Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index R > Category: Refer

Refer Quotes (13 quotes)

Confucius once said: “our greatest glory is not in never falling, but in getting up every time we do”. Scholars believe he was referring to roller coasters.
Anonymous
Science quotes on:  |  Belief (503)  |  Confucius (13)  |  Falling (6)  |  Get Up (5)  |  Glory (57)  |  Greatest (62)  |  Scholar (37)

Einstein’s space is no closer to reality than Van Gogh’s sky. The glory of science is not in a truth more absolute than the truth of Bach or Tolstoy, but in the act of creation itself. The scientist’s discoveries impose his own order on chaos, as the composer or painter imposes his; an order that always refers to limited aspects of reality, and is based on the observer's frame of reference, which differs from period to period as a Rembrandt nude differs from a nude by Manet.
In The Act of Creation (1964), 252.
Science quotes on:  |  Absolute (97)  |  Act (115)  |  Aspect (57)  |  Base (71)  |  Chaos (76)  |  Composer (6)  |  Creation (239)  |  Differ (22)  |  Discovery (676)  |  Albert Einstein (605)  |  Frame of Reference (4)  |  Glory (57)  |  Impose (22)  |  Limit (123)  |  Nude (3)  |  Observer (42)  |  Order (239)  |  Painter (20)  |  Period (64)  |  Reality (188)  |  Science (2043)  |  Scientist (519)  |  Sky (124)  |  Space (257)  |  Count Leo Tolstoy (16)  |  Truth (914)

Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid gave him the first idea. [“The anchor drops, the rushing keel is staid.”]
In Letters of Euler (1872), Vol. 1, 24.
Science quotes on:  |  Anchor (10)  |  Begin (106)  |  Drop (39)  |  Edition (5)  |  End (195)  |  Leonhard Euler (34)  |  First (313)  |  Give (200)  |  Idea (577)  |  Inform (16)  |  Keel (4)  |  Learn (281)  |  Line (89)  |  Mathematicians and Anecdotes (123)  |  Mechanic (23)  |  Memoir (11)  |  Page (27)  |  Question (404)  |  Repeat (40)  |  Rush (18)  |  Tell (110)  |  Verse (8)  |  Work (626)

I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
Science quotes on:  |  Absolute (97)  |  Accordingly (5)  |  Aesthetic (34)  |  Application (166)  |  Attainable (3)  |  Authority (65)  |  Beauty (239)  |  Best (172)  |  Both (81)  |  Case (98)  |  Certain (125)  |  Certainly (31)  |  Certainty (129)  |  Classical (16)  |  Compel (20)  |  Confine (24)  |  Conscious (43)  |  Course (83)  |  Decision (72)  |  Deduction (68)  |  Deeply (17)  |  Depend (87)  |  Dispute (22)  |  Education (333)  |  Effect (165)  |  Exception (39)  |  Exercise (64)  |  Experience (338)  |  Expression (104)  |  Extend (41)  |  Fact (725)  |  Far (154)  |  Fault (33)  |  Feel (165)  |  Find (405)  |  First (313)  |  Follow (123)  |  Form (308)  |  Genius (243)  |  Glance (19)  |  Grammar (13)  |  Grammatical (2)  |  Habit (107)  |  Happen (82)  |  Important (202)  |  Improve (54)  |  Inasmuch (5)  |  Inclined (12)  |  Independent (65)  |  Individual (215)  |  Indolence (7)  |  Inevitably (6)  |  Intelligence (165)  |  Intend (16)  |  Judgment (98)  |  Language (217)  |  Legitimate (14)  |  List (10)  |  Logical (54)  |  Long (172)  |  Mathematics (1149)  |  Medical (24)  |  Often (106)  |  Organization (84)  |  Part (220)  |  Pass (91)  |  Philological (3)  |  Place (174)  |  Position (75)  |  Possible (155)  |  Premise (25)  |  Proportion (70)  |  Question (404)  |  Range (57)  |  Reality (188)  |  Reason (454)  |  Recognize (66)  |  Rely (11)  |  Remedy (54)  |  Representative (13)  |  Rule (173)  |  Sadness (34)  |  School (117)  |  Science (2043)  |  Scientific (232)  |  Seldom (28)  |  Strict (16)  |  Strictly (13)  |  Strike (39)  |  Student (201)  |  Study (461)  |  Subsequent (19)  |  Supply (46)  |  System (191)  |  Teacher (119)  |  Thought (536)  |  Traceable (2)  |  Training (64)  |  Trust (49)  |  Universal Law (3)  |  Vagueness (10)  |  Value Of Mathematics (55)  |  Whole (189)

I never could make out what those damned dots meant.
Referring to decimal points. “But this was surely only to tease.” Quoted in W.S. Churchill, Lord Randolph Churchill (1906), Vol. 2, 184.
Science quotes on:  |  Damn (12)  |  Decimal (14)  |  Dot (11)  |  Mean (101)  |  Point (122)

In recent years it has become impossible to talk about man’s relation to nature without referring to “ecology” … such leading scientists in this area as Rachel Carson, Barry Commoner, Eugene Odum, Paul Ehrlich and others, have become our new delphic voices … so influential has their branch of science become that our time might well be called the “Age of Ecology”.
In opening paragraph of Preface, Nature’s Economy: A History of Ecological Ideas (1994), 14.
Science quotes on:  |  Age (174)  |  Branch (102)  |  Call (127)  |  Rachel Carson (42)  |  Barry Commoner (10)  |  Delphic (3)  |  Ecology (69)  |  Paul Ehrlich (8)  |  Impossible (108)  |  Influential (4)  |  Leading (17)  |  Nature (1211)  |  Eugene Pleasants Odum (3)  |  Relation (149)  |  Science (2043)  |  Scientist (519)  |  Talk (99)  |  Time (594)  |  Voice (50)

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 Ιdouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
Science quotes on:  |  Accomplishment (79)  |  Acquisition (41)  |  Active (25)  |  Admirably (3)  |  Advance (162)  |  Altitude (4)  |  Apparatus (37)  |  Application (166)  |  Ascension (3)  |  Await (5)  |  Circle (55)  |  Curvature (4)  |  Earth (635)  |  Everything (180)  |  Evolute (2)  |  Find (405)  |  Fit (48)  |  Function (128)  |  Heaven (151)  |  Impressed (15)  |  Industry (108)  |  Intense (19)  |  Latitude (4)  |  Line (89)  |  Logarithmic (5)  |  Longitude (5)  |  Machine (157)  |  Magician (13)  |  Magnitude (41)  |  Manifold (9)  |  Marvellous (9)  |  Master (93)  |  Mathematician (364)  |  Mathematics (1149)  |  Means (171)  |  Multitude (20)  |  Natural (167)  |  Nature Of Mathematics (77)  |  Network (13)  |  Normal (27)  |  Nothing (385)  |  Numerous (29)  |  Outside (48)  |  Prepare (34)  |  Really (78)  |  Realm (54)  |  Recall (10)  |  Right (196)  |  Show (90)  |  Skilful (2)  |  Skill (65)  |  Spin (15)  |  Sufficient (40)  |  System (191)  |  Tangent (5)  |  Treasure (45)  |  Trigonometry (6)  |  True (201)  |  Witness (32)

Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics.
In 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97.
Science quotes on:  |  Arbiter (5)  |  Both (81)  |  Claim (70)  |  Discoverer (15)  |  Explain (105)  |  Hypothesis (249)  |  Induction (59)  |  Judge (61)  |  Law (513)  |  Mathematics (1149)  |  Nature Of Mathematics (77)  |  Rule (173)  |  Sanction (3)  |  Theory (690)

Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.
With co-author James R. Newman, in Mathematics and the Imagination (1940), 359.
Science quotes on:  |  Actually (27)  |  Beyond (104)  |  Common Sense (126)  |  Erroneous (4)  |  Find (405)  |  Frightening (3)  |  Imagination (268)  |  Intuition (57)  |  Mathematics (1149)  |  Ordinary (71)  |  Penetrate (29)  |  Point Of View (41)  |  Science (2043)  |  Sense (315)  |  Strange (94)  |  Subject (235)  |  Transcend (17)  |  Veritable (4)

Number, place, and combination … the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.
In Philosophical Magazine (1844), 84, 285; Collected Mathematical Papers, Vol. 1, 91.
Science quotes on:  |  Admit (44)  |  Combination (91)  |  Definitions and Objects of Mathematics (31)  |  Distinct (46)  |  Idea (577)  |  Intersect (4)  |  Mathematics (1149)  |  Number (276)  |  Place (174)  |  Sphere (58)  |  Thought (536)

Science is always discovering odd scraps of magical wisdom and making a tremendous fuss about its cleverness.
Referring to Freudian theories.
The Confessions of Aleister Crowley, ch. 14 (1929, rev 1970).
Science quotes on:  |  Cleverness (12)  |  Discover (196)  |  Freudian (4)  |  Fuss (4)  |  Magic (77)  |  Odd (13)  |  Science (2043)  |  Scrap (2)  |  Theory (690)  |  Tremendous (17)  |  Wisdom (180)

The position in which we are now is a very strange one which in general political life never happened. Namely, the thing that I refer to is this: To have security against atomic bombs and against the other biological weapons, we have to prevent war, for if we cannot prevent war every nation will use every means that is at their disposal; and in spite of all promises they make, they will do it.
…...
Science quotes on:  |  Disposal (5)  |  General (156)  |  Happen (82)  |  Life (1124)  |  Means (171)  |  Namely (11)  |  Nation (132)  |  Political (36)  |  Position (75)  |  Prevent (40)  |  Promise (38)  |  Security (33)  |  Spite (13)  |  Strange (94)  |  War (161)

There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to some one or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order.
Arithmetic has for its object the properties of number in the abstract. In algebra, viewed as a science of operations, order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.
In 'A Probationary Lecture on Geometry, York British Association Report (1844), Part 2; Collected Mathematical Papers, Vol. 2, 5.
Science quotes on:  |  Abstract (79)  |  Admit (44)  |  Algebra (92)  |  Arithmetic (115)  |  Body (243)  |  Business (84)  |  Cardinal (6)  |  Combine (34)  |  Definitions and Objects of Mathematics (31)  |  Evolution (533)  |  Exist (147)  |  Geometry (215)  |  Idea (577)  |  Mathematics (1149)  |  Notion (57)  |  Number (276)  |  Object (169)  |  Operation (118)  |  Order (239)  |  Pervade (9)  |  Predominate (5)  |  Property (123)  |  Rule (173)  |  Say (228)  |  Science (2043)  |  Space (257)  |  Sphere (58)  |  Thought (536)  |  Truth (914)  |  View (171)  |  Whole (189)


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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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.