In my last column I recount how back in the 1990s two mathematicians named a geometric object after me, the “Horgan surface,” as revenge for “The Death of Proof.” The column gave me an excuse to revisit my controversial 1993 article, which argued that advances in computers, the growing complexity of mathematics and other trends were undermining the status of traditional proofs. As I wrote the column, it occurred to me that proofs generated by the Horgan surface contradict my death-of-proof thesis. I emailed a few experts to ask how they think my death-of-proof thesis has held up. Here are responses from computer scientist Scott Aaronson, mathematician-physicist Peter Woit and mathematics-software mogul Stephen Wolfram. (See Further Reading for links to my Q&As with them). I’ll add more comments if/when they come in. –John Horgan
Scott Aaronson response (which he also just posted on his blog):
John, I like you so I hate to say it, but the last quarter century has not been kind to your thesis about “the death of proof”! Those mathematicians sending you the irate letters had a point: there’s been no fundamental change to mathematics that deserves such a dramatic title. Proof-based math remains quite healthy, with (e.g.) a solution to the Poincaré conjecture since your article came out, as well as to the Erdős discrepancy problem, the Kadison-Singer conjecture, Catalan’s conjecture, bounded gaps in primes, testing primality in deterministic polynomial time, etc. — just to pick a few examples from the tiny subset of areas that I know anything about.