OpenAI releases nearly 400 AI-generated maths results; mathematicians may need years to digest them

AI company OpenAI this week published nearly 400 AI-generated mathematical results, set out in more than 700 manuscripts. They span combinatorics, geometry, number theory, theoretical computer science, algebra, topology, probability and mathematical physics. According to The Verge, which spoke to more than three dozen mathematicians, researchers believe that simply understanding what has been released could take years.

Verification is incomplete

The material sits in a GitHub repository, and OpenAI has also published guidance on how to navigate it. Some of the work comes with formalizations in Lean, a programming language and proof assistant that allows results to be checked by computer. OpenAI says 300 top-line results out of 719 manuscripts have been formalized, about 42 percent, and that it will add more to the repository.

Several researchers noted that Lean code does not settle the matter immediately, since someone must check that it actually proves what the manuscript claims. Kevin Buzzard, a mathematics professor at Imperial College London, said he found only around six standout results in his field, algebraic number theory, and that few if any appeared to be formally verified. Mathematicians also pointed to papers that were hard to follow, had short bibliographies, or seemed to cover ground already explored by others. They noted that OpenAI's earlier write-ups were criticized as sloppy and for poor attribution. The company has already retracted three of the papers.

High calibre and disruption

Still, most of those interviewed said some of the work appears to be of very high calibre. In their view, many results would have merited publication in top journals before the AI era. Jared Duker Lichtman, a Stanford mathematician, cited "tens" of results, including progress toward the Riemann hypothesis, a special case of the Hodge conjecture and a solution to the four-dimensional Kakeya conjecture.

Some researchers said entire research programs and grant proposals had been rendered moot. Francesco Fournier-Facio of Heriot-Watt University said researchers in probability, combinatorics and theoretical computer science appeared particularly shaken.