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

Today in Science History - Quickie Quiz
Who said: “I was going to record talking... the foil was put on; I then shouted 'Mary had a little lamb',... and the machine reproduced it perfectly.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index P > Category: Prime

Prime Quotes (11 quotes)

Among all highly civilized peoples the golden age of art has always been closely coincident with the golden age of the pure sciences, particularly with mathematics, the most ancient among them.
This coincidence must not be looked upon as accidental, but as natural, due to an inner necessity. Just as art can thrive only when the artist, relieved of the anxieties of existence, can listen to the inspirations of his spirit and follow in their lead, so mathematics, the most ideal of the sciences, will yield its choicest blossoms only when life’s dismal phantom dissolves and fades away, when the striving after naked truth alone predominates, conditions which prevail only in nations while in the prime of their development.
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), 191-192. From the original German, “Bei allen Kulturvölkern ist die Blüthezeit der Kunst auch immer zeitlich eng verbunden mit einer Blüthezeit der reinen Wissenschaften, insbesondere der ältesten unter ihnen, der Mathematik.
Dieses Zusammentreffen dürfte auch nicht ein zufälliges, sondern ein natürliches, ein Ergebniss innerer Notwendigkeit sein. Wie die Kunst nur gedeihen kann, wenn der Künstler, unbekümmert um die Bedrängnisse des Daseins, den Eingebungen seines Geistes lauschen und ihnen folgen kann, so kann die idealste Wissenschaft, die Mathematik, erst dann ihre schönsten Blüthen treiben, wenn des Erdenlebens schweres Traumbild sinkt und sinkt und sinkt, wenn das Streben nach der nackten Wahrheit allein bestimmend ist, was nur bei Nationen in der Vollkraft ihrer Entwickelung vorkommt.”
Science quotes on:  |   (2863)  |  Accidental (27)  |  Age (499)  |  All (4108)  |  Alone (311)  |  Ancient (189)  |  Anxiety (30)  |  Art (657)  |  Artist (90)  |  Blossom (21)  |  Civilized (18)  |  Coincidence (19)  |  Coincident (2)  |  Condition (356)  |  Development (422)  |  Dissolve (20)  |  Due (141)  |  Existence (456)  |  Fade (10)  |  Follow (378)  |  Golden (45)  |  Golden Age (10)  |  Ideal (99)  |  Inner (71)  |  Inspiration (75)  |  Lead (384)  |  Life (1795)  |  Listen (73)  |  Look (582)  |  Mathematics (1328)  |  Mathematics As A Fine Art (23)  |  Most (1731)  |  Must (1526)  |  Nation (193)  |  Natural (796)  |  Necessity (191)  |  People (1005)  |  Phantom (9)  |  Predominate (7)  |  Prevail (46)  |  Pure (291)  |  Pure Science (27)  |  Relieve (5)  |  Science (3879)  |  Spirit (265)  |  Strive (46)  |  Thrive (18)  |  Truth (1057)  |  Will (2355)  |  Yield (81)

Chebyshev said, and I say it again. There is always a prime between n and 2n.
[Referring to the theorem known as the Bertrand postulate, partially solved by Joseph Bertrand (1822-1900). Chebyshev produced a complete, but difficult, proof. Paul Erdös gave an elegant new proof at age 18, while a second-year undergraduate.] Rhyme quoted by Béla Bollobás, 'The Life and Work of Paul Erdos", in Shiing-Shen Chern and Friedrich Hirzebruch (eds.) Wolf Prize in Mathematics (2000), Vol. 1, 296.
Science quotes on:  |  Pafnuty Lvovich Chebyshev (2)  |  Say (984)  |  Theorem (112)

I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
Science quotes on:  |   (2863)  |  Accident (88)  |  Adhere (3)  |  All (4108)  |  Anticipate (18)  |  Appear (118)  |  Article (22)  |  Author (167)  |  Beard (7)  |  Begin (260)  |  Beginning (305)  |  Being (1278)  |  Board (12)  |  Book (392)  |  Bring (90)  |  Class (164)  |  Companion (19)  |  Consequence (203)  |  Constant (144)  |  Contain (68)  |  Correspond (9)  |  Critic (20)  |  Derive (65)  |  Development (422)  |  Difficulty (196)  |  Direction (175)  |  Discover (553)  |  Discovery (780)  |  Doom (32)  |  Effort (227)  |  Elementary (96)  |  Elucidate (4)  |  Emphasize (23)  |  Error (321)  |  Example (94)  |  Explain (322)  |  Field (364)  |  Figure (160)  |  Final (118)  |  Finally (26)  |  Find (998)  |  First (1283)  |  Follow (378)  |  Forehead (2)  |  Foreign (45)  |  Forest (150)  |  Formula (98)  |  Full (66)  |  Function (228)  |  Genius (284)  |  Give (202)  |  Greatly (12)  |  Hair (25)  |  Half (56)  |  Hand (143)  |  Hear (139)  |  Help (105)  |  Hew (3)  |  Ideal (99)  |  Independent (67)  |  Intention (46)  |  Journal (30)  |  Ernst Eduard Kummer (3)  |  Laboratory (196)  |  Last (426)  |  Late (118)  |  Lead (384)  |  Learn (629)  |  Learned (235)  |  Lecture (105)  |  Life (1795)  |  Likely (34)  |  Listen (73)  |  Listener (7)  |  Little (707)  |  Man (2251)  |  Manifest (21)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Mean (809)  |  Mere (84)  |  Mind (1338)  |  Mode (41)  |  Moment (253)  |  More (2559)  |  Most (1731)  |  Must (1526)  |  New (1216)  |  Next (236)  |  Notable (5)  |  Number (699)  |  Oblivion (10)  |  Often (106)  |  Other (2236)  |  Outcome (13)  |  Oversight (4)  |  Pass (238)  |  Path (144)  |  Pause (6)  |  Peculiar (113)  |  Pioneer (33)  |  Place (177)  |  Pleasure (178)  |  Point (580)  |  Possible (552)  |  Principle (507)  |  Professor (128)  |  Quality (135)  |  Rapidly (66)  |  Read (287)  |  Real (149)  |  Reason (744)  |  Reasoning (207)  |  Report (38)  |  Reproduce (11)  |  Rest (280)  |  Result (677)  |  Right (452)  |  Rugged (7)  |  Rum (3)  |  Same (157)  |  Satisfaction (74)  |  Say (984)  |  See (1081)  |  Seem (145)  |  Several (32)  |  Small (477)  |  Smith (3)  |  Society (326)  |  Something (719)  |  Soon (186)  |  Sound (183)  |  Spring (133)  |  Start (221)  |  Stop (80)  |  Subject (521)  |  Subsequently (2)  |  James Joseph Sylvester (58)  |  Synopsis (2)  |  Talk (100)  |  Term (349)  |  Textbook (36)  |  Theory (970)  |  Theory Of Numbers (7)  |  Think (1086)  |  Thought (953)  |  Trouble (107)  |  Understand (606)  |  Understanding (513)  |  Universe (857)  |  Way (1217)  |  Weakness (48)  |  White (127)  |  Work (1351)  |  Worry (33)  |  Wrinkle (4)  |  Write (230)  |  Writing (189)

If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.
In When You Were a Tadpole and I Was a Fish: And Other Speculations About This and That (), 124.
Science quotes on:  |  All (4108)  |  Being (1278)  |  Continuance (2)  |  Continue (165)  |  Disappear (82)  |  Disappearance (28)  |  Exist (443)  |  Existence (456)  |  Huge (25)  |  Mathematics (1328)  |  Number (699)  |  Object (422)  |  Prime Number (5)  |  Proof (287)  |  Remain (349)  |  Remaining (45)  |  Sense (770)  |  Sentient (7)  |  Talk (100)  |  Theorem (112)  |  Universe (857)  |  Write (230)  |  Writing (189)

In a great number of the cosmogonic myths the world is said to have developed from a great water, which was the prime matter. In many cases, as for instance in an Indian myth, this prime matter is indicated as a solution, out of which the solid earth crystallized out.
In Theories of Solutions (1912), 1.
Science quotes on:  |  Cosmogony (3)  |  Crystal (68)  |  Develop (268)  |  Development (422)  |  Earth (996)  |  Great (1574)  |  Indian (27)  |  Matter (798)  |  Myth (56)  |  Number (699)  |  Origin Of Earth (9)  |  Solid (116)  |  Solution (267)  |  Water (481)  |  World (1774)

In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 143.
Science quotes on:  |  Age (499)  |  All (4108)  |  Answer (366)  |  Beginning (305)  |  Being (1278)  |  Binomial (6)  |  Calculus (65)  |  Color (137)  |  Differentiation (25)  |  Dignity (42)  |  Direct (225)  |  Distance (161)  |  Earth (996)  |  Entrance (15)  |  Estimate (57)  |  Fluxion (7)  |  Force (487)  |  Gravity (132)  |  Invention (369)  |  Inverse Square Law (4)  |  Johannes Kepler (91)  |  Law Of Gravity (15)  |  Method (505)  |  Mind (1338)  |  Moon (237)  |  More (2559)  |  Must (1526)  |  Nearly (137)  |  Next (236)  |  Orb (20)  |  Orbit (81)  |  Philosophy (380)  |  Plague (41)  |  Planet (356)  |  Proportion (136)  |  Revolve (25)  |  Rule (294)  |  Series (149)  |  Sphere (116)  |  Square (70)  |  Surface (209)  |  Surface Of The Earth (36)  |  Tangent (6)  |  Theory (970)  |  Think (1086)  |  Time (1877)  |  Two (937)  |  Year (933)

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)  |  Mathematician (387)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1328)  |  Mere (84)  |  Modern (385)  |  Never (1087)  |  Peculiarly (4)  |  Power (746)  |  Present (619)  |  Prevail (46)  |  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)

The primes are the raw material out of which we have to build arithmetic, and Euclid’s theorem assures us that we have plenty of material for the task.
In A Mathematician's Apology (1940, 2012), 99.
Science quotes on:  |   (2863)  |  Arithmetic (136)  |  Assurance (17)  |  Build (204)  |  Euclid (54)  |  Material (353)  |  Raw (28)  |  Task (147)  |  Theorem (112)

The pulse of a newborn during the neonatal period is very rapid … the pulse of old people is rather slow … the pulse is fullest and strongest in the prime years of youth.
As quoted in Fred Rosner, The Medical Legacy of Moses Maimonides (1998), 51.
Science quotes on:  |  Baby (28)  |  Newborn (5)  |  Old (481)  |  People (1005)  |  Period (198)  |  Pulse (20)  |  Rapid (33)  |  Slow (101)  |  Strongest (38)  |  Year (933)  |  Youth (101)

To look backward for a while is to refresh the eye, to restore it, and to render it more fit for its prime function of looking forward.
…...
Science quotes on:  |  Eye (419)  |  Fit (134)  |  Forward (102)  |  Function (228)  |  Look (582)  |  Looking (189)  |  More (2559)  |  Refresh (4)  |  Render (93)  |  Restore (8)

Whoever … proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured.
In J. Heidrich (ed.), 'Von Menschlicher Proportion', Albrecht Dürer’s Schriftlicher Nachlass (1920), 270. From the original German: “Welcher aber … durch die Geometria sein Ding beweist und die gründliche Wahrheit anzeigt, dem soll alle Welt glauben. Denn da ist man gefangen.”
Science quotes on:  |  All (4108)  |  Belief (578)  |  Capture (10)  |  Demonstrate (76)  |  Geometry (255)  |  Point (580)  |  Prove (250)  |  Truth (1057)  |  Whoever (42)  |  World (1774)


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 |

- 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



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