Is the best mathematician in the world an AI model?
(Photo: Ministry of Foreign Affairs of the Netherlands)
On October 6, 2026, OpenAI published a document announcing that an artificial intelligence (AI) model had solved long-standing mathematical problems. This was not surprising by itself, because the previous few months had brought a series of exciting new mathematical results proved by different AI models. But the October 6 announcement was on a completely different scale. Some people called it a bombshell, while others described it as a major event that could change the history of science.
What caused all this excitement? The document contained summaries, called “abstracts,” of 722 mathematical papers. It was like the collection of summaries you might expect from a large conference of mathematicians. The papers had been produced by an OpenAI reasoning model that the company has not publicly identified. Each paper claimed to solve a difficult mathematical problem, including many that had puzzled scientists for a long time. Together, they covered 17 different fields and included hundreds of complex proofs. Special computer programs had formally checked several of these proofs, while groups of mathematicians were examining others. Never before in the history of mathematics had so many results been claimed in a single day.
This was like a huge wave of mathematical theorems produced by machines, flooding the field of mathematics. Mathematicians and theoretical computer scientists had to accept, whether they liked it or not, that AI was no longer just a powerful helper for human researchers. AI was now producing results much faster than people could.
Many mathematicians were shocked and felt almost unable to react. They knew that a machine had solved problems they had spent years trying to solve. Many young mathematicians began to wonder whether they would still have a future in the field.
I know some of the problems that were solved very well. Some of us had worked on one of them from time to time over several years, then given up and moved on. Now that I can see the solution, I can identify three different techniques used to solve it. I know two of those techniques very well and have taught them in lectures, but I never thought of combining them. Generative AI can do this kind of thing: it can find patterns linking areas that seem unrelated and combine ideas in new ways. People can do this in principle, too, but it might take years for us to find the right clues. AI can reach the same point much faster.
As one mathematician put it,
It is as if we have all been riding bullock carts, and this is like riding a racing car.
HOW WAS ALL THIS MADE POSSIBLE?
AI has existed for about 60 years. But ChatGPT, the software OpenAI released in November 2022, showed that AI could talk with people in a friendly way and write essays, letters, poems, and other kinds of text. ChatGPT is an example of a Large Language Model (LLM). These models use huge amounts of computing power to learn patterns in language. They can draw on vast amounts of human language data, which helps them produce text that sounds very much like something a person might write. Many LLMs have been released in the last four years.
One surprising ability of ChatGPT was that it could also write computer programs. How did this happen? Scientists realized that a language model powerful enough to understand something as complex as human language and literature could also learn to work with highly structured systems created by people, such as mathematical language.
Over the last two years, people have shown this ability many times. Throughout 2025, AI repeatedly solved mathematical problems at the level of research. But mathematicians did not consider any of those problems exceptionally difficult.
That changed in 2026. AI programs began solving famous problems that had no known solutions. In February 2026, Google DeepMind used its Gemini model to examine 700 unsolved problems posed by Erdős, a Hungarian mathematician famous for creating mathematical problems. The model solved four of them and found nine new solutions to problems that had already been solved. By May 2026, OpenAI and Anthropic were competing to show that their systems had more advanced reasoning abilities. They tried to solve difficult problems that mathematicians had worked on for decades, or even for a century or two.
In September 2026, something even more shocking happened. OpenAI announced that its system could solve a major part of one of the most difficult problems ever studied: the Navier–Stokes equation. This problem is especially important because it belongs to the seven Millennium Prize Problems announced by the Clay Mathematics Institute. Solving any one of these problems earns a prize of one million US dollars. However, mathematicians have found OpenAI's 146-page proof so dense that even they struggle to understand it. Checking the proof will take a long time. Some people have also accused OpenAI of taking the idea from mathematicians.
How can AI do all this? Thousands of AI agents can work at the same time, exploring many possible approaches in parallel. They can try paths that fail, go back, and try again, repeating this process for much longer than human researchers usually can without becoming frustrated or bored. AI agents can also check their work with computer programs called proof assistants. These programs check whether the logic is mathematically sound, even when the proofs are very long. This makes it much faster to search for a solution, check it, and try again if needed.
REACTIONS AND THE ROAD AHEAD
Some mathematicians have praised OpenAI's latest release as a remarkable breakthrough. Others have reacted with shock and dismay. Mathematical proofs are not just collections of statements that are logically true. They are also supposed to help people understand mathematics. AI-generated proofs may use unusual symbols, complicated structures, and unnatural shortcuts that make them hard for humans to follow or understand intuitively. OpenAI also skipped the peer-review process that the mathematical community has developed over many years. Its methods are not transparent, because the company has not revealed which reasoning model it uses, describing it as “internal” to the company.
One worrying effect of AI is that people are sharing less knowledge in public spaces online. From 2022 to now, the number of researchers posting questions on the internet and helping one another has fallen by half. Among students, it has fallen to less than one-tenth of its earlier level. Both groups are now using AI privately instead.
What cannot be denied is that October 6 marks the beginning of a new era and a major change in how mathematical research is likely to be done. As machines produce more and more mathematics, checking mathematical results with computers will also become increasingly important. We may be entering an era of industrial mathematics. Instead of individual mathematicians or teams producing results, automated systems may do much of the work, with mathematicians checking the quality of what the systems produce.
All this reveals at least one basic weakness in the way mathematics has been practiced. For the last couple of centuries, mathematics has placed greater importance on results than on the process of finding them. Solving unsolved problems is highly valued, and people celebrate whoever solves them first. But the process of doing mathematics is different and important in its own right. People who love mathematics enjoy discovering things, working creatively through difficult problems, learning from repeated failures, talking with colleagues, and taking part in shared efforts to investigate questions. They also value the long process through which ideas and solutions develop, and the sudden flashes of insight that come after a long period of thinking. Mathematicians share these experiences with their students, but they rarely write them down. Yet these detours and early, incomplete ideas can lead to important results later by preparing us to explore new questions. If machines take over the production of results, will these human processes survive? Are they not worth protecting? Will societies, taxpayers, and governments be willing to support mathematicians so that these ways of working can continue? Without them and a lively community of people exploring mathematics, how will humanity develop the ability to ask the right questions?
On the other hand, industrial mathematics could help people use mathematics to investigate new questions that society considers important. Divisions such as pure versus applied mathematics and deductive versus experimental mathematics may disappear. This could open the way to new kinds of exploration that benefit humanity. Today, mathematical models often cannot work directly with real-world data and objects. Instead, researchers simplify them, removing messy details and turning them into idealized objects. They then study these simplified versions and apply the results back to the real world, making corrections where needed. This approach makes sense for work done by humans. When computing power became available, people expected that they would be able to skip these steps and work directly with real objects in all their complexity. But the necessary reasoning ability was missing. Perhaps AI has now shown that this ability is possible.
Before getting carried away by these hopeful possibilities, we should remember that the current wave of machine-generated mathematics is driven entirely by corporate greed. Under the current system, large companies are more likely to seek ownership of this new machine-driven mathematics, make money from it, and turn it into commercial products, while ignoring many worthwhile goals.
The future of mathematics is uncertain. Could this be a chance to create a new era in mathematics that helps humanity solve its most important problems? Yes, but only if the social and political systems behind it support and enable this change instead of simply giving in to machine-generated solutions. The outcome depends on who builds the machines, why they build them, who controls them, and how they are controlled.