Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

The mathematician’s tricks

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A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdős’s work. You admire Erdős’s contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdős’s work could be “reduced” to a few tricks which Erdős repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert’s beautiful results have been completely forgotten. But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory, it was surprising to verify that Hilbert’s proofs relied on the same few tricks. Even Hilbert had only a few tricks!

Gian-Carlo Rota, “Ten Lessons I Wish I Had Been Taught”

Written by nevalalee

February 4, 2018 at 7:30 am

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