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The modern scientific worldview with all its hope for clarity and precision, has a "flipside," a complementary set of views which it generates as its train. And this is its misology, sophistry, its abandonment of rationality in the world of human significance. There is thus a quite literal type of schizophrenia in the world bequeathed to us by the Cartesians. It is, on the one hand, hyper-rational; it seeks to extend the purview of mathematical physics throughout the universe. On the other hand, it relegates the world in which the physicist himself dwells, the unique world of humanity and its communities, to the junkpile of the irrational. We who know so much are prohibited from knowing ourselves.
David Roochnik
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In short, I do not write for mathematicians, nor as a mathematician, but as an economist wishing to convince other economists that their science can only be satisfactorily treated on an explicitly mathematical basis.
William Stanley Jevons
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The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.
Ronald Fisher
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[Einstein's cosmological constant] is a name without any meaning.... We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality.
Willem de Sitter
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Do you know what the mathematical expression is for longing?... The negative numbers. The formalization of the feeling that you are missing something.
Peter Høeg
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The principle of deduction is, that things which agree with the same thing agree with one another. The principle of induction is, that in the same circumstances and in the same substances, from the same causes the same effects will follow. The mathematical and metaphysical sciences are founded on deduction; the physical sciences rest on induction.
William Fleming
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Treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis.
Henri Poincaré
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This book... is primarily and essentially an account of the discovery or invention of mathematical concepts, and the historical material is... divided and classified, neither chronologically nor biographically, but philosophically.
George Frederick James Temple
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The illiterate expression 'given data' constantly recurs in Lange. It appears to have an irresistable attraction to mathematical economists because it doubly assures them that they know what they do not know. It seems to bewitch them into making assertions about the real world for which they have no empirical justification whatever.
Friedrich Hayek
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Heisenberg now approached the problem from a new philosophical angle. He discarded all models, pictures and parables, and made a clear distinction between sure knowledge we gain from observation of nature and the conjectural knowledge we introduce when we use models, pictures and parables. Sure knowledge... can only be numerical, so that Heisenberg's results were inevitably mathematical in form, and could not disclose anything about the true nature of physical properties or entities.
James Jeans
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The concept of 'number' in its most elementary sense as the signless integer appears to be an immediate abstraction from quantitative reality subjected to processes of counting and measurement. Vulgar fractions arise from division of a quantity into equal parts. But in what sense is zero a number? Are there negative numbers? Are there numbers corresponding to incommensurable ratios? Each question requires for its solution a fresh exercise of that kind of creative imagination which we call mathematical abstraction.
George Frederick James Temple
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Unlike physics, for example, such parts of the bare bones of economic theory as are expressible in mathematical form are extremely easy compared with the economic interpretation of the complex and incompletely known facts of experience, and lead one a very little way towards establishing useful results.
John Maynard Keynes
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Don't talk to me of your Archimedes' lever. He was an absent-minded person with a mathematical imagination. Mathematics commands all my respect, but I have no use for engines. Give me the right word and the right accent and I will move the world.
Joseph Conrad
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A good deal of my research work in physics has consisted in not setting out to solve some particular problems, but simply examining mathematical quantities of a kind that physicists use and trying to get them together in an interesting way regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later that the work does have an application. Then one has had good luck.
Paul Dirac
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There are, roughly speaking, two kinds of mathematical creativity. One, akin to conquering a mountain peak, consists of solving a problem which has remained unsolved for a long time and has commanded the attention of many mathematicians. The other is exploring new territory.
Mark Kac
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The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space.
Charles Davies (professor)
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Experience has taught most mathematicians that much that looks solid and satisfactory to one mathematical generation stands a fair chance of dissolving into cobwebs under the steadier scrutiny of the next...
Eric Temple Bell
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Daniel Bernoulli has been called the father of mathematical physics.
Eric Temple Bell
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For such [mathematical] exercises of the mind pursued with determination render it averse from poetry, and all the imaginative study of human affairs, preclude it from appreciating all the loveliness of life, leave it untouched by the sanguine emotions, and quite indifferent to the glamour of the arts, or to the divine gift of taste.
Stephen Coleridge
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The belief that the underlying order of the world can be expressed in mathematical form lies at the very heart of science. So deep does this belief run that a branch of science is considered not to be properly understood until it can be cast in mathematics.
Paul Davies
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The potential usefulness of a mathematical concept or technique in helping to advance scientific understanding has very little to do with what one can foresee before that concept or technique has appeared.
Saunders Mac Lane
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The Universe can be best pictured, although still very imperfectly and inadequately, as consisting of pure thought, the thought of what, for want of a wider word, we must describe as a mathematical thinker.
Robert Jastrow
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There is, strictly, no such thing as mathematical proof; that we can::: do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lectures, devices to stimulate the imagination of pupils.
G. H. Hardy
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We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.
Steven Weinberg
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To my view there are two methods of research, the apparatus and the calculation. Whoever prefers the first method is an experimenter; otherwise, he is a mathematical physicist. Both of them set up theories and hypotheses...
Wilhelm Röntgen
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