What mathematicians think of OpenAI's 372 maths results

On 6 October 2026, OpenAI released 372 results on open questions in mathematics and theoretical computer science in one go. Theoretical computer science is the mathematics behind computers and calculation methods. According to the company, each result solves an important open problem, or comes much closer to solving it. One result often comes with several related papers on the same problem. In total, that makes 719 scientific manuscripts, which OpenAI put on the developer platform GitHub instead of in journals.

The news came about a month after OpenAI claimed that the same internal model had solved the famous Navier-Stokes problem, one of the biggest open questions in mathematics. That solution is being formally reviewed. Mathematicians are impressed by what has now been added, and at the same time want to know exactly how it was made.

One prompt instead of a swarm

According to an OpenAI spokesperson, almost every result came from a single prompt to a single AI agent. An AI agent is an AI program that carries out a task step by step on its own. This agent runs on a new model that is not yet public. Some results may have needed more attempts, the spokesperson added. According to OpenAI, a result took about three hours of computing on average.

That is a big difference from the Navier-Stokes solution. According to the company, that came from a swarm of 10,000 agents working together and cost millions of dollars in computing power. If the new claim holds up, this kind of mathematical computing power could soon be within reach of many more people.

What OpenAI says it has proved

Mathematicians who spoke to Scientific American pointed to a number of results as the most important. In all cases these are claims by OpenAI that are still being reviewed.

• Prime numbers. The Riemann hypothesis is considered the hardest open problem in mathematics. It is about the places where a complicated formula comes out at zero, and those places say a lot about the prime numbers. According to OpenAI, the model proved a weaker version, the quasi-Riemann hypothesis. According to the Chilean mathematician Hector Pasten, that is already more than enough for many applications. As a result, mathematicians now know better than ever how the prime numbers are distributed. A second result rules out a particularly tricky kind of zero, the so-called Siegel zero. According to Pasten, that question is now settled.
• Sorting equations. Hilbert's tenth problem asks whether a computer can divide all simple equations into two piles: those with and those without a solution in whole numbers. In 1970 it was proved that this is impossible. According to OpenAI, the model proved that it is also impossible when fractions are allowed as solutions. Pasten calls the approach original. The model combined two of his own ideas in a way he had not seen himself.
• A turning piece of chalk. Imagine sliding and turning a piece of chalk across a board so that it has pointed in every direction, using as little chalk on the board as possible. That is the Kakeya conjecture. The three-dimensional version earned a Fields Medal this summer, the highest prize in mathematics. According to OpenAI, the model solved the version in four dimensions.
• Faster calculating with tables. Computers constantly calculate with matrices: tables full of numbers. This happens in computer graphics, simulations and also in training AI. How much computing it takes to multiply two matrices depends on a number that mathematicians call the exponent. With the school method it is 3; the lower the number, the less computing is needed for large tables. A few years ago researchers got it down to about 2.37. OpenAI now claims 2.25.
• Physics and quantum computers. A number of papers deal with a simplified physics model, the non-linear sigma model. According to Michael Douglas of Harvard University, it is seen as the warm-up for the Yang-Mills problem. That is one of the great prize problems of mathematics, about the mathematical basis of particle physics. Another result gives indications that hard problems for quantum computers are not much harder than hard problems for ordinary computers.

Checking by computer and by humans

Many proofs have already been checked in Lean, a programming language that lets a computer check the logic of a proof. OpenAI wants more proofs to be checked this way. That is necessary too, because mathematicians could never check so many results at once by hand. Not all proofs have been checked yet. A few results have been withdrawn after scientists outside OpenAI found errors in them.

The review by humans will take months. Mathematicians want to know whether the proofs really contain new ideas or mainly combine known techniques in a clever way. On the sigma model, opinions differ. Roland Bauerschmidt of New York University finds the first paper very reasonable. He is much less positive about the later papers: he finds them so unclear that even an expert would find them hard to check. According to the spokesperson, OpenAI's own mathematicians do not yet fully understand many of the new results either.

A call for openness

Mathematician Andrew Sutherland of the Massachusetts Institute of Technology (MIT) believes that claims about results from a single prompt should be treated as unconfirmed. That should remain so until the model is public and others can reproduce the results. In his view, mathematicians should ask for evidence.

After the discussion about the Navier-Stokes solution, OpenAI set up an independent advisory group of mathematicians on 21 September. It advises companies to publish, for each result, the model, the exact prompt and the computing time used. OpenAI follows this in part. The company shares an average computing time and some statistics, but no prompts. According to the spokesperson, OpenAI takes the guidelines seriously and does its best to follow them, although it is not bound by them. The company also says it is working on releasing the model as quickly and responsibly as possible. In addition, OpenAI wants to pay for workshops and conferences where mathematicians can study the AI results together.

Reactions vary. Daniel Litt of the University of Toronto sees no reason to keep the answers secret and calls the publication good for mathematics. Terence Tao, one of the best-known mathematicians in the world, criticises what he calls the insane pace of AI labs. In an open letter, 25 Fields Medal winners warned that mathematics is ultimately about understanding and insight, not just about solving problems.

Meanwhile, OpenAI is already taking a different approach. On 26 October the company announced three new results in mathematics, computer science and physics. This time hundreds of papers did not appear online at once: well-known scientists are guiding the checks from the start and are free to publish what they find. That meets the call for openness from mathematicians such as Sutherland.

What does this mean for the road to the singularity?

If the claims hold up, AI can now deliver mathematical work in a short time on which humans were stuck for years. According to experts, a number of these results could have earned a human researcher a top prize a year ago. That most of them, according to OpenAI, came from a single prompt to a single agent, and not from an expensive swarm, points to a model that has itself become much smarter.

One result affects AI itself. If matrix multiplication really takes less computing, that could make AI faster in the long run. MIT researcher Virginia Vassilevska Williams remarked, half jokingly, that you can see the progress as an attempt by AI models to speed themselves up.

The next step lies with humans. Computer checks with Lean, a public model and time for mathematicians to really understand the new ideas must show which breakthroughs will stand. If that succeeds, researchers will have a powerful new tool in their hands.

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