AI Is Taking Over Math: Breakthroughs, Hype and Hard Questions

Mathematics used to be the quiet corner of science. Then the AI labs arrived, and it now has press releases, rivalries and the occasional public embarrassment. Over the past year, OpenAI, Google DeepMind and a swarm of smaller players have announced results on long-standing problems. Some of those results are real and impressive. Others turned out to be hype. Telling them apart is becoming a skill in itself.

A caveat first. The headlines about AI reaching for the biggest prizes in mathematics, including claims around the famous Millennium Prize problems, are still being fought over. I could not read the original coverage that prompted this piece, so I will not repeat claims I cannot check. Instead I will stick to what is well documented: the best-attested breakthrough so far, how it happened, and the arguments it set off. Those arguments tell us more about where math is heading than any single headline.

The result that changed the mood: the unit distance problem

On May 20, 2026, OpenAI announced that an internal reasoning model had disproved a conjecture posed by Paul Erdős in 1946. According to TechCrunch, this was a famous unsolved question in geometry. The company described it as the first time AI had autonomously solved a prominent open problem central to a field of mathematics.

The problem is easy to state. Put a number of dots on a flat surface. What is the largest number of pairs you can make that sit exactly the same distance apart? Science News explains that Erdős thought a regular grid, with points spaced so that many fall on circles, was essentially the best you could do. For nearly 80 years, mathematicians believed the best arrangements looked roughly like square grids. The AI found an entirely new family of constructions that does better.

The surprise is how it did it. The model reportedly built a complicated grid in a high-dimensional space and then projected it onto the plane. It used tools from algebra and number theory, fields that seem to have little to do with a geometry puzzle. Harvard mathematician Melanie Matchett Wood called it a beautiful piece of mathematics and said it shows that tools from one area can be applied very fruitfully in another.

Not just OpenAI's word for it

One reason this announcement landed differently is that OpenAI did not ask people to take its word. TechCrunch notes that the company published companion remarks from outside mathematicians, including Noga Alon, Melanie Wood and Thomas Bloom. Bloom runs the Erdős Problems website, and he had previously called an earlier OpenAI claim a dramatic misrepresentation.

That earlier episode matters. In October 2025, a then-OpenAI executive posted that GPT-5 had found solutions to ten previously unsolved Erdős problems. It turned out the model had located solutions that already existed in the literature. Rivals mocked the claim and the post came down. The lesson, which I think the whole field has absorbed, is that a model finding an old answer is not the same as a model discovering a new one.

According to Quanta Magazine, the companion paper featured nine world-class mathematicians. Tim Gowers wrote that had a human submitted the paper to the Annals of Mathematics, he would have recommended acceptance without hesitation. Jacob Tsimerman called it impressive and intimidating. Few people would dismiss that as marketing.

Why Erdős problems, of all things?

The Erdős problems have become a kind of proving ground for AI, and the reason is partly a happy accident. Quanta tells the story. In 2023, mathematician Thomas Bloom started a website to keep track of the many problems Erdős scattered across papers and letters. He gradually added a comments section, and a real community formed, including professionals, students and hobbyists.

The problems suit language models for practical reasons. Most sit in number theory, combinatorics and graph theory, areas that have proved more accessible to these systems than others. Their difficulty also varies widely, which suits a technology whose abilities vary widely too. And once the problems were gathered in one place, the labs noticed that the list works as a benchmark.

Quanta describes how it unfolded. In January, a DeepMind-led team reported solving four problems and finding old forgotten solutions to nine more. In May, another DeepMind team said its agent autonomously resolved 9 of 353 open Erdős problems at a cost of a few hundred dollars per problem. Then, on August 1, OpenAI announced that an unreleased model called Astra had made ten further mathematical advances, including three more Erdős problems.

The amateurs got there first

My favourite detail in the Quanta piece is that the early wins did not come from the big labs. Two young enthusiasts, Kevin Barreto and Liam Price, began feeding problems to publicly available models in December. Their first claimed triumph, on Christmas morning, collapsed within hours when someone pointed out that Erdős himself had solved it in 1977. Barreto owned up publicly and asked the community to search the literature more carefully.

They kept going. By early January they had a proof for another problem that nobody could trace to earlier work, and they used a separate AI tool to certify that the logic held together. Price built a routine: ask a chatbot for a solution, feed it to a fresh instance to check, and repeat. In May, Barreto and Price joined Terence Tao and other mathematicians as co-authors on a paper resolving Erdős Problem 1196.

I find this reassuring and a little unnerving. It shows that capable tools in curious hands can do real work. It also shows that the people steering these tools sometimes lack the background to verify what comes out, and that they depend on professional mathematicians to do the checking.

The verification problem

This is where the drama sits. Bloom told Science News that the AI's unit distance proof happened to be fairly easy for an expert to verify. But he has also seen people post hundreds of pages of AI-generated mathematics that they cannot read or understand. In his words, it could be right or it could be nonsense, and the question is who will check it.

In Quanta, he describes a growing flood of 100- to 200-page papers where an AI produced the proof, checked the proof and wrote the paper, and no human has read it or ever will. That is a genuinely new problem. Mathematics runs on trust that is earned by scrutiny, and scrutiny is a scarce human resource.

Statistics could help, but they are missing. Science News reports that OpenAI's Sébastien Bubeck said the model solved the Erdős prompt correctly in half of the trials. A colleague said the new model is better at saying it cannot solve something. The reporter notes that data backing those claims has not been released or peer-reviewed, and that OpenAI has not shared how often the model fails or produces flawed reasoning. For a field built on proofs, selective reporting is uncomfortable.

Credit, access and the Leiden declaration

Two more worries run through the coverage. The first is credit. Mathematicians habitually acknowledge the work that inspired a result. A language model has read essentially everything and cannot show which ideas it drew on. Wood said it is not clear there is any reasonable way for AI to attribute the sources of its ideas. The original unit distance paper listed its author simply as OpenAI.

The second is access. Bloom warned that if the most powerful tools are expensive and private, mathematics could become less open and less democratic, and some people might wonder why they should learn it at all. The model behind the unit distance result was not even publicly available when it was announced.

These concerns fed into a declaration published on June 2 calling for tight guardrails around AI in mathematical research. By June 5 it had 1,590 signatures, according to Science News. It is not an anti-AI manifesto. Wood and Bloom are cautiously optimistic, and Wood expects AI to become an indispensable tool. The declaration asks for responsible, verifiable and ethical practice.

Brilliant, but is it a spark?

There is a fair debate about how impressive the achievement is as AI. Wood told Science News she suspected publicly available models could have produced the proof, and one researcher reportedly reproduced it with one. Bubeck himself conceded it was not exactly a spark of genius. The model won by perseverance, patiently working through unlikely strategies, rather than by the kind of creative leap that defines great mathematics. Bloom said a proof of the conjecture itself would have been truly incredible. A counterexample is still a big deal, but it is a different kind of big.

Quanta adds a note of humility. The model's result was not definitive, and human mathematicians improved on it within weeks. Related techniques were quickly used to disprove a version of another Erdős conjecture, the sum-product conjecture, for real numbers. That, to me, is the healthiest outcome: the AI opens a door and people rush through it.

What it feels like from inside

The human reactions are the most revealing part. Noga Alon, who has solved dozens of Erdős problems, told Quanta he has stopped trying, because once AI started to solve them there was no point. Tao has stepped away from the Erdős community to focus on getting work done. Tsimerman, on the day he won the Fields Medal in July, announced he was leaving academia for OpenAI.

Then there is Wouter van Doorn, a customer-service worker who does math for love. He says the models are clearly better than he is at the thinking, but that the proofs he ends up writing are simpler and easier for others to read. His analogy is a good one: you do not hire a machine to play the piano for you, because you like playing the piano.

That sums up my own view. AI will probably settle many questions faster than any person could. Math is not only a pile of solved problems, though. It is understanding, taste and a community that decides what counts as a proof. The labs are moving fast, and some of what they claim will be wrong, so the checking, crediting and sharing deserve as much attention as the breakthroughs.

If you have ever struggled with a maths problem and felt the joy of finally seeing it, ask yourself what you would want to keep for yourself in a world where a machine can often get there first. And what should we demand of the companies that build those machines, so that discovery stays open, honest and shared?