The floodgates of AI mathematics have opened. On 7 October, OpenAI released 722 mathematical papers using an AI model to examine an astonishing range of topics, from longstanding mathematical mysteries to small improvements in rarely considered curiosities.

Of course, there hasn’t yet been time for mathematicians to comb through all of these results, let alone to actually check them: some of the papers are hundreds of pages long, dense with complex computations. Many of them have not been formalised – reduced to steps that can be checked by a computer – meaning there is little assurance that they are accurate. Three have already been retracted. Nevertheless, even a preliminary comb through the thicket of papers turns up some that are likely to make a splash.

Several of the papers relate to Millennium problems, a set of seven mathematical problems generally considered to be among the most important and challenging in the field. Solving any of these problems comes with a $1 million prize from the Clay Mathematics Institute. Since its inception in 2000, only one of them has been solved, although mathematicians are currently investigating a recent claim from OpenAI that one of its models has solved another, related to the Navier-Stokes equations of fluid dynamics.

Now, the company has taken aim at the Riemann hypothesis, an unproven rule about the distribution of prime numbers that, if proven, would provide a map of how prime numbers are spread out across the number line. OpenAI isn’t claiming to have proven the Riemann hypothesis itself, but a variation called the quasi-Riemann hypothesis that deals with how far prime numbers can be from their expected position. It is less strict than the original hypothesis, but if the result stands up it could be the biggest step towards a solution in years.

Two other Millennium problems are mentioned in the papers: the Birch and Swinnerton-Dyer conjecture and the Hodge conjecture. Similar to the Riemann hypothesis, the papers on both of these problems claim to prove simpler, partial versions of the conjectures that could help mathematicians along the path to full solutions.

Another potentially major result relates to a problem called the Kakeya conjecture, which is about the shape traced out by a rotating needle. In 2025, mathematician Nets Katz at Rice University in Texas called a paper claiming to solve the puzzle in three dimensions “perhaps the biggest breakthrough in mathematics of the current century.” One of the OpenAI papers purports to expand the solution into four dimensions, which could be a similarly seismic breakthrough.

Other papers provide minuscule improvements in algorithmic power. One claims that multiplication of integers could in theory be performed 2⁻¹⁸² faster than researchers previously thought: if a multiplication currently takes a millisecond, then the improvement is a little less than 1 divided by 14 million billion billion billion times the age of the universe. In other words, it is a very small improvement. Other speed improvements, such as one in performing Fourier transforms – breaking down a waveform into its constituent frequencies – are slightly more significant, but still tend to be marginal at most. Still, the papers show that improvements are possible.

Not all of the problems tackled in the OpenAI papers are quite so technical. For example, one is about the problem of colouring individual points on a plane so that no two adjacent points are the same colour. We already knew that this would require between five and seven different colours, and this new work seems to eliminate the possibility that it is five.

The bottom line is that with such a huge body of mathematical research all dropping at once, it could take years for mathematicians to check the AI model’s work, and far longer to understand its significance, if it holds up to scrutiny. And that is assuming that this dump is a one-time thing, which is far from a safe assumption. If AI maths continues at this pace, it could be a real boon or a real problem for the field of mathematics as a whole, and there is no way to predict which it will be until the work is validated.