OpenAI's new model has solved or made major progress on 372 mathematical problems, many of which the world's leading mathematicians have worked on for decades without solving.
The results include progress on two of the seven Millennium Prize Problems, the hardest questions in mathematics, each carrying a one million dollar prize.
The mathematical world is in shock, and it will take researchers months or years to work through the more than 700 papers.
372 results at once
On October 6, 2026, OpenAI published 372 new mathematical results. They were produced by an internal AI model that is not yet available to the public. Each result solves, or makes major progress on, an important open question in mathematics or theoretical computer science.
The work took a few weeks. The results are described in more than 700 papers written by the AI agents. Many of the papers are longer than 100 pages. They cover large parts of mathematics, from algebra and geometry to probability and logic.
OpenAI gave its AI agents a total of 4,000 problems. 372 of them led to results.
A shock to the world of mathematics
Mathematicians have never seen anything like it. The magazine Scientific American describes a field in shock. The Economist writes that the day may go down as one of the most important in the history of mathematics.
Just a month earlier, OpenAI announced that the same model had solved the Navier-Stokes problem. It has been described as the biggest advance in mathematics in 20 years. Now hundreds of new results arrived on a single day.
The volume is so large that it will take mathematicians months, perhaps years, to go through it all. According to OpenAI, even the company's own mathematicians have not yet understood many of the results.
Not just any problems
These are not school exercises. They are questions the world's leading mathematicians have worked on without reaching an answer. Several have been unsolved for decades, some for more than a hundred years.
In 2000, the Clay Mathematics Institute selected seven problems considered the very hardest in mathematics. They are called the Millennium Prize Problems. Anyone who solves one receives one million dollars. Until last month, only one of them had been solved. Now OpenAI's model has, according to the company, solved the Navier-Stokes problem and also made progress on two of the others.
The pattern of prime numbers
The most famous of the Millennium Prize Problems is the Riemann hypothesis. It was formulated in 1859 and has been unsolved for more than 160 years.
The hypothesis is about prime numbers. These are numbers that can only be divided by 1 and by themselves, such as 2, 3, 5 and 7. Prime numbers seem to appear more or less at random. The hypothesis says there is still a clear order in how they are spread out. Prime numbers are used, among other things, in the encryption that protects payments on the internet.
The AI model has not solved the whole problem. But it has shrunk the area where an error in the hypothesis could be hiding.
Turning a needle
Another result concerns the Kakeya conjecture. It began with a simple question in 1917. How small an area do you need to turn a needle all the way around?
If you spin the needle around its middle, the area is a circle. But with clever back-and-forth movements, a bit like parallel parking, the area can be made almost zero. Even so, the shape the needle sweeps out never seems to be able to become completely flat. That is what the conjecture says.
For a flat table, it was proven in 1971. For three dimensions, it took until 2025. That year, mathematician Hong Wang at NYU presented a proof together with a colleague. In July she received the Fields Medal, the mathematical equivalent of the Nobel Prize, partly for that work. The AI model has now presented a proof that goes one step further.
The problem is linked to how waves behave and is a foundation for many other questions in mathematics.
More big questions
The AI model has also proven part of the Hodge conjecture, another of the Millennium Prize Problems. It is about shapes in many dimensions and whether they can be built from simpler pieces.
Other results deal with how closely the number pi can be approximated with ordinary fractions and how magnetism arises in certain materials. Some provide faster versions of important computer algorithms.
From ten thousand agents to one
The solution to the Navier-Stokes problem took 88 hours and required 10,000 AI agents working together. The computing power cost millions of dollars.
This time, a single AI agent produced almost all the results from a single instruction, according to an OpenAI spokesperson. On average, each result required computing power equal to about three hours of thinking in ChatGPT Pro.
Proofs that computers can check
127 of the proofs are written in Lean, a programming language in which a computer checks that every step of a proof holds. This means those results are almost certainly correct. OpenAI will add more such verified proofs over time.
Everything is collected on GitHub. There, OpenAI also publishes ten summaries of how the model reasoned, details of how much computing power was used, and statistics on how many problems the model attempted.
Conferences and access for researchers
Before publishing, OpenAI took advice from an independent group of nine mathematicians at the Institute for Advanced Study. The company will fund workshops, conferences and special programs where mathematicians can work through and understand the results.
OpenAI is also working to make the model available to researchers.
Mathematician Daniel Litt at the University of Toronto believes it is good for mathematics that the results are published. He sees no reason why the company should keep the answers to mathematical questions secret.
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