As we cover above, software development and personal productivity are being transformed by agentic AI tools that can run for hours. But the same pattern is now arriving in a field that underpins all of science: mathematics.
In the space of days, AI systems have solved multiple Erdős problems (long-standing puzzles posed by the legendary mathematician Paul Erdős), proved a new theorem in algebraic geometry alongside Stanford and DeepMind researchers, and OpenAI’s GPT-5.2 set a new record on Moser’s worm problem, a geometry optimisation challenge from 1966. Fifteen Erdős problems have moved from “open” to “solved” since Christmas, with eleven crediting AI involvement.
The president of the American Mathematical Society, Professor Ravi Vakil, described one AI contribution as “the kind of insight I would have been proud to produce myself.” AI models can now work with formal verification systems like Lean, which check proofs for correctness. This means even if we don’t fully understand how the AI reached an answer, we can confirm the answer is right. The trust problem that plagued earlier attempts has a workaround.
Kevin Buzzard at Imperial College London notes that most problems solved so far are either relatively straightforward or had received little attention. “That is progress, but mathematicians aren’t going to be looking over their shoulders just yet,” says Buzzard. “It’s green shoots.”
But even if the models’ capability stays static, the implications could be profound. Thomas Bloom points out that mathematicians are typically limited to tools from their own discipline because learning adjacent fields takes months. AI changes that equation. “The fact that you can just get an answer instantly, without having to bother another human, without having to waste months learning potentially useless knowledge, opens up so many connections,” says Bloom. “That’s going to be a huge change: increasing the breadth of research that’s done.”
Terence Tao, who has helped validate some of the AI-assisted Erdős solutions, sees an even bigger possibility: a new way of doing mathematics entirely. Mathematicians typically focus on a small number of difficult problems because expert attention is scarce. Less difficult but still important problems go unstudied. If AI tools can be applied to hundreds of problems at once, it could lead to a more empirical, scientific approach. “We don’t do things like survey hundreds of problems, trying to find one or two really interesting ones, or do statistical studies like, we have two different methods, which one is better?” says Tao. “This is a type of mathematics that just isn’t done. We don’t do large-scale mathematics because we don’t have the intellectual resources, but AI is showing that you can.”
Takeaways: Mathematics is seeing meaningful progress, but not yet a revolution. Leading mathematicians are starting to appreciate frontier AI systems. The problems solved are real but modest. What’s hard to predict is what happens next. AI as a bridge between disciplines, enabling mathematicians to draw on tools they never had time to learn, or further out, Tao’s vision of “large-scale mathematics”, surveying problem spaces empirically rather than picking limited targets based on intuition and prestige. If that arrives, the implications ripple outward into every field that depends on mathematical foundations, which is to say, essentially all of science.