TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The Superfund legislation... may prove to be as far-reaching and important as any accomplishment of my administration. The reduction of the threat to America's health and safety from thousands of toxic-waste sites will continue to be an urgent�issue �”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index G > Category: Geometer

Geometer Quotes (24 quotes)

Une même expression, dont les géomètres avaient considéré les propriétés abstraites, … représente'aussi le mouvement de la lumière dans l’atmosphère, quelle détermine les lois de la diffusion de la chaleur dans la matière solide, et quelle entre dans toutes les questions principales de la théorie des probabilités.
The same expression whose abstract properties geometers had considered … represents as well the motion of light in the atmosphere, as it determines the laws of diffusion of heat in solid matter, and enters into all the chief problems of the theory of probability.
From Théorie Analytique de la Chaleur (1822), translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
Science quotes on:  |  Abstract (141)  |  Atmosphere (117)  |  Chief (99)  |  Consider (428)  |  Determine (152)  |  Diffusion (13)  |  Enter (145)  |  Expression (181)  |  Heat (180)  |  Law (913)  |  Light (635)  |  Matter (821)  |  Motion (320)  |  Probability (135)  |  Problem (731)  |  Property (177)  |  Question (649)  |  Represent (157)  |  Same (166)  |  Solid (119)  |  Theory (1015)

A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.
From 'On Some Recent Tendencies in Geometrical Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
Science quotes on:  |  Account (195)  |  Analysis (244)  |  Discover (571)  |  Divide (77)  |  Genius (301)  |  Geometry (271)  |  Great (1610)  |  Happen (282)  |  Himself (461)  |  Ignorant (91)  |  Implicit (12)  |  Instrument (158)  |  Making (300)  |  Matter (821)  |  Modern (402)  |  Never (1089)  |  New (1273)  |  Possess (157)  |  Powerful (145)  |  Progress (492)  |  Publish (42)  |  Remain (355)  |  Research (753)  |  Result (700)  |  Student (317)  |  Study (701)  |  Study And Research In Mathematics (61)  |  Toil (29)  |  Use (771)  |  Whole (756)  |  Will (2350)  |  Writing (192)

An old French geometer used to say that a mathematical theory was never to be considered complete till you had made it so clear that you could explain it to the first man you met in the street.
In Nature (1873), 8, 458.
Science quotes on:  |  Clear (111)  |  Complete (209)  |  Consider (428)  |  Explain (334)  |  First (1302)  |  French (21)  |  Man (2252)  |  Mathematics (1395)  |  Meet (36)  |  Never (1089)  |  Old (499)  |  Say (989)  |  Street (25)  |  Study And Research In Mathematics (61)  |  Theory (1015)

As plants convert the minerals into food for animals, so each man converts some raw material in nature to human use. The inventors of fire, electricity, magnetism, iron, lead, glass, linen, silk, cotton; the makers of tools; the inventor of decimal notation, the geometer, the engineer, the musician, severally make an easy way for all, through unknown and impossible confusions.
In 'Uses of Great Men', Representative Men (1850), 5-6.
Science quotes on:  |  Animal (651)  |  Confusion (61)  |  Convert (22)  |  Cotton (8)  |  Decimal (21)  |  Easy (213)  |  Electricity (168)  |  Engineer (136)  |  Fire (203)  |  Food (213)  |  Glass (94)  |  Human (1512)  |  Impossible (263)  |  Inventor (79)  |  Iron (99)  |  Lead (391)  |  Linen (8)  |  Magnetism (43)  |  Maker (34)  |  Man (2252)  |  Material (366)  |  Mineral (66)  |  Musician (23)  |  Nature (2017)  |  Notation (28)  |  Plant (320)  |  Raw (28)  |  Silk (14)  |  Through (846)  |  Tool (129)  |  Unknown (195)  |  Use (771)  |  Way (1214)

Euler’s Tentamen novae theorae musicae had no great success, as it contained too much geometry for musicians, and too much music for geometers.
Paraphrase by Brewster to describe Fuss’ opinion of Euler’s 'Attempt at a New Theory of Music' (1739). In David Brewster, Letters of Euler on Different Subjects in Natural Philosophy (1872), Vol. 1, 26. The remark by Fuss appears in his eulogy, read at the Imperial Academy of Sciences of Saint Petersburg (23 Oct 1783). Published in the original French in 'Éloge de Léonard Euler, Prononcé en Français par Nicolas Fuss'. Collected in Leonard Euler, Oeuvres Complètes en Français de L. Euler (1839), Vol. 1, xii.
Science quotes on:  |  Leonhard Euler (35)  |  Geometry (271)  |  Great (1610)  |  Mathematicians and Anecdotes (141)  |  Music (133)  |  Musician (23)  |  Success (327)

He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.
In 'A Probationary Lecture on Geometry, in Collected Mathematical Papers (1908), Vol. 2, 9. [The Latin phrase, “abeunt studia in mores” translates as “studies pass on into character”. —Webmaster]
Science quotes on:  |  Abeunt Studia In Mores (2)  |  Accord (36)  |  According (236)  |  Adage (4)  |  Admit (49)  |  Awaken (17)  |  Beautiful (271)  |  Being (1276)  |  Belief (615)  |  Boldly (5)  |  Character (259)  |  Conscious (46)  |  Constitution (78)  |  Convert (22)  |  Depth (97)  |  Do (1905)  |  Enhance (17)  |  Expressive (6)  |  Feel (371)  |  Find (1014)  |  Fix (34)  |  Foundation (177)  |  Geometry (271)  |  Impossible (263)  |  Integrity (21)  |  Invention (400)  |  Invigorate (3)  |  Know (1538)  |  Learn (672)  |  Mental (179)  |  Moral (203)  |  More (2558)  |  Must (1525)  |  Old (499)  |  Orderly (38)  |  Principle (530)  |  Quicken (7)  |  Reason (766)  |  Reverence (29)  |  Sentiment (16)  |  Study (701)  |  Teach (299)  |  Think (1122)  |  Truth (1109)  |  Value Of Mathematics (60)  |  Venture (19)

Hippocrates is an excellent geometer but a complete fool in everyday affairs.
Aristotle
…...
Science quotes on:  |  Affair (29)  |  Complete (209)  |  Everyday (32)  |  Excellent (29)  |  Fool (121)  |  Hippocrates (49)

I am the most travelled of all my contemporaries; I have extended my field of enquiry wider than anybody else, I have seen more countries and climes, and have heard more speeches of learned men. No one has surpassed me in the composition of lines, according to demonstration, not even the Egyptian knotters of ropes, or geometers.
In Alan L. Mackay, A Dictionary of Scientific Quotations (1992, 1994), 71.
Science quotes on:  |  According (236)  |  Anybody (42)  |  Composition (86)  |  Contemporary (33)  |  Country (269)  |  Demonstration (120)  |  Egypt (31)  |  Enquiry (89)  |  Extend (129)  |  Extension (60)  |  Field (378)  |  Hearing (50)  |  Knot (11)  |  Learn (672)  |  Learned (235)  |  Learning (291)  |  Line (100)  |  More (2558)  |  Most (1728)  |  Rope (9)  |  Seeing (143)  |  Speech (66)  |  Surpass (33)  |  Surpassing (12)  |  Traveler (33)

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:  |  Addition (70)  |  Admirer (9)  |  Ardent (6)  |  Attitude (84)  |  British (42)  |  Bury (19)  |  Arthur Cayley (17)  |  Deep (241)  |  Desire (212)  |  Difference (355)  |  Enthusiastic (7)  |  Euclid (60)  |  Foremost (11)  |  Geometry (271)  |  Grotesque (6)  |  Keep (104)  |  Mathematician (407)  |  Mathematicians and Anecdotes (141)  |  Mixture (44)  |  Original (61)  |  Plummet (2)  |  Question (649)  |  Reach (286)  |  Reform (22)  |  Remind (16)  |  Retention (5)  |  Schoolboy (9)  |  Sound (187)  |  Strictly (13)  |  Strike (72)  |  Striking (48)  |  Suggest (38)  |  Supporter (4)  |  James Joseph Sylvester (58)  |  Teach (299)  |  Teaching (190)  |  Treatise (46)  |  Two (936)  |  Wish (216)

Logic has borrowed the rules of geometry without understanding its power. … I am far from placing logicians by the side of geometers who teach the true way to guide the reason. … The method of avoiding error is sought by every one. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration.
From De l’Art de Persuader, (1657). Pensées de Pascal (1842), Part 1, Article 3, 41-42. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202. From the original French, “La logique a peut-être emprunté les règles de la géométrie sans en comprendre la force … je serai bien éloigné de les mettre en parallèle avec les géomètres, qui apprennent la véritable méthode de conduire la raison. … La méthode de ne point errer est recherchée de tout le monde. Les logiciens font profession d'y conduire, les géomètres seuls y arrivent; et, hors de leur science …, il n'y a point de véritables démonstrations ….”
Science quotes on:  |  Alone (324)  |  Avoid (123)  |  Borrow (31)  |  Demonstration (120)  |  Error (339)  |  Geometry (271)  |  Guide (107)  |  Lead (391)  |  Logic (311)  |  Logician (18)  |  Mathematics And Logic (27)  |  Method (531)  |  Power (771)  |  Profess (21)  |  Reach (286)  |  Reason (766)  |  Rule (307)  |  Seek (218)  |  Side (236)  |  Teach (299)  |  Understand (648)  |  Understanding (527)  |  Way (1214)

One of Euler’s main recreations was music, and by cultivating it he brought with it all his geometrical spirit; … he rested his serious researches and composed his Essay of a New Theory of Music, published in 1739; a book full of new ideas presented in a new point of view, but that did not have a great success, apparently for the sole reason that it contains too much of geometry for the musician and too much music for the geometer.
From his Eulogy of Leonhard Euler, read at the Imperial Academy of Sciences of Saint Petersburg (23 Oct 1783). Published in 'Éloge de Léonard Euler, Prononcé en Français par Nicolas Fuss'. Collected in Leonard Euler, Oeuvres Complètes en Français de L. Euler (1839), Vol. 1, xii. From the original French, “Un des principaux délassements d'Euler était la musique, et en la cultivant il y apporta tout son esprit géométrique; … il accordait à ses recherches profondes, il composa son Essai d'une nouvelle théorie de la musique, publié en 1739; ouvrage rempli d'idées neuves ou présentées sous un nouveau point de vue, mais qui n’eut pas un grand succès, apparemment par la seule raison qu’il renferme trop de géométrie pour le musicien et trop de musique pour le géomètre.” English version by Webmaster using Google translate.
Science quotes on:  |  Apparently (22)  |  Book (413)  |  Compose (20)  |  Contain (68)  |  Essay (27)  |  Leonhard Euler (35)  |  Geometry (271)  |  Great (1610)  |  Idea (881)  |  Music (133)  |  Musician (23)  |  New (1273)  |  New Ideas (17)  |  Point (584)  |  Point Of View (85)  |  Present (630)  |  Publish (42)  |  Reason (766)  |  Recreation (23)  |  Research (753)  |  Rest (287)  |  Serious (98)  |  Sole (50)  |  Spirit (278)  |  Success (327)  |  Theory (1015)  |  View (496)

One striking peculiarity of mathematics is its unlimited power of evolving examples and problems. A student may read a book of Euclid, or a few chapters of Algebra, and within that limited range of knowledge it is possible to set him exercises as real and as interesting as the propositions themselves which he has studied; deductions which might have pleased the Greek geometers, and algebraic propositions which Pascal and Fermat would not have disdained to investigate.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 82.
Science quotes on:  |  Algebra (117)  |  Algebraic (5)  |  Book (413)  |  Chapter (11)  |  Deduction (90)  |  Disdain (10)  |  Euclid (60)  |  Evolution (635)  |  Example (98)  |  Exercise (113)  |  Pierre de Fermat (15)  |  Greek (109)  |  Interest (416)  |  Interesting (153)  |  Investigate (106)  |  Knowledge (1647)  |  Limit (294)  |  Limited (102)  |  Mathematics (1395)  |  Pascal (2)  |  Peculiarity (26)  |  Please (68)  |  Possible (560)  |  Power (771)  |  Problem (731)  |  Proposition (126)  |  Range (104)  |  Read (308)  |  Real (159)  |  Set (400)  |  Strike (72)  |  Striking (48)  |  Student (317)  |  Study (701)  |  Themselves (433)  |  Unlimited (24)  |  Value Of Mathematics (60)

The discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers. But for this discovery, which was probably regarded in Plato’s tune and long after him, as the unprofitable amusement of a speculative brain, the whole course of practical philosophy of the present day, of the science of astronomy, of the theory of projectiles, of the art of navigation, might have run in a different channel; and the greatest discovery that has ever been made in the history of the world, the law of universal gravitation, with its innumerable direct and indirect consequences and applications to every department of human research and industry, might never to this hour have been elicited.
In 'A Probationary Lecture on Geometry, Collected Mathematical Papers, Vol. 2 (1908), 7.
Science quotes on:  |  Amusement (37)  |  Application (257)  |  Art (680)  |  Astronomy (251)  |  Attribute (65)  |  Brain (281)  |  Channel (23)  |  Conic Section (8)  |  Consequence (220)  |  Contemplation (75)  |  Course (413)  |  Department (93)  |  Different (595)  |  Direct (228)  |  Discovery (837)  |  Elicit (2)  |  First (1302)  |  Form (976)  |  Gravitation (72)  |  Great (1610)  |  Greatest (330)  |  High (370)  |  History (716)  |  Hour (192)  |  Human (1512)  |  Indirect (18)  |  Industry (159)  |  Innumerable (56)  |  Law (913)  |  Law Of Universal Gravitation (3)  |  Long (778)  |  Navigation (26)  |  Never (1089)  |  Open (277)  |  Philosophy (409)  |  Plato (80)  |  Practical (225)  |  Present (630)  |  Present Day (5)  |  Probably (50)  |  Projectile (3)  |  Regard (312)  |  Research (753)  |  Run (158)  |  Species (435)  |  Speculative (12)  |  Study And Research In Mathematics (61)  |  Theory (1015)  |  Throw (45)  |  Tune (20)  |  Universal (198)  |  Unprofitable (7)  |  Whole (756)  |  World (1850)

The Geometer has the special privilege to carry out, by abstraction, all constructions by means of the intellect.
In Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (1999), 138-139.
Science quotes on:  |  Abstraction (48)  |  Carry (130)  |  Construction (114)  |  Intellect (251)  |  Mean (810)  |  Means (587)  |  Privilege (41)  |  Special (188)

The great truths with which it [mathematics] deals, are clothed with austere grandeur, far above all purposes of immediate convenience or profit. It is in them that our limited understandings approach nearest to the conception of that absolute and infinite, towards which in most other things they aspire in vain. In the pure mathematics we contemplate absolute truths, which existed in the divine mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven. They existed not merely in metaphysical possibility, but in the actual contemplation of the supreme reason. The pen of inspiration, ranging all nature and life for imagery to set forth the Creator’s power and wisdom, finds them best symbolized in the skill of the surveyor. "He meted out heaven as with a span;" and an ancient sage, neither falsely nor irreverently, ventured to say, that “God is a geometer”.
In Orations and Speeches (1870), Vol. 3, 614.
Science quotes on:  |  Absolute (153)  |  Actual (118)  |  Ancient (198)  |  Approach (112)  |  Aspire (15)  |  Austere (7)  |  Best (467)  |  Conception (160)  |  Contemplate (29)  |  Contemplation (75)  |  Continue (179)  |  Convenience (54)  |  Creator (97)  |  Deal (192)  |  Divine (112)  |  Estimates of Mathematics (30)  |  Exist (458)  |  Fall (243)  |  Falsely (2)  |  Find (1014)  |  Forth (14)  |  God (776)  |  Grandeur (35)  |  Great (1610)  |  Heaven (266)  |  Host (16)  |  Imagery (3)  |  Immediate (98)  |  In Vain (12)  |  Infinite (243)  |  Inspiration (80)  |  Irreverent (2)  |  Last (425)  |  Life (1870)  |  Limit (294)  |  Limited (102)  |  Mathematics (1395)  |  Merely (315)  |  Metaphysical (38)  |  Mind (1377)  |  Morning (98)  |  Most (1728)  |  Nature (2017)  |  Other (2233)  |  Pen (21)  |  Possibility (172)  |  Power (771)  |  Profit (56)  |  Pure (299)  |  Pure Mathematics (72)  |  Purpose (336)  |  Radiant (15)  |  Range (104)  |  Reason (766)  |  Sage (25)  |  Say (989)  |  Set (400)  |  Sing (29)  |  Skill (116)  |  Span (5)  |  Star (460)  |  Stars (304)  |  Supreme (73)  |  Surveyor (5)  |  Symbolize (8)  |  Thing (1914)  |  Together (392)  |  Truth (1109)  |  Understanding (527)  |  Vain (86)  |  Venture (19)  |  Will (2350)  |  Wisdom (235)

The love of mathematics is daily on the increase, not only with us but in the army. The result of this was unmistakably apparent in our last campaigns. Bonaparte himself has a mathematical head, and though all who study this science may not become geometricians like Laplace or Lagrange, or heroes like Bonaparte, there is yet left an influence upon the mind which enables them to accomplish more than they could possibly have achieved without this training.
In Letter (26 Jan 1798) to Von Zach. As quoted in translation in Karl Bruhns (ed.), Jane Lassell (trans.) and Caroline Lassell (trans.), Life of Alexander von Humboldt (1872), Vol. 1, 232. [Webmaster assigns this quote to Jérôme Lalande as an informed guess for the following reasons. The cited text gives only the last names, Lalande and von Zach, but it does also give a source footnote to a Allgemeine geographische Ephemeriden, 1, 340. The journal editor, Franz Xaver von Zach, was a Hungarian astronomer. Jérôme Lalande was a French astronomer, living at the same time, who called himself Jérôme Le Français de la Lande. Their names are seen referred to together in the same journal, Vol. 6, 360.]
Science quotes on:  |  Accomplishment (102)  |  Achieve (75)  |  Apparent (85)  |  Army (35)  |  Become (821)  |  Emperor Napoléon Bonaparte (20)  |  Campaign (6)  |  Daily (91)  |  Enable (122)  |  Estimates of Mathematics (30)  |  Head (87)  |  Hero (45)  |  Himself (461)  |  Increase (225)  |  Influence (231)  |  Count Joseph-Louis de Lagrange (26)  |  Pierre-Simon Laplace (63)  |  Last (425)  |  Leave (138)  |  Love (328)  |  Mathematics (1395)  |  Mind (1377)  |  More (2558)  |  Possibly (111)  |  Result (700)  |  Study (701)  |  Training (92)  |  Unmistakable (6)

The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been lead quite naturally, one might say by intuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of the modern studios, are designated by the term fourth dimension.
The Cubist Painters: Aesthetic Meditations (1913) translated by Lionel Abel (1970), 13. Quoted in Michele Emmer, The Visual Mind II (2005), 352.
Science quotes on:  |  Art (680)  |  Artist (97)  |  Dimension (64)  |  Do (1905)  |  Euclid (60)  |  Fourth Dimension (3)  |  Geometry (271)  |  Intuition (82)  |  Language (308)  |  Lead (391)  |  Limit (294)  |  Measurement (178)  |  Modern (402)  |  More (2558)  |  New (1273)  |  Painter (30)  |  Plastic (30)  |  Predecessor (29)  |  Preoccupy (4)  |  Say (989)  |  Scholar (52)  |  Term (357)  |  Themselves (433)  |  Today (321)  |  Writer (90)

The object of geometry in all its measuring and computing, is to ascertain with exactness the plan of the great Geometer, to penetrate the veil of material forms, and disclose the thoughts which lie beneath them? When our researches are successful, and when a generous and heaven-eyed inspiration has elevated us above humanity, and raised us triumphantly into the very presence, as it were, of the divine intellect, how instantly and entirely are human pride and vanity repressed, and, by a single glance at the glories of the infinite mind, are we humbled to the dust.
From 'Mathematical Investigation of the Fractions Which Occur in Phyllotaxis', Proceedings of the American Association for the Advancement of Science (1850), 2, 447, as quoted by R. C. Archibald in 'Benjamin Peirce: V. Biographical Sketch', The American Mathematical Monthly (Jan 1925), 32, No. 1, 12.
Science quotes on:  |  Ascertain (41)  |  Beneath (68)  |  Compute (19)  |  Disclose (19)  |  Divine (112)  |  Dust (68)  |  Elevated (3)  |  Entirely (36)  |  Exactness (29)  |  Form (976)  |  Generous (17)  |  Geometry (271)  |  Glance (36)  |  Great (1610)  |  Heaven (266)  |  Human (1512)  |  Humanity (186)  |  Infinite (243)  |  Inspiration (80)  |  Instantly (20)  |  Intellect (251)  |  Lie (370)  |  Material (366)  |  Measuring (2)  |  Mind (1377)  |  Object (438)  |  Penetrate (68)  |  Plan (122)  |  Presence (63)  |  Pride (84)  |  Research (753)  |  Single (365)  |  Successful (134)  |  Thought (995)  |  Vanity (20)  |  Veil (27)

The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we say a right angle to mean a square corner. But you go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the single phrase “functional exponent.” How much more impossible, if we may say so, would it be to explain a whole treatise like Hamilton’s Quaternions, in such a wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all modes of expression. It discloses the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University of England; or adopt the briefest and clearest forms, as under the pens of the geometers of our Cambridge; but it always reveals to us precisely the writer’s thought.
In North American Review (Jul 1857), 85, 224-225.
Science quotes on:  |  Adopt (22)  |  Beauty (313)  |  Brief (37)  |  Cambridge (17)  |  Cambridge University (2)  |  Clear (111)  |  Conceive (100)  |  Corner (59)  |  Defy (11)  |  Delight (111)  |  Disclose (19)  |  Dispense (10)  |  England (43)  |  Exact (75)  |  Explain (334)  |  Exponent (6)  |  Expression (181)  |  Form (976)  |  French (21)  |  Function (235)  |  Hamilton_William (2)  |  Himself (461)  |  Ignorant (91)  |  Impossible (263)  |  Judge (114)  |  Language (308)  |  Learn (672)  |  Learned (235)  |  Little (717)  |  Mathematician (407)  |  Mathematics (1395)  |  Mathematics As A Language (20)  |  Mean (810)  |  Mercury (54)  |  Metamorphose (2)  |  More (2558)  |  More Or Less (71)  |  Most (1728)  |  Never (1089)  |  Obscure (66)  |  Peculiar (115)  |  Pen (21)  |  Person (366)  |  Phrase (61)  |  Possible (560)  |  Power (771)  |  Precise (71)  |  Precisely (93)  |  Prolix (2)  |  Prominent (6)  |  Quaternion (9)  |  Reason (766)  |  Reveal (152)  |  Right (473)  |  Right Angle (4)  |  Say (989)  |  Simple (426)  |  Single (365)  |  Special (188)  |  Square (73)  |  Thought (995)  |  Translate (21)  |  Treatise (46)  |  University (130)  |  Use (771)  |  Value (393)  |  Verbal (10)  |  Whole (756)  |  Why (491)  |  Wise (143)  |  Writer (90)

The school of Plato has advanced the interests of the race as much through geometry as through philosophy. The modern engineer, the navigator, the astronomer, built on the truths which those early Greeks discovered in their purely speculative investigations. And if the poetry, statesmanship, oratory, and philosophy of our day owe much to Plato’s divine Dialogues, our commerce, our manufactures, and our science are equally indebted to his Conic Sections. Later instances may be abundantly quoted, to show that the labors of the mathematician have outlasted those of the statesman, and wrought mightier changes in the condition of the world. Not that we would rank the geometer above the patriot, but we claim that he is worthy of equal honor.
In 'Imagination in Mathematics', North American Review, 85, 228.
Science quotes on:  |  Abundantly (2)  |  Advance (298)  |  Astronomer (97)  |  Build (211)  |  Change (639)  |  Claim (154)  |  Commerce (23)  |  Condition (362)  |  Conic Section (8)  |  Dialogue (10)  |  Discover (571)  |  Divine (112)  |  Early (196)  |  Engineer (136)  |  Equal (88)  |  Equally (129)  |  Estimates of Mathematics (30)  |  Geometry (271)  |  Greek (109)  |  Honor (57)  |  Indebted (8)  |  Instance (33)  |  Interest (416)  |  Investigation (250)  |  Labor (200)  |  Late (119)  |  Manufacture (30)  |  Mathematician (407)  |  Mighty (13)  |  Modern (402)  |  Navigator (8)  |  Outlast (3)  |  Owe (71)  |  Patriot (5)  |  Philosophy (409)  |  Plato (80)  |  Poetry (150)  |  Purely (111)  |  Quote (46)  |  Race (278)  |  Rank (69)  |  School (227)  |  Show (353)  |  Speculative (12)  |  Statesman (20)  |  Statesmanship (2)  |  Through (846)  |  Truth (1109)  |  Work (1402)  |  World (1850)  |  Worthy (35)

There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.
In 'Imagination in Mathematics', North American Review, 86, 223.
Science quotes on:  |  Act (278)  |  Analyst (8)  |  Appear (122)  |  Applause (9)  |  Archimedes (63)  |  Being (1276)  |  Calculus (65)  |  Competitor (4)  |  Connection (171)  |  Contemporary (33)  |  Create (245)  |  Deed (34)  |  Depend (238)  |  René Descartes (83)  |  Deserve (65)  |  Elapse (3)  |  Far (158)  |  Find (1014)  |  Follow (389)  |  Force (497)  |  Form (976)  |  Galileo Galilei (134)  |  Generation (256)  |  Great (1610)  |  Judge (114)  |  Judgment (140)  |  Jury (3)  |  Gottfried Wilhelm Leibniz (51)  |  Live (650)  |  Living (492)  |  Man (2252)  |  Mathematician (407)  |  Mention (84)  |  More (2558)  |  Must (1525)  |  Name (359)  |  Sir Isaac Newton (363)  |  Outstrip (4)  |  Peer (13)  |  People (1031)  |  Popular (34)  |  Race (278)  |  Reach (286)  |  Really (77)  |  Say (989)  |  Secrecy (2)  |  Sit (51)  |  Something (718)  |  Sublime (50)  |  Succeed (114)  |  Succeeding (14)  |  Testimony (21)  |  Thousand (340)  |  Title (20)  |  Truly (118)  |  Try (296)  |  Unable (25)  |  Understand (648)  |  Usually (176)  |  Work (1402)  |  Worthy (35)  |  Year (963)

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
From 'Les Mathématiques et la Logique', Science et Méthode (1908, 1920), Livre 2, Chap. 3, Sec. 2, 157. English as in Henri Poincaré and George Bruce Halsted (trans.), 'Mathematics and Logic', Science and Method collected in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method (1913), 451. From the French, “Ainsi, c’est bien entendu, pour démontrer un théorème, il n’est pas nécessaire ni même utile de savoir ce qu’il veut dire. On pourrait remplacer le géomètre par le piano à raisonner imaginé par Stanley Jevons; ou, si l’on aime mieux, on pourrait imaginer une machine où l’on introduirait les axiomes par un bout pendant qu’on recueillerait les théorèmes à l’autre bout, comme cette machine légendaire de Chicago où les porcs entrent vivants et d’où ils sortent transformés en jambons et en saucisses. Pas plus que ces machines, le mathématicien n’a besoin de comprendre ce qu’il fait”.
Science quotes on:  |  Advantageous (10)  |  Alive (97)  |  Assumption (96)  |  Chicago (2)  |  Choose (116)  |  Demonstrate (79)  |  End (603)  |  Ham (2)  |  Imagine (176)  |  Know (1538)  |  Logic (311)  |  Machine (271)  |  Mathematician (407)  |  Mean (810)  |  Meaning (244)  |  Means (587)  |  More (2558)  |  Necessary (370)  |  Need (320)  |  Other (2233)  |  Piano (12)  |  Pig (8)  |  Prove (261)  |  Replace (32)  |  Sausage (2)  |  Theorem (116)  |  Transform (74)  |  Understand (648)  |  Understood (155)

To fully understand the mathematical genius of Sophus Lie, one must not turn to books recently published by him in collaboration with Dr. Engel, but to his earlier memoirs, written during the first years of his scientific career. There Lie shows himself the true geometer that he is, while in his later publications, finding that he was but imperfectly understood by the mathematicians accustomed to the analytic point of view, he adopted a very general analytic form of treatment that is not always easy to follow.
In Lectures on Mathematics (1911), 9.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Adopt (22)  |  Analytic (11)  |  Book (413)  |  Career (86)  |  Collaboration (16)  |  Early (196)  |  Easy (213)  |   Ernst Engel, (2)  |  Find (1014)  |  First (1302)  |  Follow (389)  |  Form (976)  |  Fully (20)  |  General (521)  |  Genius (301)  |  Himself (461)  |  Imperfect (46)  |  Late (119)  |  Lie (370)  |  Sophus Lie (6)  |  Mathematician (407)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1395)  |  Memoir (13)  |  Must (1525)  |  Point (584)  |  Point Of View (85)  |  Publication (102)  |  Publish (42)  |  Recently (3)  |  Scientific (955)  |  Show (353)  |  Treatment (135)  |  True (239)  |  Turn (454)  |  Understand (648)  |  Understood (155)  |  View (496)  |  Write (250)  |  Year (963)

When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.
In Sprüche in Reimen. Sprüche in Prosa. Ethisches (1850), Vol. 3, 214. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 67. From the original German, “Wenn der knabe zu begreifen anfängt, daß einem sichtbaren Punkte ein unsichtbarer vorhergehen müsse, daß der nächste Weg zwischen zwei Punkten schon als Linie gedacht werde, ehe sie mit dem Bleistift aufs Papier gezogen wird, so fühlt er einen gewissen Stolz, ein Behagen. Und nicht mit Unrecht; denn ihm ist die Quelle alles Denkens aufgeschlossen, Idee und Verwirklichtes, potentia et actu, ist ihm klargeworden; der Philosoph entdeckt ihm nichts Neues; dem Geometer war von seiner Seite der Grund alles Denkens aufgegangen.” The Latin phrase, “potentia et actu” means “potentiality and actuality”.
Science quotes on:  |  Basis (180)  |  Become (821)  |  Begin (275)  |  Boy (100)  |  Clear (111)  |  Conceive (100)  |  Difference (355)  |  Discover (571)  |  Distance (171)  |  Draw (140)  |  Experience (494)  |  Feeling (259)  |  Fountain (18)  |  Ideal (110)  |  Invisible (66)  |  Justly (7)  |  New (1273)  |  Nothing (1000)  |  Open (277)  |  Paper (192)  |  Pencil (20)  |  Philosopher (269)  |  Point (584)  |  Potentia (3)  |  Precede (23)  |  Pride (84)  |  Real (159)  |  Reveal (152)  |  Satisfaction (76)  |  Shortest (16)  |  Shortest Distance (2)  |  Straight (75)  |  Straight Line (34)  |  Thought (995)  |  Two (936)  |  Understand (648)  |  Visible (87)


Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
Thank you for sharing.
- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.