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: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index I > Category: Indefinable

Indefinable Quotes (5 quotes)

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 (680)  |  Creative (144)  |  Feeling (259)  |  Fitness (9)  |  Generality (45)  |  Guide (107)  |  Inspire (58)  |  Mathematician (407)  |  Mathematics (1395)  |  Past (355)  |  Prospect (31)  |  Sense (785)  |  Simplicity (175)  |  Symmetry (44)  |  Thing (1914)  |  Ultimate (152)  |  Usefulness (92)

Symbolism is useful because it makes things difficult. Now in the beginning everything is self-evident, and it is hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious. … Thus the whole of Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions.
In International Monthly (1901), 4, 85-86.
Science quotes on:  |  Algebra (117)  |  Arithmetic (144)  |  Begin (275)  |  Beginning (312)  |  Correct (95)  |  Difficult (263)  |  Enemy (86)  |  Everything (489)  |  Evident (92)  |  Follow (389)  |  Hard (246)  |  Invent (57)  |  Mathematics As A Language (20)  |  Must (1525)  |  New (1273)  |  Nothing (1000)  |  Notion (120)  |  Obvious (128)  |  Obviousness (3)  |  Proposition (126)  |  Require (229)  |  See (1094)  |  Self (268)  |  Self-Evident (22)  |  Show (353)  |  Symbolism (5)  |  Thing (1914)  |  Useful (260)  |  Whole (756)

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 (49)  |  Answer (389)  |  Apodictic (3)  |  Certainty (180)  |  Character (259)  |  Characteristic (154)  |  Clear (111)  |  Completeness (19)  |  Concept (242)  |  Conclusion (266)  |  Correctness (12)  |  Deal (192)  |  Definition (238)  |  Distinctive (25)  |  Do (1905)  |  Due (143)  |  Idea (881)  |  Involve (93)  |  Involved (90)  |  Mathematician (407)  |  Mathematics (1395)  |  Mode (43)  |  Mysterious (83)  |  Nature Of Mathematics (80)  |  Other (2233)  |  Precision (72)  |  Quality (139)  |  Ratiocination (4)  |  Sharpness (9)  |  Special (188)  |  Term (357)  |  Thought (995)  |  Trick (36)

The edge of the sea is a strange and beautiful place. All through the long history of Earth it has been an area of unrest where waves have broken heavily against the land, where the tides have pressed forward over the continents, receded, and then returned. For no two successive days is the shore line precisely the same. Not only do the tides advance and retreat in their eternal rhythms, but the level of the sea itself is never at rest. It rises or falls as the glaciers melt or grow, as the floor of the deep ocean basins shifts under its increasing load of sediments, or as the Earth’s crust along the continental margins warps up or down in adjustment to strain and tension. Today a little more land may belong to the sea, tomorrow a little less. Always the edge of the sea remains an elusive and indefinable boundary.
Opening paragraph in The Edge of the Sea (1955), 1.
Science quotes on:  |  Adjustment (21)  |  Advance (298)  |  Against (332)  |  Area (33)  |  Basin (2)  |  Beautiful (271)  |  Belong (168)  |  Boundary (55)  |  Break (109)  |  Broken (56)  |  Continent (79)  |  Continental (2)  |  Crust (43)  |  Deep (241)  |  Do (1905)  |  Down (455)  |  Earth (1076)  |  Edge (51)  |  Elusive (8)  |  Eternal (113)  |  Fall (243)  |  Floor (21)  |  Forward (104)  |  Glacier (17)  |  Grow (247)  |  Heavily (14)  |  History (716)  |  History Of Earth (2)  |  Increase (225)  |  Land (131)  |  Less (105)  |  Level (69)  |  Line (100)  |  Little (717)  |  Load (12)  |  Long (778)  |  Margin (6)  |  Melt (16)  |  More (2558)  |  Never (1089)  |  Ocean (216)  |  Place (192)  |  Precisely (93)  |  Press (21)  |  Recede (11)  |  Remain (355)  |  Rest (287)  |  Retreat (13)  |  Return (133)  |  Rhythm (21)  |  Rise (169)  |  Same (166)  |  Sea (326)  |  Sediment (9)  |  Shift (45)  |  Shore (25)  |  Strain (13)  |  Strange (160)  |  Successive (73)  |  Tension (24)  |  Through (846)  |  Tide (37)  |  Today (321)  |  Tomorrow (63)  |  Two (936)  |  Unrest (2)  |  Warp (7)  |  Wave (112)

When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
Science and Method (1914 edition, reprint 2003), 126.
Science quotes on:  |  Constitute (99)  |  Correct (95)  |  Demonstration (120)  |  Elementary (98)  |  Intuition (82)  |  Logic (311)  |  Logician (18)  |  Look (584)  |  Must (1525)  |  Operation (221)  |  Operations (107)  |  Possession (68)  |  Pure (299)  |  Reality (274)  |  Resolve (43)  |  Something (718)  |  Unity (81)  |  View (496)  |  Whole (756)  |  Will (2350)


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.