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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Precise Quotes (30 quotes)

A precisian professor had the habit of saying: “… quartic polynomial ax4+bx3+cx2+dx+e, where e need not be the base of the natural logarithms.”
Given, without citation, in A Mathematician’s Miscellany (1953), reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 60. [Note: a precisian is a rigidly precise or punctilious person. —Webmaster]
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As for “Don’t be evil,” we have tried to define precisely what it means to be a force for good—always do the right, ethical thing. Ultimately, “Don’t be evil” seems the easiest way to summarize it.
From interview, 'Google Guys', Playboy (Sep 2004).
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Careful and correct use of language is a powerful aid to straight thinking, for putting into words precisely what we mean necessitates getting our own minds quite clear on what we mean.
In The Art of Scientific Investigation (1950,1957), 91.
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Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.
In 'The Future of Data Analysis', Annals of Mathematical Statistics (1962), 33, No. 1, 13-14.
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Here I am at the limit which God and nature has assigned to my individuality. I am compelled to depend upon word, language and image in the most precise sense, and am wholly unable to operate in any manner whatever with symbols and numbers which are easily intelligible to the most highly gifted minds.
In Letter to Naumann (1826), in Vogel, Goethe's Selbstzeugnisse (1903), 56.
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I found out that the main ability to have was a visual, and also an almost tactile, way to imagine the physical situations, rather than a merely logical picture of the problems. … Very soon I discovered that if one gets a feeling for no more than a dozen … radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships.
In Adventures of a Mathematician (1976), 147.
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It is difficult even to attach a precise meaning to the term “scientific truth.” So different is the meaning of the word “truth” according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. “Religious truth” conveys nothing clear to me at all.
From 'Scientific Truth' in Essays in Science (1934, 2004), 11.
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It is our great collective misfortune that the scientific community made its decisive diagnosis of the climate threat at the precise moment when an elite minority was enjoying more unfettered political, cultural, and intellectual power than at any point since the 1920s.
From This Changes Everything: Capitalism vs. the Climate (2014), 18.
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Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
From La Valeur de la Science (1904), 142, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La loi sort de l’expérience, mais elle n’en sort pas immédiatement. L’expérience est individuelle, la loi qu’on en tire est générale, l’expérience n’est qu’approchée, la loi est précise ou du moins prétend l’élre. L’expérience se fait dans des conditions toujours complexes, l’énoncé de la loi élimine ces complications. C’est ce qu’on appelle ‘corriger les erreurs systématiques’.”
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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.
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Mathematics as we practice it is much more formally complete and precise than other sciences, but it is much less formally complete and precise for its content than computer programs.
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.
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Nor do I know any study which can compete with mathematics in general in furnishing matter for severe and continued thought. Metaphysical problems may be even more difficult; but then they are far less definite, and, as they rarely lead to any precise conclusion, we miss the power of checking our own operations, and of discovering whether we are thinking and reasoning or merely fancying and dreaming.
In Conflict of Studies (1873), 13.
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Physiology is the basis of all medical improvement and in precise proportion as our survey of it becomes more accurate and extended, it is rendered more solid.
In 'An Inquiry, Analogical and Experimental, into the Different Electrical conditions of Arterial and Venous Blood', New Orleans Medical and Surgical Journal (1853-4), 10, 584-602 & 738-757. As cited in George B. Roth, 'Dr. John Gorrie—Inventor of Artificial Ice and Mechanical Refrigeration', The Scientific Monthly (May 1936) 42 No. 5, 464-469.
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Precise facts alone are worthy of science. They cast premature theories into oblivion.
From the French original, “Les faits précis sont seuls dignes de la science. Ils rejettent dans l’oubli les théories prématurées”, by F. Marguet, 'Les “Souvenirs entomologiques” de J.-H. Fabre', Revue des Deux Mondes (1910), 60, 870. As translated in Augustin Fabre, The Life of Jean Henri Fabre: The Entomologist, 1823-1910 (1921), 315. Marguet gives no source citation for quote. It might be synthesized by Marguet from the writings of Fabre, to represent Fabre’s work ethic. (Webmaster so far has not found a primary source for the French sentences as verbatim. Can you help?)
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Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations.
In Probability, Statistics, and Truth (1939), 1. In the 1957 edition, this was rewritten as, “Starting from statistical observations and applying to them a clear and precise concept of probability it is possible to arrive at conclusions which are just as reliable and “truth-full” and quite as practically useful as those obtained in any other exact science.”
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That the master manufacturer, by dividing the work to be executed into different processes, each requiring different degrees of skill or of force, can purchase precisely the precise quantity of both which is necessary for each process; whereas, if the whole work were executed by one workman, that person must possess sufficient skill to perform the most difficult, and sufficient strength to execute the most laborious, of the operations into which the art is divided.
In 'On the Division of Labour', Economy of Machinery and Manufactures (1st ed., 1832), chap. 18, 127.
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The axioms of geometry are—according to my way of thinking—not arbitrary, but sensible. statements, which are, in general, induced by space perception and are determined as to their precise content by expediency.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 142.
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The laboratory work was the province of Dr Searle, an explosive, bearded Nemesis who struck terror into my heart. If one made a blunder one was sent to ‘stand in the corner’ like a naughty child. He had no patience with the women students. He said they disturbed the magnetic equipment, and more than once I heard him shout ‘Go and take off your corsets!’ for most girls wore these garments then, and steel was beginning to replace whalebone as a stiffening agent. For all his eccentricities, he gave us excellent training in all types of precise measurement and in the correct handling of data.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 116.
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The method of scientific investigation is nothing but the expression of the necessary mode of working of the human mind. It is simply the mode at which all phenomena are reasoned about, rendered precise and exact.
In 'Method of Discovery', On Our Knowledge of the Causes of the Phenomena of Organic Nature (1863), 56. Also in excerpt collected in in Isabel S. Gordon and Sophie Sorkin (eds.), The Armchair Science Reader (1959), 263.
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The precise moment at which a great belief is doomed is easily recognizable; it is the moment when its value begins to be called into question.
From Psychologie des Foules (1895), 130. English text in The Crowd: A Study of the Popular Mind (1897), Book 2, Chap. 4, 143. Original French text: “Le jour précis où une grande croyance est marquée pour mourir est facile à reconnaître; c’est celui où sa valeur commence à être discutée.”
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The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. [But] precise language is not precise in any sense if you deal with the real objects of the world, and is overly pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.
Criticizing “overly pedantic” language in proposed textbooks for a modified arithmetic course for grades 1-8 in California schools. In article, 'New Textbooks for the ‘New’ Mathematics', Engineering and Science (Mar 1965), 28, No. 6. Collected in Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard Feynman (2008), 454. He was writing as a member of the California State Curriculum Committee
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The scientist explores the world of phenomena by successive approximations. He knows that his data are not precise and that his theories must always be tested. It is quite natural that he tends to develop healthy skepticism, suspended judgment, and disciplined imagination.
In Commencement Address, California Institute of Technology (10 Jun 1938), 'Experiment and Experience'. Collected in abridged form in The Huntington Library Quarterly (Apr 1939), 2, No. 3, 245
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There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.
In Pascal’s Pensées (1958), 3.
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Vagueness is very much more important in the theory of knowledge than you would judge it to be from the writings of most people. Everything is vague to a degree you do not realize till you have tried to make it precise, and everything precise is so remote from everything that we normally think, that you cannot for a moment suppose that is what we really mean when we say what we think.
In The Philosophy of Logical Atomism (1918, 1919), 2.
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We love to discover in the cosmos the geometrical forms that exist in the depths of our consciousness. The exactitude of the proportions of our monuments and the precision of our machines express a fundamental character of our mind. Geometry does not exist in the earthly world. It has originated in ourselves. The methods of nature are never so precise as those of man. We do not find in the universe the clearness and accuracy of our thought. We attempt, therefore, to abstract from the complexity of phenomena some simple systems whose components bear to one another certain relations susceptible of being described mathematically.
In Man the Unknown (1935), 8.
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Where, precisely, is the location of—a rainbow? In the air? In the eye? In between? Or somewhere else?
In 'Philosophy, Religion, and So Forth', A Voice Crying in the Wilderness (1989), 11.
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While the dogmatist is harmful, the sceptic is useless …; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying ‘I know this’, we ought to say ‘I more or less know something more or less like this’. … Knowledge in practical affairs has not the certainty or the precision of arithmetic.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 38-39.
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Why, it is asked, since the scientist, by means of classification and experiment, can predict the “action of the physical world, shall not the historian do as much for the moral world”! The analogy is false at many points; but the confusion arises chiefly from the assumption that the scientist can predict the action of the physical world. Certain conditions precisely given, the scientist can predict the result; he cannot say when or where in the future those conditions will obtain.
In 'A New Philosophy of History', The Dial (2 Sep 1915), 148. This is Becker’s review of a book by L. Cecil Jane, The Interpretation of History. Becker refutes Jane’s idea that the value of history lies in whether it consists in furnishing “some clue as to what the future will bring.”
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[Mathematics] has for its object the indirect measurement of magnitudes, and it proposes to determine magnitudes by each other, according to the precise relations which exist between them.
In The Positive Philosophy of Auguste Comte, translated by Harriet Martineau, (1896), Vol. 1, 40.
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~~[No source found]~~ There’s no sense in being precise when you don't even know what you're talking about.
Webmaster has looked for, but so far has been unable to find, a primary source with this wording. Please help if you can. Meanwhile it is included here to note its status.
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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
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- 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



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