tact and which is the only thing in our science which cannot be taught or acquired, and is yet the indispensable endowment of every mathematician.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 28. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 92. From the original German, “Es ist, so zu sagen, ein wissenschaftlicher Tact, welcher die Mathematiker bei ihren Untersuchungen leiten, und sie davor bewahren muss, ihre Kräfte auf wissenschaftlich werthlose Probleme und abstruse Gebiete zu wenden, ein Tact, der dem ästhetischen nahe verwandt, das einzige ist, was in unserer Wissenschaft nicht gelehrt und gelernt werden kann, aber eine unentbehrliche Mitgift eines Mathematikers sein sollte.”
Science quotes on:  |  Abstruse (10)  |  Acquire (39)  |  Acquired (78)  |  Closely (12)  |  Endowment (16)  |  Esthetic (3)  |  Force (487)  |  Guard (18)  |  Guide (97)  |  Indispensable (28)  |  Investigation (230)  |  Must (1526)  |  Problem (676)  |  Realm (85)  |  Science (3879)  |  Scientific (941)  |  Speak (232)  |  Spend (95)  |  Spending (24)  |  Study And Research In Mathematics (61)  |  Tact (6)  |  Teach (277)  |  Thing (1915)  |  Worthless (21)

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.
Quoted in Mark Kac, Statistical Independence in Probability, Analysis and Number Theory (1959), 52.
Science quotes on:  |  Appropriate (61)  |  Appropriateness (7)  |  Conviction (97)  |  Doubt (304)  |  Jest (4)  |  Law (894)  |  Law Of Nature (72)  |  Must (1526)  |  Mysterious (79)  |  Mystery (177)  |  Nature (1926)  |  Physicist (259)  |  Quotation (18)  |  Quote (42)  |  Something (719)  |  Statement (142)  |  Theorem (112)  |  Think (1086)

It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, chusing [choosing] rather to acknowledge their ignorance, than affirm anything rashly. They affirm nothing among their arguments or assertions which is not most manifestly known and examined with utmost rigour, rejecting all probable conjectures and little witticisms. They submit nothing to authority, indulge no affection, detest subterfuges of words, and declare their sentiments, as in a Court of Judicature [Justice], without passion, without apology; knowing that their reasons, as Seneca testifies of them, are not brought to persuade, but to compel.
Mathematical Lectures (1734), 64.
Science quotes on:  |  Acknowledge (33)  |  Affection (43)  |  Affirm (2)  |  All (4108)  |  Apology (7)  |  Argument (138)  |  Authority (95)  |  Certain (550)  |  Choose (112)  |  Compel (30)  |  Confirm (57)  |  Conjecture (49)  |  Court (33)  |  Declare (45)  |  Detest (5)  |  Do (1908)  |  Doubt (304)  |  Doubtful (29)  |  Good (889)  |  Ignorance (240)  |  Indulge (14)  |  Invincible (6)  |  Judgment (132)  |  Justice (39)  |  Know (1518)  |  Knowing (137)  |  Knowledge (1529)  |  Known (454)  |  Little (707)  |  Manifestly (11)  |  Meddle (3)  |  Most (1731)  |  Nature Of Mathematics (80)  |  Nothing (966)  |  Observed (149)  |  Other (2236)  |  Pass (238)  |  Passing (76)  |  Passion (114)  |  Persuade (11)  |  Probable (20)  |  Profess (20)  |  Publish (36)  |  Rashly (2)  |  Reason (744)  |  Reject (63)  |  Rigour (21)  |  Lucius Annaeus Seneca (20)  |  Sentiment (14)  |  Silent (29)  |  Speak (232)  |  Submit (18)  |  Testify (5)  |  Theorem (112)  |  Thing (1915)  |  Truth (1057)  |  Unknown (182)  |  Witticism (2)  |  Word (619)

It may be true that people who are merely mathematicians have certain specific shortcomings; however that is not the fault of mathematics, but is true of every exclusive occupation. Likewise a mere linguist, a mere jurist, a mere soldier, a mere merchant, and so forth. One could add such idle chatter that when a certain exclusive occupation is often connected with certain specific shortcomings, it is on the other hand always free of certain other shortcomings.
Letter to Heinrich Schumacher (1-5 Jan 1845). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.
Science quotes on:  |  Certain (550)  |  Connect (125)  |  Exclusive (29)  |  Fault (54)  |  Free (232)  |  Idle (33)  |  Mathematics (1328)  |  Merely (316)  |  Occupation (48)  |  Other (2236)  |  People (1005)  |  Soldier (26)  |  Specific (95)

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.
In Gauss-Schumacher Briefwechsel, Bd. 4, (1862), 387.
Science quotes on:  |  Certain (550)  |  Certainly (185)  |  Couple (9)  |  Divorce (6)  |  Equally (130)  |  Exclusive (29)  |  Fault (54)  |  Idle (33)  |  Jurist (4)  |  Mathematics (1328)  |  Merchant (6)  |  Mere (84)  |  Occupation (48)  |  Other (2236)  |  Philologist (2)  |  Shortcoming (4)  |  Soldier (26)  |  Specific (95)  |  Talk (100)  |  True (212)  |  Whenever (81)

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.
In a letter to Madame Schabelskoy, quoted in Sónya Kovalévsky: Her Recollections of Childhood, translated by Isabel F. Hapgood (1895), 317.
Science quotes on:  |  Deep (233)  |  Do (1908)  |  Look (582)  |  Must (1526)  |  Other (2236)  |  Perception (97)  |  Poet (83)  |  Thing (1915)

It was a dark and stormy night, so R. H. Bing volunteered to drive some stranded mathematicians from the fogged-in Madison airport to Chicago. Freezing rain pelted the windscreen and iced the roadway as Bing drove on—concentrating deeply on the mathematical theorem he was explaining. Soon the windshield was fogged from the energetic explanation. The passengers too had beaded brows, but their sweat arose from fear. As the mathematical description got brighter, the visibility got dimmer. Finally, the conferees felt a trace of hope for their survival when Bing reached forward—apparently to wipe off the moisture from the windshield. Their hope turned to horror when, instead, Bing drew a figure with his finger on the foggy pane and continued his proof—embellishing the illustration with arrows and helpful labels as needed for the demonstration.
In 'R. H. Bing', Biographical Memoirs: National Academy of Sciences (2002), 49. Anecdote based on the recollections of Bing's colleagues, Steve Armentrout and C. E. Burgess. The narrative was given in a memorial tribute at the University of Texas at Austin.
Science quotes on:  |  Arrow (20)  |  Brow (3)  |  Concentrate (26)  |  Dark (140)  |  Demonstration (113)  |  Description (84)  |  Draw (137)  |  Drive (55)  |  Embellish (4)  |  Energetic (6)  |  Explanation (234)  |  Fear (197)  |  Figure (160)  |  Finger (44)  |  Fog (10)  |  Forward (102)  |  Freezing (16)  |  Hope (299)  |  Horror (14)  |  Ice (54)  |  Illustration (48)  |  Label (11)  |  Moisture (20)  |  Night (120)  |  Passenger (10)  |  Proof (287)  |  Rain (62)  |  Reach (281)  |  Roadway (2)  |  Soon (186)  |  Stormy (2)  |  Strand (9)  |  Survival (94)  |  Sweat (15)  |  Theorem (112)  |  Trace (103)  |  Turn (447)  |  Visibility (6)  |  Volunteer (7)  |  Windshield (2)  |  Wipe (6)

It was long before I got at the maxim, that in reading an old mathematician you will not read his riddle unless you plough with his heifer; you must see with his light, if you want to know how much he saw.
Letter to W. R. Hamilton, 27 January 1853. In R. P. Graves (ed.), A Life of Sir W. R. Hamilton (1889), Vol. 3, 438.
Science quotes on:  |  Know (1518)  |  Light (607)  |  Long (790)  |  Must (1526)  |  Old (481)  |  Plough (13)  |  Read (287)  |  Reading (133)  |  Riddle (28)  |  Saw (160)  |  See (1081)  |  Want (497)  |  Will (2355)

It would be better for the true physics if there were no mathematicians on earth.
Quoted in The Mathematical Intelligencer (Winter 1991), 13, No. 1, 6.
Science quotes on:  |  Better (486)  |  Earth (996)  |  Physic (517)  |  Physics (533)

It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
Science quotes on:  |  Access (20)  |  Accessibility (3)  |  Acquaint (9)  |  Additional (6)  |  Area (31)  |  Arise (158)  |  Arising (22)  |  Attain (125)  |  Become (815)  |  Becoming (96)  |  Belief (578)  |  Both (493)  |  Branch (150)  |  Brilliant (53)  |  Bring (90)  |  Certainly (185)  |  Chosen (48)  |  Communication (94)  |  Complicated (115)  |  Conduct (69)  |  Counteract (4)  |  Course (409)  |  Daily (87)  |  Danger (115)  |  Decipher (7)  |  Devise (14)  |  Difficult (246)  |  Difficulty (196)  |  Discover (553)  |  Display (56)  |  Ease (35)  |  Effect (393)  |  Enable (119)  |  Exaggeration (15)  |  Exercise (110)  |  Expansion (41)  |  Exploration (134)  |  Express (186)  |  Extent (139)  |  Facility (11)  |  Faith (203)  |  Field (364)  |  First (1283)  |  First Sight (6)  |  Form (959)  |  Future (429)  |  General (511)  |  Genius (284)  |  Grapple (10)  |  Great (1574)  |  Greatest (328)  |  Himself (461)  |  Improvement (108)  |  Increase (210)  |  Invent (51)  |  Keep (101)  |  Knowledge (1529)  |  Labour (98)  |  Language (293)  |  Less (103)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Mere (84)  |  Merely (316)  |  Method (505)  |  Methods (204)  |  More (2559)  |  Most (1731)  |  Must (1526)  |  New (1216)  |  Notation (27)  |  Number (699)  |  Of Course (20)  |  Open (274)  |  Other (2236)  |  Power (746)  |  Powerful (139)  |  Predict (79)  |  Previously (11)  |  Principle (507)  |  Progress (465)  |  Rapid (33)  |  Rapidly (66)  |  Region (36)  |  Remote (83)  |  Rest (280)  |  Result (677)  |  Safe (54)  |  Satisfactory (17)  |  Say (984)  |  Seem (145)  |  Sight (132)  |  Simplification (20)  |  Simplify (13)  |  Source (93)  |  Specialized (8)  |  Study (653)  |  Study And Research In Mathematics (61)  |  Subject (521)  |  Symbolic (15)  |  Tend (124)  |  Territory (24)  |  Theory (970)  |  Think (1086)  |  True (212)  |  Truth (1057)  |  Understand (606)  |  Way (1217)  |  Well-Chosen (2)  |  Widen (10)  |  Will (2355)  |  Work (1351)  |  Worker (31)

J. J. Sylvester was an enthusiastic supporter of reform [in the teaching of geometry]. The difference in attitude on this question between the two foremost British mathematicians, J. J. Sylvester, the algebraist, and Arthur Cayley, the algebraist and geometer, was grotesque. Sylvester wished to bury Euclid “deeper than e’er plummet sounded” out of the schoolboy’s reach; Cayley, an ardent admirer of Euclid, desired the retention of Simson’s Euclid. When reminded that this treatise was a mixture of Euclid and Simson, Cayley suggested striking out Simson’s additions and keeping strictly to the original treatise.
In History of Elementary Mathematics (1910), 285.
Science quotes on:  |   (2863)  |  Addition (66)  |  Admirer (9)  |  Ardent (6)  |  Attitude (82)  |  British (41)  |  Bury (16)  |  Arthur Cayley (17)  |  Deep (233)  |  Desire (204)  |  Difference (337)  |  Enthusiastic (6)  |  Euclid (54)  |  Foremost (11)  |  Geometer (24)  |  Geometry (255)  |  Grotesque (6)  |  Keep (101)  |  Mathematicians and Anecdotes (141)  |  Mixture (41)  |  Original (58)  |  Plummet (2)  |  Question (621)  |  Reach (281)  |  Reform (22)  |  Remind (13)  |  Retention (5)  |  Schoolboy (9)  |  Sound (183)  |  Strictly (13)  |  Strike (68)  |  Striking (48)  |  Suggest (34)  |  Supporter (4)  |  James Joseph Sylvester (58)  |  Teach (277)  |  Teaching (188)  |  Treatise (44)  |  Two (937)  |  Wish (212)

Just as it will never be successfully challenged that the French language, progressively developing and growing more perfect day by day, has the better claim to serve as a developed court and world language, so no one will venture to estimate lightly the debt which the world owes to mathematicians, in that they treat in their own language matters of the utmost importance, and govern, determine and decide whatever is subject, using the word in the highest sense, to number and measurement.
In 'Sprüche in Prosa', Natur, III, 868.
Science quotes on:  |  Better (486)  |  Challenge (85)  |  Claim (146)  |  Court (33)  |  Debt (13)  |  Decide (41)  |  Determine (144)  |  Develop (268)  |  Estimate (57)  |  Estimates of Mathematics (30)  |  French (20)  |  Govern (64)  |  Grow (238)  |  Growing (98)  |  High (362)  |  Importance (286)  |  Language (293)  |  Lightly (2)  |  Matter (798)  |  Measurement (174)  |  More (2559)  |  Never (1087)  |  Number (699)  |  Owe (71)  |  Perfect (216)  |  Progressive (17)  |  Sense (770)  |  Serve (59)  |  Subject (521)  |  Successful (123)  |  Treat (35)  |  Utmost (12)  |  Venture (18)  |  Whatever (234)  |  Will (2355)  |  Word (619)  |  World (1774)

Just as the musician is able to form an acoustic image of a composition which he has never heard played by merely looking at its score, so the equation of a curve, which he has never seen, furnishes the mathematician with a complete picture of its course. Yea, even more: as the score frequently reveals to the musician niceties which would escape his ear because of the complication and rapid change of the auditory impressions, so the insight which the mathematician gains from the equation of a curve is much deeper than that which is brought about by a mere inspection of the curve.
In Jahresbericht der Deutschen Mathematiker Vereiningung, 13, 864. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 190
Science quotes on:  |  Acoustic (3)  |  Auditory (2)  |  Change (593)  |  Complete (204)  |  Complication (29)  |  Composition (84)  |  Course (409)  |  Curve (49)  |  Deep (233)  |  Ear (68)  |  Equation (132)  |  Escape (80)  |  Form (959)  |  Frequent (23)  |  Gain (145)  |  Hear (139)  |  Image (96)  |  Impression (114)  |  Insight (102)  |  Inspection (7)  |  Looking (189)  |  Mathematics As A Fine Art (23)  |  Mere (84)  |  Merely (316)  |  More (2559)  |  Musician (21)  |  Never (1087)  |  Nice (13)  |  Picture (143)  |  Play (112)  |  Rapid (33)  |  Reveal (148)  |  Score (8)

Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s The Mathematical Analysis of Logic.
Co-authored with James R. Newman in Gödel's Proof (1986, 2005), 30.
Science quotes on:  |   (2863)  |  All (4108)  |  Analysis (233)  |  Aware (31)  |  Become (815)  |  Begin (260)  |  Being (1278)  |  George Boole (10)  |  Craft (10)  |  Doing (280)  |  Evident (91)  |  Knowing (137)  |  Life (1795)  |  Logic (287)  |  Mathematical Analysis (20)  |  Mathematics (1328)  |  Millennia (4)  |  Modern (385)  |  Nature (1926)  |  Principle (507)  |  Prose (11)  |  Publication (101)  |  Real (149)  |  Reasoning (207)  |  Recent (77)  |  Renaissance (14)  |  Study (653)  |  Time (1877)  |  Tool (117)  |  Two (937)  |  Underlying (30)

Littlewood, on Hardy’s own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.
(1943). In Béla Bollobás, Littlewood's Miscellany (1986), Foreward, 22.
Science quotes on:  |   (2863)  |  Biography (240)  |  Combination (144)  |  Command (58)  |  Deep (233)  |  Estimate (57)  |  G. H. Hardy (71)  |  Insight (102)  |  Known (454)  |  Man (2251)  |  Most (1731)  |  Power (746)  |  Problem (676)  |  Proof (287)  |  Smash (4)  |  Storm (51)  |  Technique (80)

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
As quoted, without citation, in Morris Kline, 'Logic Versus Pedagogy', The American Mathematical Monthly (Mar 1970), 77, No. 3, 272.
Science quotes on:  |  Healthy (68)  |  Hygiene (12)  |  Idea (843)  |  Keep (101)  |  Logic (287)  |  Practice (204)  |  Strong (174)

Man is full of desires: he loves only those who can satisfy them all. “This man is a good mathematician,” someone will say. But I have no concern for mathematics; he would take me for a proposition. “That one is a good soldier.” He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way.
From Pensées (1670), Sect. 6, Aphorism 18. As translated in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966), 199. From the original French, “L’homme est plein de besoins: il n’aime que ceux qui peuvent les remplir tous. ‘C’est un bon mathématicien,’ dira-t-on. Mais je n’ai que faire de mathématiques; il me prendroit pour une proposition. ‘C’est un bon guerrier.’ Il me prendroit pour une place assiégée. Il faut donc un honnête homme qui puisse s’accommoder à tous mes besoins généralement,” in Oeuvres Complètes de Blaise Pascal (1858), Vol. 1, 276.
Science quotes on:  |  Accommodate (15)  |  All (4108)  |  Besiege (2)  |  Concern (228)  |  Decent (10)  |  Desire (204)  |  Full (66)  |  General (511)  |  Good (889)  |  Himself (461)  |  Love (309)  |  Man (2251)  |  Mathematics (1328)  |  Need (290)  |  Proposition (123)  |  Satisfy (27)  |  Say (984)  |  Soldier (26)  |  Town (27)  |  Way (1217)  |  Will (2355)

Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
In 'Prop. 47: The human mind possesses an adequate knowledge of the eternal and infinite essence of God', Ethic, translated by William Hale White (1883), 93-94. Collected in The English and Foreign Philosophical Library, Vol. 21.
Science quotes on:  |  All (4108)  |  Application (242)  |  Center (33)  |  Circle (110)  |  Circumference (23)  |  Consist (223)  |  Definition (221)  |  Drawing (56)  |  Else (4)  |  Equal (83)  |  Error (321)  |  Event (216)  |  Man (2251)  |  Merely (316)  |  Name (333)  |  Nomenclature (146)  |  Say (984)  |  French Saying (67)  |  Something (719)  |  Thing (1915)  |  Time (1877)  |  Truth (1057)  |  Understand (606)  |  Understanding (513)  |  Wrong (234)

Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.
Opening paragraph in Chap. 1 of Mathematician's Delight (1943, 2012), 7.
Science quotes on:  |  Attempt (251)  |  Bad (180)  |  Learn (629)  |  People (1005)  |  Possess (156)  |  Power (746)  |  Race (268)  |  Reason (744)  |  Regard (305)  |  Subject (521)  |  Successful (123)  |  Supernatural (25)

Many professional mathematicians regard their work as a form of play, in the same way professional golfers or basketball stars might.
In his final retrospective article, 'A Quarter-Century of Recreational Mathematics', Scientific American (Aug 1998).
Science quotes on:  |  Basketball (3)  |  Form (959)  |  Golfer (3)  |  Play (112)  |  Professional (70)  |  Regard (305)  |  Star (427)  |  Stars (304)  |  Way (1217)  |  Work (1351)

Mark all Mathematical heads which be wholly and only bent on these sciences, how solitary they be themselves, how unfit to live with others, how unapt to serve the world. (c.1550)
The Scholemaster (1570), Book 1.
Science quotes on:  |  All (4108)  |  Live (628)  |  Other (2236)  |  Science (3879)  |  Solitude (18)  |  Themselves (433)  |  Unfit (12)  |  Wholly (88)  |  World (1774)

Mathematical knowledge is not—as all Cambridge men are surely aware—the result of any special gift. It is merely the development of those conceptions of form and number which every human being possesses; and any person of average intellect can make himself a fair mathematician if he will only pay continuous attention; in plain English, think enough about the subject.
'Science', a lecture delivered at the Royal Institution. The Works of Charles Kingsley (1880), 241.
Science quotes on:  |  All (4108)  |  Attention (190)  |  Average (82)  |  Being (1278)  |  Conception (154)  |  Continuous (82)  |  Development (422)  |  Enough (340)  |  Form (959)  |  Gift (104)  |  Himself (461)  |  Human (1468)  |  Human Being (175)  |  Intellect (233)  |  Knowledge (1529)  |  Merely (316)  |  Number (699)  |  Person (363)  |  Result (677)  |  Special (184)  |  Subject (521)  |  Surely (101)  |  Think (1086)  |  Will (2355)

Mathematical studies … when combined, as they now generally are, with a taste for physical science, enlarge infinitely our views of the wisdom and power displayed in the universe. The very intimate connexion indeed, which, since the date of the Newtonian philosophy, has existed between the different branches of mathematical and physical knowledge, renders such a character as that of a mere mathematician a very rare and scarcely possible occurrence.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 3, 184.
Science quotes on:  |  Branch (150)  |  Character (243)  |  Connection (162)  |  Different (577)  |  Display (56)  |  Enlarge (35)  |  Exist (443)  |  Indeed (324)  |  Knowledge (1529)  |  Mathematics (1328)  |  Mere (84)  |  Sir Isaac Newton (333)  |  Occurrence (53)  |  Philosophy (380)  |  Physical (508)  |  Physical Science (101)  |  Possible (552)  |  Power (746)  |  Rare (89)  |  Render (93)  |  Scarcely (74)  |  Science (3879)  |  Taste (90)  |  Universe (857)  |  View (488)  |  Wisdom (221)

Mathematicians always strive to confuse their audiences; where there is no confusion, there is no prestige.
In Mathematics Made Difficult (1971). As quoted in Ian Stewart, Professor Stewart’s Hoard of Mathematical Treasures (2010), 155-156.
Science quotes on:  |  Audience (26)  |  Confuse (19)  |  Confusion (57)  |  Prestige (14)  |  Strive (46)

Mathematicians are inexorably drawn to nature, not just describing what is to be found there, but in creating echoes of natural laws.
In Gary William Flake, The Computational Beauty of Nature (2000), 361.
Science quotes on:  |  Create (235)  |  Echo (11)  |  Law (894)  |  Natural (796)  |  Natural Law (41)  |  Nature (1926)

Mathematicians are like a certain type of Frenchman: when you talk to them they translate it into their own language, and then it soon turns into something completely different.
Maxims and Reflections (1998), trans. E. Stopp, 162.
Science quotes on:  |  Certain (550)  |  Completely (135)  |  Different (577)  |  Language (293)  |  Something (719)  |  Soon (186)  |  Translate (19)  |  Turn (447)  |  Type (167)

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.
From Maximen und Reflexionen (1907), Vol. 21, 266, Maxim 1279. Translation as quoted in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 94. From the original German, “Mathematiker sind eine Art Franzosen: redet man zu ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes.”
Science quotes on:  |  Different (577)  |  Entirely (34)  |  Forthwith (2)  |  Frenchman (4)  |  Language (293)  |  Say (984)  |  Something (719)  |  Translate (19)  |  Whatever (234)

Mathematicians are only dealing with the structure of reasoning, and they do not really care what they are talking about. They do not even need to know what they are talking about … But the physicist has meaning to all his phrases. … In physics, you have to have an understanding of the connection of words with the real world.
In The Character of Physical Law (1965), 55.
Science quotes on:  |  All (4108)  |  Care (186)  |  Connection (162)  |  Do (1908)  |  Know (1518)  |  Meaning (233)  |  Phrase (61)  |  Physic (517)  |  Physicist (259)  |  Physics (533)  |  Real (149)  |  Reasoning (207)  |  Structure (344)  |  Talking (76)  |  Understand (606)  |  Understanding (513)  |  Word (619)  |  World (1774)

Mathematicians assume the right to choose, within the limits of logical contradiction, what path they please in reaching their results.
In A Letter to American Teachers of History (1910), Introduction, v.
Science quotes on:  |  Assume (38)  |  Choose (112)  |  Contradiction (68)  |  Limit (280)  |  Logical (55)  |  Nature Of Mathematics (80)  |  Path (144)  |  Please (65)  |  Reach (281)  |  Result (677)  |  Right (452)

Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this esthetic satisfaction is bound up with the economy of thought.
In 'The Future of Mathematics', Monist, 20, 80. Translated from the French by George Bruce Halsted.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Adaptation (58)  |  Aesthetic (46)  |  Aggregate (23)  |  All (4108)  |  Analogy (71)  |  Attach (56)  |  Balance (77)  |  Better (486)  |  Both (493)  |  Bound (119)  |  Chance (239)  |  Complexity (111)  |  Comprehend (40)  |  Contrast (44)  |  Demonstration (113)  |  Detail (146)  |  Diverse (17)  |  Due (141)  |  Elegance (37)  |  Ensemble (7)  |  Fact (1210)  |  Feeling (250)  |  Fruitful (58)  |  Generalization (57)  |  Glance (34)  |  Great (1574)  |  Happy (105)  |  Harmony (102)  |  Importance (286)  |  Indeed (324)  |  Instrument (144)  |  Introduce (63)  |  Law (894)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Meeting (20)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  More (2559)  |  Neighboring (5)  |  Object (422)  |  Order (632)  |  Other (2236)  |  Permit (58)  |  Possible (552)  |  Problem (676)  |  Pure (291)  |  Reason (744)  |  Result (677)  |  Satisfaction (74)  |  See (1081)  |  Set (394)  |  Simplicity (167)  |  Single (353)  |  Solution (267)  |  Study And Research In Mathematics (61)  |  Symmetry (43)  |  Think (1086)  |  Thought (953)  |  Together (387)  |  Unexpected (52)  |  Unforeseen (10)  |  Unity (78)  |  Word (619)  |  Yield (81)

Mathematicians boast of their exacting achievements, but in reality they are absorbed in mental acrobatics and contribute nothing to society.
From Complete Works on Japan’s Philosophical Thought (1956). As quoted and cited in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 185.
Science quotes on:  |  Absorb (49)  |  Achievement (179)  |  Acrobat (2)  |  Boast (22)  |  Contribute (27)  |  Exact (68)  |  Exacting (4)  |  Mental (177)  |  Nothing (966)  |  Reality (261)  |  Society (326)

Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be backed up. It’s just that the reliability does not primarily come from mathematicians checking formal arguments; it come from mathematicians thinking carefully and critically about mathematical ideas.
Concerning revision of proofs. In 'On Proof and Progress in Mathematics', For the Learning of Mathematics (Feb 1995), 15, No. 1, 33. Reprinted from Bulletin of the American Mathematical Society (1994), 30, No. 2, 170.
Science quotes on:  |   (2863)  |  Argument (138)  |  Back (390)  |  Call (769)  |  Careful (24)  |  Carefully (65)  |  Checking (3)  |  Correct (86)  |  Critical (66)  |  Detail (146)  |  Do (1908)  |  Error (321)  |  Formal (33)  |  Gap (33)  |  Good (889)  |  Idea (843)  |  Mathematics (1328)  |  More (2559)  |  Motivate (6)  |  Motivated (14)  |  Primarily (12)  |  Reliability (17)  |  Reliable (12)  |  Scholarship (20)  |  Supply (93)  |  System (537)  |  Theorem (112)  |  Thinking (414)

Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure.
In Mathematics in Western Culture (1964), 408.
Science quotes on:  |  Act (272)  |  Add (40)  |  Base (117)  |  Build (204)  |  Change (593)  |  Clearly (41)  |  Conquest (28)  |  Create (235)  |  Deep (233)  |  Define (49)  |  Firmly (6)  |  Fundamental (250)  |  Ground (217)  |  Healthy (68)  |  Height (32)  |  Human (1468)  |  Hygiene (12)  |  Idea (843)  |  Insight (102)  |  Intuition (75)  |  Keep (101)  |  Less (103)  |  Logic (287)  |  Mathematics (1328)  |  Moreover (3)  |  Nature (1926)  |  Pillar (9)  |  Practice (204)  |  Precise (68)  |  Process (423)  |  Replace (31)  |  Rest (280)  |  Sanction (7)  |  Strength (126)  |  Strong (174)  |  Structure (344)  |  Thought (953)  |  Ultimate (144)  |  Ultimately (55)  |  Uncertain (44)  |  Whole (738)

Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe.
Lecture to Sigma Xi, 'The Problem of the Expanding Universe' (1941), printed in Sigma Xi Quarterly (1942), 30, 104-105. Reprinted in Smithsonian Institution Report of the Board of Regents (1943), 97, 123. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 63.
Science quotes on:  |  Actual (117)  |  Advance (280)  |  Attempt (251)  |  Common (436)  |  Compatibility (4)  |  Consistency (31)  |  Consistent (48)  |  Deal (188)  |  Exploration (134)  |  Fact (1210)  |  Furnish (96)  |  Goal (145)  |  Include (90)  |  Inclusion (5)  |  Infinite (231)  |  Information (166)  |  Knowledge (1529)  |  Logic (287)  |  Minimum (12)  |  Must (1526)  |  New (1216)  |  Number (699)  |  Observation (555)  |  Observer (43)  |  Other (2236)  |  Possible (552)  |  Reduce (94)  |  Reduction (51)  |  Science (3879)  |  Segregation (2)  |  Stand (274)  |  Structure (344)  |  Study (653)  |  System (537)  |  Theorist (44)  |  Theory (970)  |  Together (387)  |  Two (937)  |  Universe (857)  |  Word (619)  |  World (1774)

Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.
In Science and Hypothesis (1901, 1907). Translated by W.J.G. from the original French, “Les mathématiciens n'étudient pas des objets, mais des relations entre les objets ; il leur est donc indifférent de remplacer ces objets par d'autres, pourvu que les relations ne changent pas. La matière ne leur importe pas, la forme seule les intéresse.”
Science quotes on:  |  Alone (311)  |  Attention (190)  |  Change (593)  |  Do (1908)  |  Engage (39)  |  Form (959)  |  Indifference (13)  |  Interest (386)  |  Matter (798)  |  Object (422)  |  Other (2236)  |  Provide (69)  |  Relation (157)  |  Replace (31)  |  Study (653)

Mathematicians do not write for the circulating library.
From 'The Principles of Success in Literature', The Fortnightly (1865), 1, 90.
Science quotes on:  |  Do (1908)  |  Library (48)  |  Write (230)  |  Writing (189)

Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that the danger does lie in logic, not in imagination.
In Orthodoxy (1908), 27.
Science quotes on:  |  Artist (90)  |  Creative (137)  |  Creativity (76)  |  Danger (115)  |  Imagination (328)  |  Lie (364)  |  Logic (287)  |  Mad (53)  |  Say (984)  |  Seldom (65)  |  Sense (770)  |  Will (2355)

Mathematicians have long since regarded it as demeaning to work on problems related to elementary geometry in two or three dimensions, in spite of the fact that it it precisely this sort of mathematics which is of practical value.
As coauthor with and G.C. Shephard, in Handbook of Applicable Mathematics, Volume V, Combinatorics and Geometry (1985), v.
Science quotes on:  |  Demeaning (2)  |  Dimension (61)  |  Elementary (96)  |  Fact (1210)  |  Geometry (255)  |  Long (790)  |  Mathematics (1328)  |  Practical (200)  |  Precisely (92)  |  Problem (676)  |  Regard (305)  |  Relate (21)  |  Sort (49)  |  Spite (55)  |  Two (937)  |  Value (365)  |  Work (1351)

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
As quoted in G. Simmons Calculus Gems (1992).
Science quotes on:  |  Belief (578)  |  Discover (553)  |  Human (1468)  |  Human Mind (128)  |  In Vain (9)  |  Mind (1338)  |  Mystery (177)  |  Never (1087)  |  Number (699)  |  Order (632)  |  Penetrate (67)  |  Prime Number (5)  |  Reason (744)  |  Sequence (68)  |  Try (283)  |  Vain (83)  |  Will (2355)

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.
Science quotes on:  |  Aid (97)  |  Appropriate (61)  |  Doubtful (29)  |  Effort (227)  |  Enlighten (29)  |  Enlightened (24)  |  Equation (132)  |  Express (186)  |  Find (998)  |  Human (1468)  |  Idea (843)  |  Language (293)  |  Mind (1338)  |  New (1216)  |  Obligation (25)  |  Possess (156)  |  Process (423)  |  Say (984)  |  Succeed (109)  |  Symbol (93)  |  Themselves (433)  |  Way (1217)  |  Will (2355)  |  Word (619)

Mathematicians practice absolute freedom.
In A Letter to American Teachers of History (1910), 169.
Science quotes on:  |  Absolute (145)  |  Freedom (129)  |  Practice (204)

Mathematicians pretend to count by means of a system supposed to satisfy the so-called Peano axioms. In fact, the piano has only 88 keys; hence, anyone counting with these axioms is soon played out.
In Mathematics Made Difficult (1971). As quoted in Michael Stueben and Diane Sandford, Twenty Years Before the Blackboard (1998), 131.
Science quotes on:  |  Axiom (63)  |  Call (769)  |  Count (105)  |  Counting (26)  |  Fact (1210)  |  Key (50)  |  Mean (809)  |  Means (579)  |  Giuseppe Peano (2)  |  Piano (12)  |  Play (112)  |  Pretend (17)  |  Satisfy (27)  |  So-Called (71)  |  Soon (186)  |  Suppose (156)  |  System (537)

Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood.
Acceptance Speech for the Kyoto Prize (1991), 'A scientist by choice'. On kyotoprize.org website.
Science quotes on:  |  Become (815)  |  Concept (221)  |  Create (235)  |  Difficulty (196)  |  Faster (50)  |  New (1216)  |  Old (481)  |  Understand (606)  |  Understood (156)

Mathematicians … believed that prediction was just a function of keeping track of things. If you knew enough, you could predict anything. … Chaos theory throws it right out the window because … in fact there are great categories of phenomena that are inherently unpredictable.
In novel, Jurassic Park (1990, 1991), 158.
Science quotes on:  |  Belief (578)  |  Chaos (91)  |  Chaos Theory (4)  |  Enough (340)  |  Fact (1210)  |  Function (228)  |  Great (1574)  |  Inherently (5)  |  Know (1518)  |  Phenomenon (318)  |  Predict (79)  |  Prediction (82)  |  Right (452)  |  Theory (970)  |  Thing (1915)  |  Track (38)  |  Unpredictable (17)  |  Window (58)

Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
Science quotes on:  |  Accomplishment (93)  |  Acquisition (45)  |  Active (76)  |  Admirably (3)  |  Advance (280)  |  Altitude (4)  |  Apparatus (68)  |  Application (242)  |  Ascension (4)  |  Await (5)  |  Circle (110)  |  Curvature (8)  |  Earth (996)  |  Everything (476)  |  Evolute (2)  |  Find (998)  |  Fit (134)  |  Function (228)  |  Heaven (258)  |  Heavens (125)  |  Impress (64)  |  Impressed (38)  |  Industry (137)  |  Intense (20)  |  Latitude (4)  |  Line (91)  |  Logarithmic (5)  |  Longitude (6)  |  Look (582)  |  Machine (257)  |  Magician (14)  |  Magnitude (83)  |  Manifold (22)  |  Marvellous (25)  |  Master (178)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Multitude (47)  |  Natural (796)  |  Nature Of Mathematics (80)  |  Network (21)  |  Normal (28)  |  Nothing (966)  |  Numerous (68)  |  Outside (141)  |  Prepare (37)  |  Really (78)  |  Realm (85)  |  Recall (10)  |  Refer (14)  |  Right (452)  |  Show (346)  |  Skill (109)  |  Skillful (14)  |  Spin (26)  |  Sufficient (128)  |  System (537)  |  Tangent (6)  |  Treasure (57)  |  Trigonometry (6)  |  True (212)  |  Wherever (51)  |  Witness (54)

Mathematics associates new mental images with ... physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience. For example, a mathematician represents the motion of planets of the solar system by a flow line of an incompressible fluid in a 54-dimensional phase space, whose volume is given by the Liouville measure
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
Science quotes on:  |  Abstraction (47)  |  Associate (25)  |  Dimension (61)  |  Directly (22)  |  Example (94)  |  Experience (467)  |  Far (154)  |  Flow (83)  |  Fluid (51)  |  Give (202)  |  Image (96)  |  Life (1795)  |  Line (91)  |  Mathematics (1328)  |  Measure (232)  |  Mental (177)  |  Mind (1338)  |  Motion (310)  |  New (1216)  |  Phase (36)  |  Phase Space (2)  |  Physical (508)  |  Planet (356)  |  Remove (45)  |  Represent (155)  |  Solar System (77)  |  Space (500)  |  System (537)  |  Tangible (15)  |  Train (114)  |  Volume (19)

Mathematics is not yet capable of coping with the naivete of the mathematician himself.
In 'The Study of Man: Sociology Learns the Language of Mathematics', Commentary (1 Sep 1952). Reprinted in James Roy Newman, The World of Mathematics (1956), Vol. 2, 1301.
Science quotes on:  |  Capable (168)  |  Cope (6)  |  Himself (461)  |  Mathematics (1328)  |  Naivete (2)

Mathematics is the life supreme. The life of the gods is mathematics. All divine messengers are mathematicians. Pure mathematics is religion. Its attainment requires a theophany.
In Schriften (1901), Bd.. 2, 223.
Science quotes on:  |  All (4108)  |  Attainment (47)  |  Divine (112)  |  Estimates of Mathematics (30)  |  God (757)  |  Life (1795)  |  Mathematics (1328)  |  Messenger (3)  |  Pure (291)  |  Pure Mathematics (67)  |  Religion (361)  |  Require (219)  |  Supreme (71)

Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges.
From In Mathematical Circles (1969), 7.
Science quotes on:  |  Appear (118)  |  Attempt (251)  |  Blast (13)  |  Charge (59)  |  Chisel (2)  |  Composition (84)  |  Cutter (2)  |  Demolish (8)  |  Drill (11)  |  Examine (78)  |  Expert (65)  |  Hammer (25)  |  Interior (32)  |  Internal (66)  |  Large (394)  |  Later (18)  |  Mathematics (1328)  |  Miner (9)  |  Older (7)  |  Outside (141)  |  Place (177)  |  Resemble (63)  |  Rock (161)  |  Seek (213)  |  Stone (162)  |  Vein (25)  |  Vulnerable (5)  |  Wish (212)

Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
Science quotes on:  |  Adapt (66)  |  Aid (97)  |  All (4108)  |  Allow (45)  |  Apparatus (68)  |  Avoid (116)  |  Borrow (30)  |  Brevity (8)  |  Clarity (47)  |  Clear (100)  |  Composition (84)  |  Concept (221)  |  Connect (125)  |  Definite (110)  |  Demand (123)  |  Departure (9)  |  Description (84)  |  Develop (268)  |  Development (422)  |  Direct (225)  |  Do (1908)  |  Due (141)  |  Elegant (36)  |  Empty (80)  |  Enter (141)  |  Entirely (34)  |  Excel (4)  |  Exclusion (16)  |  Exercise (110)  |  Expression (175)  |  Find (998)  |  First (1283)  |  Fit (134)  |  Flight (98)  |  Foreign (45)  |  Form (959)  |  Furnish (96)  |  Give (202)  |  Ground (217)  |  Guarantee (30)  |  Immediate (95)  |  Indispensable (28)  |  Knowledge (1529)  |  Language (293)  |  Law (894)  |  Logical (55)  |  Manner (58)  |  Mathematics (1328)  |  Measure (232)  |  Most (1731)  |  Mother (114)  |  Mother Tongue (3)  |  Natural (796)  |  Natural Science (128)  |  Never (1087)  |  Object (422)  |  Offer (141)  |  Other (2236)  |  Particularly (21)  |  Pattern (110)  |  Perception (97)  |  Phrase (61)  |  Place (177)  |  Poetry (143)  |  Precision (68)  |  Presentation (23)  |  Process (423)  |  Proper (144)  |  Prose (11)  |  Pupil (61)  |  Regard (305)  |  Respect (207)  |  Rhetoric (12)  |  Rigour (21)  |  Same (157)  |  School (219)  |  Science (3879)  |  Sense (770)  |  Short (197)  |  Shortest (16)  |  Statement (142)  |  Study (653)  |  Subject (521)  |  Sufficiently (9)  |  Syntax (2)  |  Teach (277)  |  Thought (953)  |  Tongue (43)  |  Training (80)  |  Translation (21)  |  Use (766)  |  Value (365)  |  Value Of Mathematics (60)  |  Want (497)  |  Way (1217)  |  Word (619)

May not Music be described as the Mathematic of sense, Mathematic as Music of the reason? the soul of each the same! Thus the musician feels Mathematic, the mathematician thinks Music, Music the dream, Mathematic the working life each to receive its consummation from the other when the human intelligence, elevated to its perfect type, shall shine forth glorified in some future Mozart-Dirichlet or Beethoven-Gauss a union already not indistinctly foreshadowed in the genius and labours of a Helmholtz!
In paper read 7 Apr 1864, printed in 'Algebraical Researches Containing a Disquisition On Newton’s Rule for the Discovery of Imaginary Roots', Philosophical Transactions of the Royal Society of London (1865), 154, 613, footnote. Also in Collected Mathematical Papers, Vol. 2, 419.
Science quotes on:  |  Already (222)  |  Beethoven (13)  |  Beethoven_Ludwig (8)  |  Consummation (7)  |  Describe (128)  |  Peter Gustav Lejeune Dirichlet (3)  |  Dream (208)  |  Elevate (12)  |  Feel (367)  |  Foreshadow (5)  |  Future (429)  |  Carl Friedrich Gauss (77)  |  Genius (284)  |  Glorify (6)  |  Human (1468)  |  Indistinct (2)  |  Intelligence (211)  |  Labour (98)  |  Life (1795)  |  Mathematics (1328)  |  Mathematics As A Fine Art (23)  |  Mozart_Amadeus (2)  |  Music (129)  |  Musician (21)  |  Other (2236)  |  Perfect (216)  |  Reason (744)  |  Receive (114)  |  Sense (770)  |  Shine (45)  |  Soul (226)  |  Think (1086)  |  Type (167)  |  Union (51)  |  Work (1351)

Men of science belong to two different types—the logical and the intuitive. Science owes its progress to both forms of minds. Mathematics, although a purely logical structure, nevertheless makes use of intuition. Among the mathematicians there are intuitives and logicians, analysts and geometricians. Hermite and Weierstrass were intuitives. Riemann and Bertrand, logicians. The discoveries of intuition have always to be developed by logic.
In Man the Unknown (1935), 123.
Science quotes on:  |  Analyst (8)  |  Belong (162)  |  Joseph Bertrand (6)  |  Both (493)  |  Develop (268)  |  Different (577)  |  Discovery (780)  |  Form (959)  |  Geometrician (6)  |  Charles Hermite (10)  |  Intuition (75)  |  Intuitive (14)  |  Logic (287)  |  Logician (17)  |  Mathematics (1328)  |  Men Of Science (143)  |  Mind (1338)  |  Nevertheless (90)  |  Owe (71)  |  Progress (465)  |  Pure (291)  |  Purely (109)  |  Bernhard Riemann (7)  |  Science (3879)  |  Structure (344)  |  Two (937)  |  Type (167)  |  Use (766)  |  Karl Weierstrass (9)

Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
Science quotes on:  |   (2863)  |  Add (40)  |  Algebra (113)  |  All (4108)  |  Analysis (233)  |  Appear (118)  |  Arithmetical (11)  |  Author (167)  |  Authority (95)  |  Automaton (12)  |  Become (815)  |  Being (1278)  |  Blow (44)  |  Branch (150)  |  Calculus (65)  |  Cause (541)  |  Chair (24)  |  Characterize (20)  |  Compound (113)  |  Connect (125)  |  Construction (112)  |  Continue (165)  |  Demonstration (113)  |  Development (422)  |  Discovery (780)  |  Doctrine (75)  |  Double (15)  |  Effort (227)  |  Elasticity (8)  |  Equation (132)  |  Leonhard Euler (35)  |  Face (212)  |  Fact (1210)  |  Feel (367)  |  Pierre de Fermat (15)  |  Flame (40)  |  Form (959)  |  Foundation (171)  |  Fraction (13)  |  Fresh (67)  |  Carl Friedrich Gauss (77)  |  Genius (284)  |  Geometry (255)  |  Great (1574)  |  Christiaan Huygens (10)  |  Idea (843)  |  Influence (222)  |  Inform (47)  |  Instance (33)  |  Integral (26)  |  Integral Calculus (6)  |  Investigation (230)  |  Karl Jacobi (10)  |  Count Joseph-Louis de Lagrange (26)  |  Laid (7)  |  Law (894)  |  Lead (384)  |  Leave (130)  |  Adrien-Marie Legendre (3)  |  Light (607)  |  Lip (4)  |  Mathematics (1328)  |  Mechanic (119)  |  Mechanical (140)  |  Mechanics (131)  |  Memory (134)  |  Method (505)  |  Midst (7)  |  Mind (1338)  |  Modern (385)  |  Modern Mathematics (50)  |  Molecular (7)  |  Moment (253)  |  Most (1731)  |  Motion (310)  |  Myriad (31)  |  Nature Of Mathematics (80)  |  New (1216)  |  Observation (555)  |  Origin (239)  |  Pendulum (17)  |  Periodicity (6)  |  Physic (517)  |  Physics (533)  |  Planetary (29)  |  Predecessor (29)  |  Present (619)  |  Principal (63)  |  Proof (287)  |  Purely (109)  |  Reach (281)  |  Reason (744)  |  Reciprocity (2)  |  Reduce (94)  |  Resist (15)  |  Result (677)  |  Right (452)  |  Root (120)  |  Say (984)  |  Serve (59)  |  Speak (232)  |  Speaking (119)  |  William Spottiswoode (3)  |  Star (427)  |  Stare (9)  |  Theorem (112)  |  Theory (970)  |  Through (849)  |  Transcendent (2)  |  Transfigure (2)  |  Transformation (69)  |  Turn (447)  |  Variation (90)  |  Year (933)  |  Yield (81)

Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
In 'Reminiscences of an Octogenarian Mathematician', The American Mathematical Monthly (Nov 1971), 78, No. 9, 960-961.
Science quotes on:  |  Anybody (42)  |  Cleverness (15)  |  Consider (416)  |  Expert (65)  |  Find (998)  |  Geologist (75)  |  Golden (45)  |  Ignorant (90)  |  Illustration (48)  |  Know (1518)  |  Lucky (13)  |  Miner (9)  |  Nugget (3)  |  Question (621)  |  Tick (9)  |  Two (937)

Newton was the greatest creative genius physics has ever seen. None of the other candidates for the superlative (Einstein, Maxwell, Boltzmann, Gibbs, and Feynman) has matched Newton’s combined achievements as theoretician, experimentalist, and mathematician. … If you were to become a time traveler and meet Newton on a trip back to the seventeenth century, you might find him something like the performer who first exasperates everyone in sight and then goes on stage and sings like an angel.
In Great Physicists (2001), 39.
Science quotes on:  |   (2863)  |  17th Century (16)  |  Achievement (179)  |  Angel (44)  |  Back (390)  |  Become (815)  |  Ludwig Eduard Boltzmann (17)  |  Candidate (8)  |  Century (310)  |  Creative (137)  |  Einstein (101)  |  Albert Einstein (605)  |  Experimentalist (20)  |  Richard P. Feynman (122)  |  Find (998)  |  First (1283)  |  Genius (284)  |  Gibbs_Josiah (2)  |  Greatest (328)  |  Match (29)  |  Maxwell (42)  |  James Clerk Maxwell (87)  |  Sir Isaac Newton (333)  |  Other (2236)  |  Performer (2)  |  Physic (517)  |  Physics (533)  |  Sight (132)  |  Sing (26)  |  Something (719)  |  Stage (143)  |  Superlative (3)  |  Theorist (44)  |  Time (1877)  |  Time Travel (4)  |  Traveler (30)

No mathematician now-a-days sets any store on the discovery of isolated theorems, except as affording hints of an unsuspected new sphere of thought, like meteorites detached from some undiscovered planetary orb of speculation.
In Notes to the Exeter Association Address, Collected Mathematical Papers (1908), Vol. 2, 715.
Science quotes on:  |  Detach (5)  |  Discovery (780)  |  Hint (21)  |  Isolate (22)  |  Meteorite (9)  |  New (1216)  |  Orb (20)  |  Planetary (29)  |  Set (394)  |  Speculation (126)  |  Sphere (116)  |  Store (48)  |  Study And Research In Mathematics (61)  |  Theorem (112)  |  Thought (953)  |  Undiscovered (15)  |  Unsuspected (7)

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
In A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 70-71.
Science quotes on:  |   (2863)  |  Niels Henrik Abel (15)  |  Advance (280)  |  Age (499)  |  Art (657)  |  Do (1908)  |  Enough (340)  |  Expect (200)  |  Forget (115)  |  Évariste Galois (4)  |  Game (101)  |  Great (1574)  |  Idea (843)  |  Know (1518)  |  Major (84)  |  Man (2251)  |  Mathematics (1328)  |  More (2559)  |  Other (2236)  |  Past (337)  |  Srinivasa Ramanujan (17)  |  Science (3879)  |  Single (353)  |  Still (613)  |  Work (1351)  |  Young (227)  |  Youth (101)

No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without regard to any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study, they were found to be the necessary key with which to attain the knowledge of the most important laws of nature.
In Introduction to Mathematics (1911), 136-137.
Science quotes on:  |  Abstract (124)  |  Apparently (20)  |  Attain (125)  |  Confine (26)  |  Conic Section (8)  |  Crave (9)  |  End (590)  |  Find (998)  |  Give (202)  |  Hundred (229)  |  Important (209)  |  Impressive (25)  |  Key (50)  |  Knowledge (1529)  |  Law (894)  |  Long (790)  |  Merely (316)  |  More (2559)  |  Most (1731)  |  Nature (1926)  |  Necessary (363)  |  Other (2236)  |  Part (222)  |  Period (198)  |  Reflection (90)  |  Regard (305)  |  Research (664)  |  Satisfy (27)  |  Science (3879)  |  Study (653)  |  Study And Research In Mathematics (61)  |  Useful (250)  |  Utility (49)  |  Warn (5)  |  Warning (17)  |  Year (933)

Not seldom did he [Sir William Thomson], in his writings, set down some mathematical statement with the prefacing remark “it is obvious that” to the perplexity of mathematical readers, to whom the statement was anything but obvious from such mathematics as preceded it on the page. To him it was obvious for physical reasons that might not suggest themselves at all to the mathematician, however competent.
As given in Life of Lord Kelvin (1910), Vol. 2, 1136. [Note: William Thomson, later became Lord Kelvin —Webmaster]
Science quotes on:  |  All (4108)  |  Competent (20)  |  Down (456)  |  Baron William Thomson Kelvin (71)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Obvious (126)  |  Page (30)  |  Perplex (6)  |  Physical (508)  |  Precede (23)  |  Preface (8)  |  Reader (40)  |  Reason (744)  |  Remark (28)  |  Seldom (65)  |  Set (394)  |  Statement (142)  |  Suggest (34)  |  Themselves (433)  |  Writing (189)  |  Writings (6)

Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 537.
Science quotes on:  |  Accomplishment (93)  |  Ask (411)  |  Beautiful (258)  |  Complex (188)  |  Complex Number (3)  |  Equation (132)  |  Experience (467)  |  Function (228)  |  General (511)  |  Genius (284)  |  Indeed (324)  |  Indignation (4)  |  Interest (386)  |  Justify (24)  |  Most (1731)  |  Nothing (966)  |  Number (699)  |  Origin (239)  |  Owe (71)  |  Point (580)  |  Power (746)  |  Series (149)  |  Theorem (112)  |  Theory (970)  |  Will (2355)  |  Willing (44)

Of all the sciences that pertain to reason, Metaphysics and Geometry are those in which imagination plays the greatest part. … Imagination acts no less in a geometer who creates than in a poet who invents. It is true that they operate differently on their object. The first shears it down and analyzes it, the second puts it together and embellishes it. … Of all the great men of antiquity, Archimedes is perhaps the one who most deserves to be placed beside Homer.
From the original French: “La Métaphysique & la Géométrie sont de toutes les Sciences qui appartiennent à la raison, celles où l’imagination à le plus de part. … L’imagination dans un Géometre qui crée, n’agit pas moins que dans un Poëte qui invente. Il est vrai qu’ils operent différemment sur leur objet; le premier le dépouille & l’analyse, le second le compose & l’embellit. … De tous les grands hommes de l’antiquité, Archimede est peut-être celui qui mérite le plus d’être placé à côté d’Homere.” In Discours Preliminaire de L'Encyclopedie (1751), xvi. As translated by Richard N. Schwab and Walter E. Rex, Preliminary Discourse to the Encyclopedia of Diderot (1963, 1995), xxxvi. A footnote states “Note that ‘geometer’ in d’Alembert’s definition is a term that includes all mathematicians and is not strictly limited to practitioners of geometry alone.” Also seen in a variant extract and translation: “Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this …. The imagination in a mathematician who creates makes no less difference than in a poet who invents…. Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.” This latter translation may be from The Plan of the French Encyclopædia: Or Universal Dictionary of Arts, Sciences, Trades and Manufactures (1751). Webmaster has not yet been able to check for a verified citation for this translation. Can you help?
Science quotes on:  |  Act (272)  |  All (4108)  |  Antiquity (33)  |  Archimedes (55)  |  Create (235)  |  Delicate (43)  |  Deserve (65)  |  Difference (337)  |  Down (456)  |  First (1283)  |  Geometry (255)  |  Great (1574)  |  Greatest (328)  |  Homer (9)  |  Imagination (328)  |  Invent (51)  |  Mathematics (1328)  |  Metaphysics (50)  |  Most (1731)  |  Object (422)  |  Place (177)  |  Poet (83)  |  Reason (744)  |  Role (86)  |  Science (3879)  |  Spirit (265)  |  Together (387)

Oh these mathematicians make me tired! When you ask them to work out a sum they take a piece of paper, cover it with rows of A’s, B’s, and X's and Y’s … scatter a mess of flyspecks over them, and then give you an answer that’s all wrong!
Matthew Josephson, Edison (1959), 283.
Science quotes on:  |   (2863)  |  Algebra (113)  |  All (4108)  |  Answer (366)  |  Ask (411)  |  Paper (182)  |  Sum (102)  |  Work (1351)  |  Wrong (234)

Ohm (a distinguished mathematician, be it noted) brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Even as late as 20 years ago, “quantity” and “tension” were much used by men who did not fully appreciate Ohm's law. (Is it not rather remarkable that some of Germany's best men of genius should have been, perhaps, unfairly treated? Ohm; Mayer; Reis; even von Helmholtz has mentioned the difficulty he had in getting recognised. But perhaps it is the same all the world over.)
Science quotes on:  |   (2863)  |  All (4108)  |  Appreciate (63)  |  Best (459)  |  Conductor (16)  |  Current (118)  |  Difficulty (196)  |  Distinguish (160)  |  Distinguished (83)  |  Electric (76)  |  Electrician (6)  |  Electricity (159)  |  Fact (1210)  |  Facts (553)  |  Force (487)  |  Genius (284)  |  Germany (13)  |  Hermann von Helmholtz (28)  |  Late (118)  |  Law (894)  |  Robert Mayer (9)  |  Men Of Science (143)  |  Mention (82)  |  Ohm (5)  |  Georg Simon Ohm (3)  |  Order (632)  |  Puzzle (44)  |  Puzzling (8)  |  Quantity (132)  |  Recognition (88)  |  Johann Philipp Reis (2)  |  Statement (142)  |  Succeed (109)  |  Tension (24)  |  Together (387)  |  Treatment (130)  |  Unfair (8)  |  Vague (47)  |  World (1774)  |  Year (933)

Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at roughly. By Ohm's discovery a large part of the domain of electricity became annexed by Coulomb's discovery of the law of inverse squares, and completely annexed by Green's investigations. Poisson attacked the difficult problem of induced magnetisation, and his results, though differently expressed, are still the theory, as a most important first approximation. Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. Then there were the remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Unfortunately, in my opinion, Faraday was not a mathematician. It can scarely be doubted that had he been one, he would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann’s theory, and the connected work of Helmholtz and Thomson. But it is perhaps too much to expect a man to be both the prince of experimentalists and a competent mathematician.
From article 'Electro-magnetic Theory II', in The Electrician (16 Jan 1891), 26, No. 661, 331.
Science quotes on:  |   (2863)  |  André-Marie Ampère (11)  |  Approximation (31)  |  Attack (84)  |  Being (1278)  |  Both (493)  |  Compact (13)  |  Completely (135)  |  Conductor (16)  |  Connect (125)  |  Charles-Augustin Coulomb (3)  |  Crude (31)  |  Current (118)  |  Difficult (246)  |  Discovery (780)  |  Domain (69)  |  Doubt (304)  |  Electricity (159)  |  Electrodynamics (10)  |  Electromagnetism (18)  |  Electrostatic (7)  |  Electrostatics (6)  |  Essence (82)  |  Expect (200)  |  Experimental (192)  |  Experimentalist (20)  |  Express (186)  |  Michael Faraday (85)  |  First (1283)  |  Force (487)  |  Green (63)  |  Guess (61)  |  Hermann von Helmholtz (28)  |  Induction (77)  |  Investigation (230)  |  Knowing (137)  |  Large (394)  |  Law (894)  |  Long (790)  |  Magnet (20)  |  Man (2251)  |  Mechanical (140)  |  Most (1731)  |  Multitude (47)  |  Ohm (5)  |  Georg Simon Ohm (3)  |  Opinion (281)  |  Siméon-Denis Poisson (7)  |  Predict (79)  |  Problem (676)  |  Read (287)  |  Result (677)  |  Run (174)  |  Simple (406)  |  Square (70)  |  State (491)  |  Still (613)  |  System (537)  |  Theory (970)  |  Sir J.J. Thomson (18)  |  Unfortunately (38)  |  Work (1351)

Old mathematicians never die; they just lose some of their functions.
Anonymous
Science quotes on:  |  Die (86)  |  Function (228)  |  Joke (83)  |  Lose (159)  |  Never (1087)  |  Old (481)

Once when lecturing to a class he [Lord Kelvin] used the word “mathematician,” and then interrupting himself asked his class: “Do you know what a mathematician is?” Stepping to the blackboard he wrote upon it:— [an integral expression equal to the square root of pi]
Then putting his finger on what he had written, he turned to his class and said: “A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville was a mathematician.”
In Life of Lord Kelvin (1910), 1139.
Science quotes on:  |  Ask (411)  |  Blackboard (11)  |  Class (164)  |  Do (1908)  |  Equal (83)  |  Expression (175)  |  Finger (44)  |  Himself (461)  |  Integral (26)  |  Interrupt (6)  |  Baron William Thomson Kelvin (71)  |  Know (1518)  |  Lecture (105)  |  Lord (93)  |  Obvious (126)  |  Pi (13)  |  Root (120)  |  Say (984)  |  Square (70)  |  Square Root (12)  |  Step (231)  |  Turn (447)  |  Twice (17)  |  Two (937)  |  Word (619)  |  Write (230)

One began to hear it said that World War I was the chemists’ war, World War II was the physicists’ war, World War III (may it never come) will be the mathematicians’ war.
Co-author with and Reuben Hersh, The Mathematical Experience (1981), 96.
Science quotes on:  |  Chemist (156)  |  Hear (139)  |  Never (1087)  |  Physicist (259)  |  War (225)  |  Will (2355)  |  World (1774)  |  World War I (3)  |  World War II (8)  |  World War Iii (3)

One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Add (40)  |  Admiration (59)  |  All (4108)  |  Analysis (233)  |  Ancient (189)  |  Anyone (35)  |  Appreciate (63)  |  Approach (108)  |  Archimedes (55)  |  Assent (12)  |  Bear (159)  |  Belief (578)  |  Blow (44)  |  Calculate (54)  |  Certain (550)  |  Characteristic (148)  |  Conducive (3)  |  Contrary (141)  |  Cover (37)  |  Dark (140)  |  Deceive (26)  |  Decidedly (2)  |  Deliberation (5)  |  Depend (228)  |  Difficult (246)  |  Difficulty (196)  |  Discover (553)  |  Easier (53)  |  Easiness (4)  |  Easy (204)  |  Effect (393)  |  Elaboration (11)  |  Element (310)  |  Eliminate (21)  |  Equal (83)  |  Everything (476)  |  Exaggeration (15)  |  Excite (15)  |  Execution (25)  |  Explanation (234)  |  Extort (2)  |  Fact (1210)  |  Feature (44)  |  Final (118)  |  Find (998)  |  Finish (59)  |  Foresee (19)  |  Generality (45)  |  Geometry (255)  |  Great (1574)  |  Grudge (2)  |  Hide (69)  |  Himself (461)  |  Immediately (114)  |  Impress (64)  |  Incidental (15)  |  Inquiry (78)  |  Invent (51)  |  Investigation (230)  |  Involve (90)  |  Late (118)  |  Lead (384)  |  Leave (130)  |  Lucid (8)  |  Main (28)  |  Master (178)  |  Mathematicians and Anecdotes (141)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  Modern (385)  |  More (2559)  |  Most (1731)  |  Mystery (177)  |  Nearly (137)  |  New (1216)  |  Object (422)  |  Obscure (62)  |  Obvious (126)  |  Old (481)  |  Order (632)  |  Original (58)  |  Outset (7)  |  Perfect (216)  |  Plan (117)  |  Plutarch (15)  |  Position (77)  |  Possible (552)  |  Posterity (29)  |  Precede (23)  |  Present (619)  |  Probably (49)  |  Problem (676)  |  Proposition (123)  |  Purpose (317)  |  Question (621)  |  Rapidity (26)  |  Read (287)  |  Reason (744)  |  Remark (28)  |  Result (677)  |  Same (157)  |  Say (984)  |  Scarcely (74)  |  Scheme (57)  |  Secret (194)  |  Secure (22)  |  Secured (18)  |  Seek (213)  |  Set (394)  |  Simple (406)  |  Simplicity (167)  |  Solution (267)  |  Spectator (10)  |  Stage (143)  |  Step (231)  |  Strike (68)  |  Study (653)  |  Successive (73)  |  Suddenly (88)  |  Suggest (34)  |  Tactic (7)  |  Time (1877)  |  Trace (103)  |  Treatise (44)  |  Troublesome (7)  |  Truth (1057)  |  Ultimate (144)  |  John Wallis (3)  |  Will (2355)  |  Wish (212)

One may be a mathematician of the first rank without being able to compute. It is possible to be a great computer without having the slightest idea of mathematics.
In Schriften, Zweiter Teil (1901), 223.
Science quotes on:  |  Being (1278)  |  Compute (18)  |  Computer (127)  |  First (1283)  |  Great (1574)  |  Idea (843)  |  Mathematics (1328)  |  Possible (552)  |  Rank (67)  |  Slight (31)

One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work.
As quoted, without citation, in Howard W. Eves Return to Mathematical Circles, (1988), 156.
Science quotes on:  |  Avoid (116)  |  Doing (280)  |  Extent (139)  |  Real (149)  |  Thing (1915)  |  Will (2355)  |  Work (1351)

Perhaps I may without immodesty lay claim to the appellation of Mathematical Adam, as I believe that I have given more names (passed into general circulation) of the creatures of the mathematical reason than all the other mathematicians of the age combined.
In Nature (1887-1888), 87, 162. As quoted and cited in As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 178
Science quotes on:  |  Adam (7)  |  Age (499)  |  All (4108)  |  Circulation (24)  |  Claim (146)  |  Combine (57)  |  Creature (233)  |  General (511)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  More (2559)  |  Name (333)  |  Other (2236)  |  Pass (238)  |  Reason (744)

Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
Quoted in a space filler, without citation, in The Pentagon: A Mathematics Magazine for Students (Fall 1951), 11, No. 1, 12. Primary source needed (can you help).
Science quotes on:  |  Beginning (305)  |  Career (75)  |  Century (310)  |  Consequence (203)  |  Contribute (27)  |  Due (141)  |  Leonhard Euler (35)  |  Few (13)  |  Foresee (19)  |  Carl Friedrich Gauss (77)  |  Great (1574)  |  Human (1468)  |  Human Thought (7)  |  Impossible (251)  |  Independent (67)  |  Inevitable (49)  |  Knowledge (1529)  |  Language (293)  |  Literature (103)  |  Long (790)  |  Mathematics (1328)  |  More (2559)  |  Most (1731)  |  Sir Isaac Newton (333)  |  Ordinary (160)  |  Bernhard Riemann (7)  |  Rule (294)  |  Satisfy (27)  |  Something (719)  |  Study (653)  |  Surprise (86)  |  Thing (1915)  |  Thought (953)

Perhaps... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, in the same way, so to speak, as he calculates the motions of celestial bodies.
Oeuvres (1862), Vol. 2, 550-1. Trans. John Heilbron, Weighing Imponderables and Other Quantitative Science around 1800 (1993), 14.
Science quotes on:  |  Calculate (54)  |  Calculation (127)  |  Celestial (53)  |  Chemical (292)  |  Combination (144)  |  Data (156)  |  Motion (310)  |  Precision (68)  |  Reaction (104)  |  Speak (232)  |  Way (1217)  |  Will (2355)

Persons, who have a decided mathematical talent, constitute, as it were, a favored class. They bear the same relation to the rest of mankind that those who are academically trained bear to those who are not.
In Ueber die Anlage zur Mathematik (1900), 4.
Science quotes on:  |  Academic (18)  |  Bear (159)  |  Class (164)  |  Constitute (97)  |  Decide (41)  |  Favor (63)  |  Favored (5)  |  Mankind (339)  |  Mathematics (1328)  |  Person (363)  |  Relation (157)  |  Rest (280)  |  Talent (94)  |  Train (114)

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.
From the second Fubini Lecture, delivered at the Villa Gualino, Torino (2 Jun 1998), 'What is Invariant Theory, Really?' Collected in Henry H. Crapo and D. Senato (eds.), Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota (2001), 55.
Science quotes on:  |  Askance (2)  |  Change (593)  |  Erase (6)  |  Explain (322)  |  Footstep (5)  |  Habit (168)  |  Little (707)  |  Look (582)  |  Philosopher (258)  |  Psychiatrist (15)  |  Pythagoras (38)  |  Scientist (820)  |  Strange (157)  |  Systematically (7)  |  Why (491)

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
In The Man who Knew Infinity: A Life of the Genius Ramanujan (1975), 226.
Science quotes on:  |  Ability (152)  |  Assignment (12)  |  Contrive (10)  |  Count (105)  |  Discourse (18)  |  Eminence (23)  |  Follow (378)  |  G. H. Hardy (71)  |  David Hilbert (46)  |  Himself (461)  |  Informal (4)  |  J. E. Littlewood (19)  |  Mathematics (1328)  |  Most (1731)  |  Natural (796)  |  Nothing (966)  |  Srinivasa Ramanujan (17)  |  Scale (121)  |  Step (231)  |  Year (933)

Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
…...
Science quotes on:  |  Applied (177)  |  Applied Mathematics (15)  |  Better (486)  |  Branch (150)  |  Difficult (246)  |  Mathematics (1328)  |  Most (1731)  |  Poor (136)  |  Program (52)  |  Pure (291)  |  Remain (349)

Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 124.
Science quotes on:  |  Application (242)  |  Become (815)  |  Becoming (96)  |  Being (1278)  |  Branch (150)  |  Chosen (48)  |  Closely (12)  |  Connect (125)  |  Connected (8)  |  Describe (128)  |  Different (577)  |  Evident (91)  |  Find (998)  |  Game (101)  |  Himself (461)  |  Importance (286)  |  Interest (386)  |  Interesting (153)  |  Invent (51)  |  Mathematics (1328)  |  Method (505)  |  Methods (204)  |  More (2559)  |  Nature (1926)  |  Physic (517)  |  Physical (508)  |  Physicist (259)  |  Physics (533)  |  Play (112)  |  Possibly (111)  |  Proportional (4)  |  Pure (291)  |  Pure Mathematics (67)  |  Remain (349)  |  Rule (294)  |  Situation (113)  |  Subject (521)  |  Time (1877)  |  Two (937)  |  Ultimately (55)  |  Unify (6)  |  Will (2355)

Science, being human enquiry, can hear no answer except an answer couched somehow in human tones. Primitive man stood in the mountains and shouted against a cliff; the echo brought back his own voice, and he believed in a disembodied spirit. The scientist of today stands counting out loud in the face of the unknown. Numbers come back to him—and he believes in the Great Mathematician.
Concluding paragraph of chapter, 'Physics, Astronomy, and Mathematics: Or Beyond Common-Sense', contributed to Naomi Mitchison (ed.), An Outline For Boys And Girls And Their Parents (1932), 357.
Science quotes on:  |  Against (332)  |  Answer (366)  |  Back (390)  |  Being (1278)  |  Belief (578)  |  Cliff (19)  |  Couch (2)  |  Count (105)  |  Counting (26)  |  Disembodied (6)  |  Echo (11)  |  Enquiry (87)  |  Face (212)  |  Great (1574)  |  Hear (139)  |  Human (1468)  |  Man (2251)  |  Mountain (185)  |  Number (699)  |  Primitive (75)  |  Primitive Man (5)  |  Science (3879)  |  Scientist (820)  |  Shout (25)  |  Somehow (48)  |  Spirit (265)  |  Stand (274)  |  Today (314)  |  Tone (22)  |  Unknown (182)  |  Voice (52)

Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
Science quotes on:  |   (2863)  |  Achievement (179)  |  Acute (7)  |  Appear (118)  |  Avoid (116)  |  Axiom (63)  |  Completion (22)  |  Consistency (31)  |  Crown (38)  |  Enterprise (54)  |  Examination (98)  |  Explain (322)  |  Gottlob Frege (11)  |  Investigation (230)  |  Least (75)  |  Logic (287)  |  Logician (17)  |  Long (790)  |  Long Ago (10)  |  Magnificent (43)  |  Method (505)  |  Most (1731)  |  Necessary (363)  |  Number (699)  |  Number Theory (6)  |  Prepared (5)  |  Profound (104)  |  Prove (250)  |  Regard (305)  |  Bertrand Russell (184)  |  Set (394)  |  Set Theory (6)  |  Successful (123)  |  Task (147)  |  Theory (970)  |  Whole (738)  |  Work (1351)

Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
Quoted as “Einstein once joked”, in Carl Seelig, Albert Einstein: A Documentary Biography (1956), 28.
Science quotes on:  |  Anymore (5)  |  Do (1908)  |  Invade (5)  |  Myself (212)  |  Relativity (88)  |  Theory (970)  |  Theory Of Relativity (33)  |  Understand (606)

Since the seventeenth century, physical intuition has served as a vital source for mathematical porblems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from their roots of mathematics in intuition, have concentrated on refinement and emphasized the postulated side of mathematics, and at other times have overlooked the unity of their science with physics and other fields. In many cases, physicists have ceased to appreciate the attitudes of mathematicians. This rift is unquestionably a serious threat to science as a whole; the broad stream of scientific development may split into smaller and smaller rivulets and dry out. It seems therefore important to direct our efforts towards reuniting divergent trends by classifying the common features and interconnections of many distinct and diverse scientific facts.
As co-author with David Hilbert, in Methods of Mathematical Physics (1937, 1989), Preface, v.
Science quotes on:  |  17th Century (16)  |  Appreciate (63)  |  Appreciation (34)  |  Attitude (82)  |  Ceasing (2)  |  Century (310)  |  Classification (97)  |  Common (436)  |  Concentration (29)  |  Connection (162)  |  Development (422)  |  Direct (225)  |  Directing (5)  |  Distinct (97)  |  Divergence (6)  |  Divergent (6)  |  Diverse (17)  |  Dry (57)  |  Effort (227)  |  Emphasis (17)  |  Fact (1210)  |  Facts (553)  |  Fashion (30)  |  Feature (44)  |  Field (364)  |  Importance (286)  |  Interconnection (12)  |  Intuition (75)  |  Mathematics (1328)  |  Method (505)  |  Methods (204)  |  Other (2236)  |  Overlook (31)  |  Overlooking (3)  |  Physic (517)  |  Physical (508)  |  Physicist (259)  |  Physics (533)  |  Postulate (38)  |  Problem (676)  |  Recent (77)  |  Refinement (17)  |  Rift (3)  |  Rivulet (5)  |  Root (120)  |  Science (3879)  |  Scientific (941)  |  Serious (91)  |  Serving (15)  |  Side (233)  |  Source (93)  |  Stream (81)  |  Threat (30)  |  Time (1877)  |  Trend (22)  |  Turning (5)  |  Unity (78)  |  Unquestionably (3)  |  Vital (85)  |  Weakening (2)  |  Whole (738)

So the astronomer is on common ground with the physicist both in the subject and in the predicate of the conclusion, but the physicist demonstrates the predicate to belong to the subject by nature, whereas the astronomer does not care whether it belongs by nature or not. What, therefore, is the predicate for the physicist, is abstracted as the subject for the pure mathematician.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 94.
Science quotes on:  |  Abstract (124)  |  Astronomer (93)  |  Belong (162)  |  Both (493)  |  Care (186)  |  Common (436)  |  Common Ground (4)  |  Conclusion (254)  |  Demonstrate (76)  |  Ground (217)  |  Nature (1926)  |  Physicist (259)  |  Predicate (3)  |  Pure (291)  |  Scientist (820)  |  Subject (521)

Some humans are mathematicians—others aren’t.
In In the Shadow of Man (1971), 252.
Science quotes on:  |  Human (1468)  |  Other (2236)

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.
In Hyperspace:A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension (1994), 172.
Science quotes on:  |  Age (499)  |  All (4108)  |  Being (1278)  |  Bursting (3)  |  Comparison (102)  |  Corner (57)  |  Current (118)  |  Dark (140)  |  Derivation (13)  |  Down (456)  |  Field (364)  |  History (673)  |  History Of Science (63)  |  Illuminating (12)  |  Isolation (31)  |  Known (454)  |  Life (1795)  |  Man (2251)  |  Mathematics (1328)  |  Most (1731)  |  Profound (104)  |  Srinivasa Ramanujan (17)  |  Science (3879)  |  Strangest (4)  |  Supernova (7)  |  Total (94)  |  Tragedy (29)  |  Tuberculosis (8)  |  Waste (101)  |  Western (45)  |  Work (1351)  |  Working (20)  |  Worth (169)  |  Year (933)

Structures are the weapons of the mathematician.
Epigraph, without citation, in Nimal Nissanke, Introductory Logic and Sets for Computer Scientists (1999), 240. Primary source needed (can you help?)
Science quotes on:  |  Structure (344)  |  Weapon (92)  |  Weapons (58)

Sylvester was incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it would not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the theory of functions and in allied disciplines, he never became acquainted with …
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.
In Address delivered at a memorial meeting at the Johns Hopkins University (2 May 1897), published in Bulletin of the American Mathematical Society (Jun 1897), 303. Also in Johns Hopkins University Circulars, 16 (1897), 54.
Science quotes on:  |  Acquaint (9)  |  Active (76)  |  All (4108)  |  Ally (6)  |  Analysis (233)  |  Apparently (20)  |  Association (46)  |  Atmosphere (103)  |  Attention (190)  |  Become (815)  |  Berlin (10)  |  Brain (270)  |  Century (310)  |  Confidently (2)  |  Discipline (77)  |  Domain (69)  |  Effect (393)  |  Find (998)  |  Fire (189)  |  France (27)  |  Function (228)  |  Furnish (96)  |  Germany (13)  |  Grant (73)  |  Great (1574)  |  Half (56)  |  Helpful (16)  |  Human (1468)  |  Incapable (40)  |  Influence (222)  |  Laurel (2)  |  Live (628)  |  Man (2251)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Mere (84)  |  Modern (385)  |  Never (1087)  |  Peculiarly (4)  |  Power (746)  |  Present (619)  |  Prevail (46)  |  Prime (11)  |  Purely (109)  |  Read (287)  |  Reading (133)  |  Receptive (5)  |  Restless (11)  |  Retain (56)  |  Second (62)  |  Splendid (23)  |  Stimulus (26)  |  Subject (521)  |  Supply (93)  |  Surround (30)  |  James Joseph Sylvester (58)  |  Temperament (17)  |  Theory (970)  |  Thought (953)  |  Train (114)  |  Way (1217)  |  Work (1351)

Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
Science quotes on:  |  Ability (152)  |  Altogether (9)  |  Amount (151)  |  Attempt (251)  |  Boy (94)  |  Bulk (24)  |  Calculation (127)  |  Capacity (100)  |  Class (164)  |  Confuse (19)  |  Course (409)  |  Devoid (11)  |  Difference (337)  |  Do (1908)  |  Drill (11)  |  Elementary (96)  |  Estimate (57)  |  Faculty (72)  |  Fair (15)  |  Feel (367)  |  Feeling (250)  |  Fewer (8)  |  Find (998)  |  First (1283)  |  First-Class (2)  |  Former (137)  |  Furnish (96)  |  Great (1574)  |  High (362)  |  Hundred (229)  |  Interest (386)  |  Kind (557)  |  Knowledge (1529)  |  Latter (21)  |  Less (103)  |  Master (178)  |  Mathematics (1328)  |  Measure (232)  |  More (2559)  |  Natural (796)  |  Nearly (137)  |  Of Course (20)  |  Ordinary (160)  |  Original (58)  |  People (1005)  |  Pleasure (178)  |  Population (110)  |  Possess (156)  |  Possible (552)  |  Probable (20)  |  Probably (49)  |  Proportion (136)  |  Rank (67)  |  Really (78)  |  Render (93)  |  Run (174)  |  School (219)  |  Slight (31)  |  Small (477)  |  Special (184)  |  Study (653)  |  Taste (90)  |  Thousand (331)  |  Time (1877)  |  Two (937)  |  Variation (90)  |  Work (1351)

The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
Science quotes on:  |  Actual (117)  |  Actually (27)  |  All (4108)  |  Amenable (4)  |  Analogous (5)  |  Appear (118)  |  Aspect (124)  |  Belong (162)  |  Body (537)  |  Both (493)  |  Branch (150)  |  Build (204)  |  Building (156)  |  Calculus (65)  |  Capable (168)  |  Carry (127)  |  Case (99)  |  Certain (550)  |  Classification (97)  |  Comparison (102)  |  Connection (162)  |  Consideration (139)  |  Develop (268)  |  Different (577)  |  Differential (7)  |  Direct (225)  |  Discernment (4)  |  Discovery (780)  |  Distinguish (160)  |  Distinguished (83)  |  Doctrine (75)  |  Domain (69)  |  Due (141)  |  Employ (113)  |  Enable (119)  |  Essential (199)  |  Evolution (590)  |  Example (94)  |  Exhibit (20)  |  Find (998)  |  Form (959)  |  Frequent (23)  |  Fundamental (250)  |  Generalization (57)  |  Identity (19)  |  Include (90)  |  Independent (67)  |  Independently (24)  |  Induction (77)  |  Involve (90)  |  Involved (90)  |  Latin (38)  |  Percy Alexander MacMahon (3)  |  Major (84)  |  Manifest (21)  |  Manner (58)  |  Mathematics (1328)  |  Method (505)  |  Nature (1926)  |  Nature Of Mathematics (80)  |  Observation (555)  |  Obtain (163)  |  Operation (213)  |  Operations (107)  |  Operator (3)  |  Physical (508)  |  Physical Science (101)  |  Possible (552)  |  Proceed (129)  |  Process (423)  |  Really (78)  |  Recognise (9)  |  Region (36)  |  Relate (21)  |  Result (677)  |  Science (3879)  |  Simple (406)  |  Single (353)  |  Sometimes (45)  |  Special (184)  |  Species (401)  |  Square (70)  |  Strictly (13)  |  Strike (68)  |  Striking (48)  |  Subject (521)  |  Superficial (12)  |  Synthesis (57)  |  Synthesize (3)  |  Theory (970)  |  Thought (953)  |  Treatment (130)  |  Trial (57)  |  Underlying (30)  |  Wholly (88)

The advantage is that mathematics is a field in which one’s blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one’s best moments that count and not one’s worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician’s reputation.
In Ex-Prodigy: My Childhood and Youth (1953), 21.
Science quotes on:  |   (2863)  |  Advantage (134)  |  Approach (108)  |  Bad (180)  |  Best (459)  |  Blunder (21)  |  Chess (25)  |  Clearly (41)  |  Compare (69)  |  Correct (86)  |  Count (105)  |  Differ (85)  |  Erase (6)  |  Field (364)  |  Game (101)  |  Inattention (5)  |  Lose (159)  |  Mathematics (1328)  |  Moment (253)  |  Pencil (20)  |  Problem (676)  |  Reputation (33)  |  Show (346)  |  Single (353)  |  Stroke (18)  |  Successful (123)  |  Tend (124)  |  Wastebasket (2)  |  Will (2355)  |  Worst (57)

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 214.
Science quotes on:  |  Achievement (179)  |  Apex (6)  |  Closely (12)  |  Decide (41)  |  Event (216)  |  Excited (8)  |  Feel (367)  |  Field (364)  |  Intertwined (2)  |  Mathematics (1328)  |  More (2559)  |  Never (1087)  |  Occur (150)  |  Thought (953)  |  Turn (447)  |  Two (937)  |  Unrelated (6)  |  Upset (18)

The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness,* of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do.
In 'The Universe and Beyond', Hibbert Journal (1904-1905), 3, 309. An editorial footnote indicates “precision, sharpness, completeness” — i.e., in terms of the absolutely clear and indefinable.
Science quotes on:  |  Admit (45)  |  Answer (366)  |  Apodictic (3)  |  Certainty (174)  |  Character (243)  |  Characteristic (148)  |  Clear (100)  |  Completeness (19)  |  Concept (221)  |  Conclusion (254)  |  Correctness (12)  |  Deal (188)  |  Definition (221)  |  Distinctive (25)  |  Do (1908)  |  Due (141)  |  Idea (843)  |  Indefinable (5)  |  Involve (90)  |  Involved (90)  |  Mathematics (1328)  |  Mode (41)  |  Mysterious (79)  |  Nature Of Mathematics (80)  |  Other (2236)  |  Precision (68)  |  Quality (135)  |  Ratiocination (4)  |  Sharpness (8)  |  Special (184)  |  Term (349)  |  Thought (953)  |  Trick (35)

The automatic computing engine now being designed at N. P. L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 106.
Science quotes on:  |  Accuracy (78)  |  All (4108)  |  Amount (151)  |  Apply (160)  |  Atypical (3)  |  Automatic (16)  |  Being (1278)  |  Certainly (185)  |  Computer (127)  |  Construction (112)  |  Control (167)  |  Degree (276)  |  Design (195)  |  Designed (3)  |  Desired (6)  |  Detail (146)  |  Digital (10)  |  Doubtful (29)  |  Electronic (12)  |  Engine (98)  |  Engineering (175)  |  Equally (130)  |  Equipment (43)  |  Greater (288)  |  High (362)  |  Increase (210)  |  Interest (386)  |  Laboratory (196)  |  Large (394)  |  Lecture (105)  |  Long (790)  |  Machine (257)  |  Mean (809)  |