From Paul Dirac, 1938:
Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.
Great quote. I’ve been cultivating an idea that pure math (i.e., set theory) is intimately connected to the rules of Nature. We consider the axioms of set theory to be self-evident as they make sense in our universe. However, if our universe had different rules, our math and logic would change as well.
I am very curious about the source of this quote. If it’s a book, and it’s content is understandable to a non-physicist, I wanna read it!
The quote comes from The Relation between Mathematics and Physics.
Reminds me of Wigner’s Paper on the subject of Math and Science.
Interesting enough that Dirac married Wigner’s sister.
I’ve been reading Philip Davis and Reuben Hersh’s The Mathematical Experience and have just come across some passages about this type of stuff – contrasting Platonism, that the ideas of mathematics are truths of the universe, with formalism, the treatment of mathematics as consistent logical manipulations and for which the question of matching realities of nature is a “meta-” question, beyond mathematics.
Davis and Hersh describe many mathematicians as Platonists in practice, while retreating to the protective shells of formalism when necessary – they describe formalism as arising from Hilbert, Russell/Whitehead, and other turn-of-century attempts to give mathematics a more solid ground.
In part I bring this up because one reason I got started on this book at all (which I’m most of the way through and have found enjoyable) was your writing. I had to read some stuff about integrals involving the gamma function and hypergeometric functions, for which in part I read your “Notes on hypergeometric functions.” Wikipedia credits Davis with having written sections in Abramowitz and Stegun on the gamma function, and that’s how I found my way to the book.
Anyway, I should also say that I enjoy your writing and find it very thought-provoking and enlightening, please keep it up.