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[The Riemann] zeros did not appear to be scattered at random. Riemann's calculations indicated that they were lining up as if along some mystical ley line running through the landscape.
Marcus du Sautoy
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The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.
Claude Elwood Shannon
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Yes, but when I discovered it, it stayed discovered.
Lawrence Shepp
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One thing at least they have not forgotten, that geometry is nothing if it be not rigorous, and that the whole educational value of the study is lost, if strictness of demonstration be trifled with. The methods of Euclid are, by almost universal consent, unexceptionable in point of rigor. Opening Address by the President, Section A
Henry John Stephen Smith
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It has always puzzled me that so many religious people have taken it for granted that God favors those who believe in him. Isn't it possible that the actual God is a scientific God who has little patience with beliefs founded on faith rather than evidence?
Raymond Smullyan
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That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can.
G. Spencer-Brown
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I am almost inclined to coin a word and call the appearance fluorescence, from fluor-spar, as the analogous term opalescence is derived from the name of a mineral.
Sir George Stokes, 1st Baronet
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Perhaps I may without immodesty lay claim to the appellation of Mathematical Adam, as I believe that I have given more names (passed into general circulation) of the creatures of the mathematical reason than all the other mathematicians of the age combined.
James Joseph Sylvester
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To [the scientific man] the discovery of a new law of nature, or even of a new experimental fact, or the invention of a novel mathematical method, no matter who has been the first to reach it, is an event of an order altogether different from, and higher than, those which are so profusely chronicled in the newspapers.
Peter Guthrie Tait
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Just as there is an applied mathematics of games, genetics, and mechanics, so there should be an applied mathematics (at least in terms of concepts, perhaps with techniques and operations) of the applications of mathematics. When there is, mathematicians will be able to teach the applications of mathematics.
John Tukey
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It is not so much whether a theorem is useful that matters, but how elegant it is.
Stanislaw Ulam
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The conclusion seems inescapable: that formal logic has to be taken over by the mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so.
Oswald Veblen
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With the extremely small or the extremely large, with inconceivably brief or extended phenomena, science has a difficult time. It is by no means clear that our present concepts or even our existing language is suitable for these ranges.
Warren Weaver
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When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.
André Weil
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As far as I can see, all a priori statements in physics have their origin in symmetry.
Hermann Weyl
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Logic is the olive branch from the old to the young, the wand which in the hands of youth has the magic property of creating science.
Alfred North Whitehead
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It is possible to believe in progress as a fact without believing in progress as an ethical principle; but in the catechism of many Americans, the one goes with the other.
Norbert Wiener
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It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature.
Eugene Wigner
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Mathematics... is a bit like discovering oil... But mathematics has one great advantage over oil, in that no one has yet... found a way that you can keep using the same oil forever.
Andrew Wiles
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Very belatedly in 1947, Darwin [Sir Charles Darwin, great-grandson of the famous Charles Darwin] agreed to set up a very small electronics group [...] It was not easy to have the imagination to foresee that computers were to become one of the most important developments of the century.
James H. Wilkinson
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Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today.
Stephen Wolfram
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If all the theories pertinent to systems engineering could be discussed within a common framework by means of a standard set of nomenclature and definitions, many separate courses might not be required.
A. Wayne Wymore
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Mathematics is infinitely wide, while the language that describes it is finite. It follows from the pigeonhole principle that there exist distinct concepts that are referred to by the same name. Mathematics is also infinitely deep and sometimes entirely different concepts turn out to be intimately and profoundly related.
Doron Zeilberger
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Molecular dynamics is not primarily about making movies of molecules. More often it is about developing quantitative predictions of molecular size and shape, flexibilities, interactions with other molecules, behavior under pressure, and the relative frequency of one state or conformation compared to another.
Ben Leimkuhler
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In the history of the concept of number, number has been adjective (three cows, three monads) and noun (three, pure and simple), and now.... number seems to be more like a verb (to triple).
Barry Mazur
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Josiah Royce
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