This week OpenAI published a massive collection of solved math problems that were previously unsolved. The problems were all solved with significant assistance from one of their unpublished AI models. On September 8th, before this latest release of results, OpenAI published a proof of the Navier-Stokes (NS) problem found in the Clay Institute's list of Millennium Prizes Problems.
The Millennium Prize gives $1,000,000 USD to the any person to be the first to solve one of the problems on the list. A lot of the problems on the list have remained unsolved for decades, if not centuries. For example, the Riemann Hypothesis (RH) has remained unproven since 1859 when Riemann first posed it. As a problem, the RH has intrigued mathematicians and attracted efforts to prove it by some of the greatest mathematical minds humanity has to offer--all have failed.
As of this writing, only one of the Millennium problems has been declared solved. In 2003, not long after the prize was established, Grigori Perelman solved the Poincaré Conjecture (PC). The PC was posed in 1904 and remained unsolved for almost 100 years. For reasons not entirely clear, Perelman declined the one-million dollar prize.
The NS problem that OpenAI claims to have proven on Sep 8th has stood unproven since 1934. The slew of other problems that they've claimed to have proven are less prestigious, but have also remained unproven for many years.
It seems that AI is enabling dramatic progress across a broad spectrum of mathematical fields. This has put mathematicians into a quandary. It's forcing a lot of mathematicians, myself included, to reflect on what exactly it is that we do, and, do we still have a role to play in the development of new mathematics.
Mathematicians now find themselves in the same AI pickle as artists, authors, lawyers, doctors, and CPA's to name a few other affected fields. And, there is a kind of Frankenstein's monster karmic justice at play here since mathematicians are largely responsible for the development of the theory underlying this AI revolution.
As I alluded to earlier, I'm not the only mathematician chewing on this issue. There are several mathematicians that think about this issue professionally and you would probably be better served reading their writing. For starters, Terry Tao, Alison Pease, Geordie Williamson, Michael Harris, or Ursula Martin can give some really insightful commentary. That said, I'm going to share a few humble observations of my own, but not today. You've read enough already.
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Obligatory sunset photo,
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