We’ve had some wild months in mathematics. Last fall, with models already crushing it at the International Mathematical Olympiad (IMO), people began throwing open problems on AIs, and Thomas Bloom’s website of more than 1000 Erdős problems proved the perfect testbed for AI’s research capabilities. In December last year, people – sometimes with little or no mathematical training – began posting AI-generated solutions to open problems, which were subsequently verified by experts.

The first few solutions appeared to be low-hanging fruit: the solutions were soon located in prior work. However, soon enough, in January, AIs autonomously came up with new proofs, often formalising the proof in Lean. The Erdős problem craze was a fact.

The AI solution of Erdős problem no. 1196 in April marked a milestone: this was the first problem experts had given serious thought and were unable to solve. Jared Duker Lichtman, who proved a weaker bound in his PhD, was surprised at the solution from GPT-5.4, describing the first proof step as something of a move 37. Shortly after, on May 20, OpenAI announced an internal model had solved the unit distance problem, a central problem in discrete geometry, and which experts had given very very serious thought.

The mathematical community, in which things usually move extremely slowly, has a lot to digest, both with regards to mathematical content and the impact of AI on mathematics.

Some predictions #

The digestion, especially of the second part, has begun. I suppose it began a while ago, with the introduction of Google DeepMind achieving IMO silver medal performance in 2024. The AI solutions to open problems then sparked some debate in December 2025, and over the course of this spring, many world-leading experts have acknowledged that AI will play an important role in the future of mathematics.

I’ve tried staying reasonably up to date with the recent advances in AI for mathematics, reading tweets, news articles and blog posts, as well as watching videos from the Future of Mathematics Symposium and SAIR’s AI Summit – partly for fun, partly because it’s relevant to what I’m doing. Before offering my own takes, I’ll share three thought-provoking predictions.

In one Mastodon thread on April 27, Terence Tao suggests that incentive structures in mathematics will change. The mathematical research process, he says, involves proof generation, proof verification and proof digestion. In the past, proof generation was the bottleneck; with AI, the bottleneck is rather proof digestion. He likens proof generation, proof verification and proof digestion to food gathering, food cleaning and cooking, and offers the following prediction:

Just as modern societies no longer consider raw food ingredients as constituting a meal, I predict that mathematical research culture will cease considering “raw”, “undigested” proofs as constituting a solution to a problem, and focus more on how the field as a whole, as opposed to just the problem itself, is enriched by the contribution.

Timothy Gowers, who published a blog post on May 8 about his experience with GPT-5.5 Pro, similarly predicts that maths will change:

…there is still a great deal of value in struggling with a mathematics problem, but that the era where you could enjoy the thrill of having your name forever associated with a particular theorem or definition may well be close to its end. So if your aim in doing mathematics is to achieve some kind of immortality, so to speak, then you should understand that that won’t necessarily be possible for much longer — not just for you, but for anybody.

Even if AI capabilities stall, mathematics is different today than just six months ago. We’ve arguably already entered the era of proof abundance, the era without named theorems.

But we have good reason to think capabilities will increase further, and that AIs will become much like advanced chess systems in relation to humans – that is, dramatically better. Or that is at least what the Gods of Straight lines predict: mathematical capabilities of AIs have consistently been trending upwards, why should this trend stop now?

This prediction is also endorsed by humans. In a talk at the Future of Mathematics Symposium, Adam Brown, physicist and research lead at Google DeepMind, cites the following reasons to believe in continued progress within AI for science: past trends, there being low-hanging fruit to improve AI’s reasoning abilities, companies soon having more compute and more smart people working on AI.

Some optimism #

Even if I’ll never get a ‘Dahlgren lemma’, I’m excited about the recent developments within AI for mathematics, mainly because of the following two reasons.

Firstly, we’ll get more answers! Even if there are open problems AI cannot solve – chances are someone has already given GPT-5.5 Pro your favourite open problem, and you would have heard of any solution – we’ll certainly get answers to more difficult problems like the unit distance conjecture. Everyone has some problem they’d like to see solved before they die; with AI, perhaps more mathematicians will be happy on their deathbeds.

Although AIs might soon have superhuman capabilities, I suppose the AI-generated solutions will seem motivated to human mathematicians. Though the world-leading chess engine Stockfish is far better than any human, most of its moves are standard to experts, only that Stockfish makes a few unexpected moves every now and then. Assuming a tight chess-math analogy, most proofs in the future might come from various math engines, but they will likely remain understandable to humans¹.

Secondly, mathematics has never received this much attention (and funding). The AI-generated solutions have led to non-mathematicians taking interest in topics like von Mangoldt chains and class field theory. We’re seeing the same effect in mathematics as in chess after Deep Blue defeated Garry Kasparov.

As for job prospects for research mathematicians, I’m not too worried either. Quite the contrary: as Tao wrote, the bottleneck within mathematics might well become proof digestion, and unlike the steps of proof generation and proof verification, this requires expert-level knowledge. If people at AI labs can assist with proof generation and proof verification, and they care about someone digesting their work, there may well be more openings for human experts.

Mathematics might well become like chess, with AIs doing the problem solving on the verge of the unknown and humans focusing more on the distinctly human aspects of doing mathematics, like proof digestion. Much of mathematics is about humans anyway (you know what I mean), so perhaps AI won’t be as disruptive as people sometimes fear. Of course, things could also remain as they are today. Regardless, it’s a good time to be within the field.