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I had become interested in economics, an interest that was transformed into a lifetime dedication when I met with the mathematical theory of general economic equilibrium.
Gérard Debreu
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Virtually every discipline and endeavor is presently under a naturalistic pall.
William A. Dembski
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On foundations we believe in the reality of mathematics, but of course when philosophers attack us with their paradoxes we rush to hide behind formalism and say: "Mathematics is just a combination of meaningless symbols..."
Jean Dieudonné
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Authors who discover formulas should not rush into print. Even as in business and marriage, in mathematics not all that is true needs to be published.
Underwood Dudley
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It is easy to lie with statistics. It is hard to tell the truth without it.
Andrejs Dunkels
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Sane judgment abhors nothing so much as a picture perpetrated with no technical knowledge, although with plenty of care and diligence. Now the sole reason why painters of this sort are not aware of their own error is that they have not learnt Geometry, without which no one can either be or become an absolute artist; but the blame for this should be laid upon their masters, who are themselves ignorant of this art.
Albrecht Dürer
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A physicist builds theories with mathematical materials, because the mathematics enables him to imagine more than he can clearly think.
Freeman Dyson
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As a boy of six I could understand the proof of a mathematical theorem more readily than that meat had to be cut with one's knife, not one's fork.
Ferdinand Eisenstein
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Chaos cuts with two edges. We have seen how it is impossible to retrieve past history from current observations. We will now show that it is impossible to predict future states from the current observations.
Ivar Ekeland
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To have a good memory the first thing you have to do is to trust your memory.
Paul Sophus Epstein
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God created two acts of folly. First, He created the Universe in a Big Bang. Second, He was negligent enough to leave behind evidence for this act, in the form of the microwave radiation.
Paul Erdős
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It will seem not a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impressions on the senses.
Leonhard Euler
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Alekhine is a poet who creates a work of art out of something that would hardly inspire another man to send home a picture post card.
Max Euwe
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All possible "definitions" of probability fall short of the actual practice.
William Feller
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We have found a beautiful and most general proposition, namely, that every integer is either a square, or the sum of two, three or at most four squares. This theorem depends on some of the most recondite mysteries of number, and is not possible to present its proof on the margin of this page.
Pierre de Fermat
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Particulars are frequently fallible, but universals never. Occult philosophy lays bare Nature in her complete nakedness, and alone contemplates the wisdom of universals by the eyes of intelligence. Accustomed to partake of the rivers which flow from the Fountain of Life, it is unacquainted with grossness and with clouded waters.
Robert Fludd
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A very extensive class of phenomena exists, not produced by mechanical forces, but resulting simply from the presence and accumulation of heat. This part of natural philosophy cannot be connected with dynamical theories, it has principles peculiar to itself, and is founded on a method similar to that of other exact sciences.
Joseph Fourier
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One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance.
Gottlob Frege
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Fundamental definitions do not arise at the start but at the end of the exploration, because in order to define a thing you must know what it is and what it is good for.
Hans Freudenthal
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[Mathematics] is the work of the human mind, which is destined rather to study than to know, to seek the truth rather than to find it.
Évariste Galois
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The computers are not replacing mathematicians; they are breeding them.
Martin Gardner
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Either mathematics is too big for the human mind, or the human mind is more than a machine.
Kurt Gödel
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A teacher who is not always thinking about solving problems — ones he does not know the answer to — is psychologically simply not prepared to teach problem solving to his students.
Paul Halmos
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The highest reach of human science is the scientific recognition of human ignorance...
William Rowan Hamilton
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Some people believe that a theorem is proved when a logically correct proof is given; but some people believe a theorem is proved only when the student sees why it is inevitably true. The author tends to belong to this second school of thought.
Richard Hamming
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