OpenAI publishes 372 families of mathematical results

On Tuesday, October 7, OpenAI published a large collection of mathematical results. They come from an internal AI model that the company has not released. According to the US media outlets Engadget and Fortune, it involves 722 manuscripts grouped into 372 "result families" across 16 areas of mathematics. The manuscripts are on GitHub, where anyone can read them.

What happened?

OpenAI says the model has made progress on or solved a long list of open problems. These are tasks that no mathematician knew in advance could be solved at all. According to the media, the collection contains claims of solutions to some well-known conjectures and a long list of counterexamples to things mathematicians have believed for decades. A counterexample is a single case that shows a claim does not always hold.

OpenAI also says it has made progress on three other so-called Millennium Problems, but has not fully solved them. These are a set of famous mathematical problems where each solution carries a prize of one million dollars.

The model spent on average about three hours of computing time on each solution. OpenAI has also published the model's reasoning, an estimate of the computing power and information about how many problems were attempted.

Caveats

The results have not been assessed by other researchers, so-called peer review. OpenAI itself writes that some of the proofs that are not formalized may contain errors. Formalizing a proof means writing it in a form that a computer program can check step by step. This has been done for many of the problems, so others can verify them independently.

Mathematicians are therefore now trying to understand what the collection actually contains. Fortune describes the release as both a celebration and a controversy, with criticism of how the results have been presented.

What does it mean?

For ordinary users, it changes nothing right now, because the model is not available. But it shows how quickly AI has moved from school exercises to actual research. As early as August, OpenAI said the internal model Astra had solved ten open problems. Now the number has grown to hundreds. Whether all the results hold up will only be determined once experts have reviewed them.