A historic day for mathematics
May 20, 2026 will be remembered as an important milestone in the history of mathematics. It marks the first time when a breakthrough on an important, well-known mathematics research problem was made by an artificial intelligence.
What happened on May 20, 2026?
On this day, OpenAI announced that one of their AI models has autonomously solved a longstanding open problem in combinatorial geometry, the unit distance problem, that dates back to a 1946 paper by Erdős.
(The day when the actual discovery was made by the AI happened some weeks before May 20, so perhaps that is the day that will ultimately be regarded as the timestamp for the achievement. For the purposes of this post, I'll use May 20 as the date of reference.)
How important is this achievement?
It’s helpful to separate the achievement of the problem being solved from the achievement of the problem being solved by AI.
The achievement of the problem being solved is genuinely important. The problem was one of the Erdős problems, has been open for 80 years, and was the subject of an extensive literature. Well known mathematicians had worked on it and care about it. By these metrics, if the problem were to be solved, with the exact same solution found by the AI, by a human mathematician, that is something that many mathematicians would get excited about. The paper with the solution would very likely have been accepted to the Annals of Mathematics, the top journal for pure mathematics research. And the discovery would likely get written about in various blogs and attract a fair amount of attention among mathematicians, being the subject of water cooler conversations at math departments around the world, getting presented at important conferences, and so on. The problem’s solver or solvers would get quite a boost to their reputations and careers, becoming relatively well-known in the mathematics world (if they were not already well-known), and potentially making themselves competitive for tenure track positions at some of the top universities in the world, if they didn’t have such positions already.
Another exciting aspect of the solution is that it brings to bear novel techniques from number theory that were not previously used by researchers who worked on the problem. It teaches us new things and opens new directions that will be explored by mathematicians and will - in my humble opinion - almost certainly lead to additional exciting results over the coming months and years.
I should emphasize however that in the hypothetical scenario of the problem being “merely” solved by a human mathematician, the fact of the problem being solved would be a noteworthy event in the mathematics research world, but it would not be a historic event. Every year there are some exciting developments occurring in mathematics. It may be that this particular development is of a level of excitement that we only see every two or three years, but that’s still very different from something happening for the very first time in human history.
The problem being solved by AI is exactly what’s historic here. To be clear, AI models have already made respectable contributions to research mathematics over the last year. They’ve solved Erdős problems and done other notable things. But those achievements still left reasonable room for skeptics to argue that the AI was doing work that was technically novel but not that exciting, and/or was merely really good at identifying obscure results from the published research literature that happened to be relevant for the problems it was solving, and/or that it was merely opportunistically making progress on problems that ultimately weren’t that hard but simply haven’t received enough attention from mathematicians. A world in which AI is capable of making such contributions is a world that isn’t really that different for mathematicians from a world with no AI at all; it may be quantitatively a bit different, but not qualitatively.
None of these criticisms apply to the current situation. Making dramatic progress on a genuinely well-known, well-attended problem, and coming up with genuinely new ideas to achieve that progress, is exactly the type of achievement for which the very best human mathematicians are celebrated. If AI can do that, even once, it has elevated itself to a completely new level. If it can do that consistently, the consequences for mathematics, and for mathematicians, will be profound.
What does this mean for mathematics?
The ability to do research-level mathematics isn’t a single skill; it is many skills, with different problems requiring different combinations of those skills to make progress. AI has now, for the first time, shown itself capable of excelling at at least some of those skills at the level required to achieve breakthrough results - in other words, this is dramatic progress along a particular axis in a many-dimensional space. However, there are many other skills at which AI has not yet demonstrably achieved these levels. Will it achieve them in the future? How soon? We do not yet know.
More specifically, the OpenAI model’s current achievement was to find a counterexample to a conjecture of Erdős. Other recent evidence suggests that current frontier AI models are exceptionally good at finding clever constructions and counterexamples that demonstrate that a mathematical object with certain properties exists. This is indeed a very valuable capability, and progress on many important research questions will often come in the form of such constructions. But, equally, many mathematicians spend their entire careers proving results that are of a completely different flavor and do not depend much on this particular skill; and some of the most central open problems in mathematics, such as the Riemann hypothesis and P vs NP, will most likely require different modes of reasoning to crack. Mathematicians who do flavors of mathematics where constructions do not play a significant role will have to wait longer before they see an AI achieve a breakthrough in their areas of interest.
Separately from the issue of skills, my impression is that the kinds of proofs that AI models seem currently capable of discovering are relatively short - e.g., the unit distance problem solution is 18 pages long (including two pages of references, and a two-page appendix stating known results). Yet breakthroughs in mathematics often involve proofs that are hundreds of pages long, reflecting many years-long efforts by the people achieving those breakthroughs. For example, Jineon Baek's recent paper solving the moving sofa problem is 115 pages long. Current AI models have not demonstrated the ability to come up with these types of breakthroughs.
My takeaway is that we mathematicians are not (or not yet) in a “we’re all out of a job”-type situation. Despite the impressive and, as I said, historic, nature of the May 20 announcement, at this point in time there are still plenty of interesting things left to do that human mathematicians can do but AI cannot. For how much longer? We do not know.
Final thoughts
One thing that stands out to me in this story is the dizzying rate of progress in AI models’ capability to do research-level mathematical reasoning. At the Future of Mathematics Symposium, which took place at Stanford on May 1-2, Sébastien Bubeck said: "We haven't yet seen major advances brought about by AI, but it is coming, very plausibly this year." That quote caught my attention and I found it significant enough to quote it in the post I wrote about the symposium. And here we are, literally three weeks later, with his "very plausibly this year" prediction having already come true. (To be fair, given Bubeck's position as a senior person at OpenAI, there is a possibility that when he made that prediction he already knew about the soon-to-be-announced breakthrough, which I understand from sources in the know was made several weeks before the May 20 announcement and being kept quiet while it was carefully being checked by top mathematicians.)
Bubeck’s entire talk is worth watching; the story he tells is fascinating, and the fantastic rate of progress in AI mathematical reasoning is one of the recurring themes of the talk. The May 20 OpenAI announcement simply underlines the points he was making about the rapid rate of progress.
Bottom line: watch this space - and don’t blink, or you may miss additional exciting developments.