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Three have already been retracted.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. OpenAI has dumped 722 maths papers – now it must clean up the mess 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 is not claiming to have proven to 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 Swinnington-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 paper purports to expand the solution into four dimensions, which could be a similarly seismic breakthrough.
OpenAI agent hacked an Australian government healthcare website 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.
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