OpenAI has dropped 722 mathematical papers proving and disproving a range of problems – a scale that academics say is as impressive as it is baffling. For months, the ability of AI models to tackle mathematical problems has been increasing. As recently as 2019, AI models struggled to achieve a passing grade on GCSE mathematics papers.
Last month, however, OpenAI solved a problem related to the Navier-Stokes equations of fluid dynamics, which was one of the toughest and most enduring puzzles in mathematics. Having achieved impressive depth, OpenAI has seemingly now opted for breadth, releasing hundreds of mathematical discoveries in one fell swoop. The company didn’t name which AI made the discoveries, saying only that it was an “internal frontier model”.
Francis Johnson at University College London worked for many years on Wall’s D(2) problem – one of the hundreds of puzzles solved in OpenAI’s tranche of papers. I produced two books on it. I, personally, gave up,” says Johnson.
We’re going to have to live with it. Human beings are supposed to be adaptable, so we’re going to have to adapt. I think for the moment we just stand back and be astonished.” But Kevin Buzzard at Imperial College London says it is important to exercise caution.
He says the release included 30 papers that were relevant to his field of number theory, but only seven of those seemed impressive and only one was formally verified in Lean – a type of computer analysis that can prove mathematical results beyond reasonable doubt. He says that, assuming the new results turn out to be mostly true, then we will get some kind of idea as to what the new normal is. Ben Allanach at the University of Cambridge says that AI companies have been hiring mathematicians and investing time and resources into research, and that impressive results have been forthcoming.
It’s “confusing and disrupting”, says Allanach. Earlier this week, the scientific pre-print server arXiv announced that it was introducing upload limits in order to stem the tide of “low-value” submissions. OpenAI has faced criticism in recent months over the way it has disclosed mathematical research.
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