“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.”

The Mathematical Foundations of Quantum Theory (1978)

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Paul Dirac23

theoretical physicist 1902–1984

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“The central idea of the philosophy of behaviorism, that behavior and the mind have an entirely materialist basis subject to experimental analysis, is fundamentally sound.”

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“If I have had any success in mathematical physics, it is, I think, because I have been able to dodge mathematical difficulties.”

Josiah Willard Gibbs (1839–1903) physicist

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“It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power”

Paul Dirac (1902–1984) theoretical physicist

The Evolution of the Physicist's Picture of Nature (1963)
Context: It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

“The idealistic tinge in my conception of the physical world arose out of mathematical researches on the relativity theory. In so far as I had any earlier philosophical views, they were of an entirely different complexion.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

The Nature of the Physical World (1928) Context: The idealistic tinge in my conception of the physical world arose out of mathematical researches on the relativity theory. In so far as I had any earlier philosophical views, they were of an entirely different complexion. From the beginning I have been doubtful whether it was desirable for a scientist to venture so far into extra-scientific territory. The primary justification for such an expedition is that it may afford a better view of his own scientific domain. Preface http://www-groups.dcs.st-and.ac.uk/~history/Extras/Eddington_Gifford.html

“Since sounds have no natural connection with our ideas … the doubtfulness and uncertainty of their signification … has its cause more in the ideas they stand for than in any incapacity there is in one sound more than another to signify any idea.”

John Locke book An Essay Concerning Human Understanding

Book III, Ch. 9, sec. 4
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“Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.”

George Pólya (1887–1985) Hungarian mathematician

[Jon Fripp, Michael Fripp, Deborah Fripp, Speaking of Science: Notable Quotes on Science, Engineering, and the Environment, https://books.google.com/books?id=44ihCUS1XQMC&pg=PA45, 2000, Newnes, 978-1-878707-51-2, 45]

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Hermann Rauschning (1887–1982) German politician

Source: The Revolution of Nihilism: Warning to the West (1939), p. 253

“If the establishment of the thesis 'mathematics is ontology' is the basis of this book, it is in no way its goal.”

Alain Badiou (1937) French writer and philosopher

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“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.”

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