Lesson learnt? None.
A particular line from the open statement mathematicians wrote against the design of the latest Caltech Mathathon, due to happen in late October, has stuck with me:
Mathematicians do not only prove theorems: they also take measures to ensure that the future of a field remains healthy after the extraction of a result. They do so by sharing their results and explaining their methods to others at talks and conferences. They mentor students and postdocs so that the next generation can advance research further, and take care not to scoop other mathematicians at the last mile.
That mathematicians do these other things has not been acknowledged as vociferously in public as it has been in the last few weeks, as AI behemoths like OpenAI and Anthropic have raced to solve mathematical problems, in the process taking away the thing mathematicians generally work towards and yet, by solving them, producing none of the things mathematicians look for as they work. Put differently, what the models spit out eventually is a proof and just a proof, shorn of the shared methods, mentoring, collaboration, and the various other riches that emerge when human mathematicians pursue a proof.
And yet the two developments in these posts (not the posts themselves, mind) strike me as more distasteful than illuminating or even exciting:
OpenAI has told the NYT they’ve made substantial progress on another Millennium Prize problem, rumoured to be the Hodge conjecture. pic.twitter.com/t6Z64T2YaE
— Ananyo Bhattacharya (@Ananyo) September 10, 2026
Also Anthropic rumoured to have the Birch and Swinnerton-Dyer conjecture. If all of this is true,and there's a good chance it is, I hope they put significant time and effort into communicating what these theorems mean, why they're important and their impact. Will they though... https://t.co/5jaBvN6JwI
— Ananyo Bhattacharya (@Ananyo) September 11, 2026
I really do not understand what OpenAI or Anthropic expect they could gain by continuing down this path, especially after l’affair Navier-Stokes. Whatever truly happened in that dispute, the shape of it ought to have been damning enough on its face: a company raced to beat two mathematicians to a mathematical result, days after learning of their unpublished work, then disputing credit and authorship in public. But if that episode did not chasten anyone, what will? Pursuing more of the same kind of outcome, and seeking to allay it only by alluding to a “thoughtful” release, only weeks later and over the objections of more mathematicians means the lesson has not landed — as ironic as that is coming from the developers of machines capable of complex reasoning.
“Thoughtfully” in particular is a strange, if not meaningless, word to reach for right after a fight over credit, especially if Tristan Buckmaster’s version of events is to be believed.
PS: On the off chance you're interested, I've tried to explain the Birch and Swinnerton-Dyer conjecture here.
