As inscrutable AI proofs emerge, mathematicians wait in the dark

The French mathematician Hugo Duminil-Copin, who won the Fields Medal — mathematics’ Nobel — in 2022 for his work on phase transitions in statistical physics, said in a video call of the French Mathematical Society on October 8 that years of his research agenda had been “wiped out” thanks to a tumult of mathematical proofs and results released by OpenAI a day prior.

Sixteen of the AI giant’s claimed results answered questions he had spent years trying to solve. In one case the model had produced 13 papers at once, standing in for the stages of a programme that takes humans many years. Duminil-Copin said he cried so loudly that night he woke his daughter, and said his field had been “annihilated”.

OpenAI released some 700 manuscripts from an unreleased model, claiming results on a weaker form of the Riemann hypothesis, as unsurmountable so far as Mt Kailash is, with implications for prime numbers and their many applications; the nature of the number π; and the speed of multiplying matrices. Last month, OpenAI had claimed a proof, certified by the Lean proof-checking software, that Navier-Stokes equations of fluid mechanics are incomplete. The answer could potentially settle a $1-million Millennium Problem.