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Mathematical theory, tested in practice and constantly retested, is a valuable aid to play. Mathematics alone will blind you and let others rob you.
--
Chapter 9, Who Got Game, p. 279

 

Aaron C. Brown

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Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

 

David Hilbert

 

Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.

 

David Deutsch

 

Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.

 

Albert Einstein

 

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them.

 

Paul Dirac

 

Rate of change is this mathematics known as Calculus. ... Now I hope you understand this, because I've never been able to make head nor tail of it. It must be some sort of a Black Magic operation, started out by the Luce cult — some immoral people who are operating up in New York City, Rockefeller Plaza — been thoroughly condemned by the whole society. Anyway, their rate-of-change theory — I've never seen any use for that mathematics, by the way — I love that mathematics, because it — I asked an engineer, one time, who was in his 6th year of engineering, if he'd ever used Calculus, and he told me yeah, once, once I did, he said. When did you use it? And he said I used it once. Let me see, what did you use it on? Oh yeah. Something on the rate-of-change of steam particles in boilers. And then we went out and tested it and found the answer was wrong.

 

L. Ron Hubbard