The technologies known as artificial intelligence have the creative-arts fields in a massive tizzy and for good reason, since they’ve almost obliterated both the business and artistic side of things in a heartbeat. By the way, I’m moderating a panel on this topic, called “A.I. in the Literary World for” at the 603 Writers Conference in Concord on Nov. 14. James Patrick Kelly is one panelist, for you s.f. fans.
But there’s a very different field that is in just as much of a tizzy. Theoretical mathematics has seen all its core beliefs in how the field operates completely upended in the course of a month or two. I’m not talking about applied math, which seems to be taking A.I. in relative stride, but the folks who spend all day with a notepad and blackboard thinking about topics like number theory, which are so abstract that they feel closer to philosophy than arithmetic.
As you probably know, OpenAI’s recently solved parts of the Navier-Stokes Theorem of fluid dynamics, one of the great unsolved problems in math, following on some other very significant advanced by A.I.s. That rattled mathematicians but the big shock came earlier this month when Anthropic dumped the proofs of hundreds of math problems, some of them very significant, all at once.
Math is used to having a shortage of proofs and a surplus of unsolved problems; that’s the way it has been since before Euclid. All of a sudden they have an abundance of proofs and a resulting shortage of unsolved problems and it’s not clear how they should respond.
To get a sense of where things stand I can highly recommend this 25-minute interview with Fields Medal winner Terence Tao, who has become a sort of spokesman for higher math and A.I., by Brady Harran on the Numberphil video. It’s non-technical but really explains the situation well, partly because Tao is a master of the clever analogy. It’s on YouTube: https://www.youtube.com/watch?v=bAnwMdfcMVw
The video is titled “No more heroes” because Tao argues that theoretical math is being forced to dump to millennia-long model of the single genius making breakthroughs with their mind alone, and adopting more of an “industrial” approach of teams and computer support.
