Two of the world's most decorated mathematicians looked at what AI actually solves, and landed on the same missing piece
Timothy Gowers, a Fields medallist, published a post on 12 August trying to sort mathematics into the kinds that language models handle well and the kinds they do not. His finding is that models are strong where a result can be reached by assembling known techniques — counterexample hunting is unusually well represented on their hit list — and weak at the judgement of which direction is worth trying at all when the search space is enormous. He is careful to say there is no clean classification yet and asks theorists to help formalise one. Peter Sarnak, writing in the Notices of the American Mathematical Society in July, reached a similar place from a different angle: AI can derive consequences from theory that already exists, but struggles to invent the new abstractions that major proofs are usually built on. A DeepMind paper by Tom Zahavy, 'LLMs Can't Jump', names the same bottleneck in technical terms, calling it the inability to posit new foundational assumptions. None of these are controlled experiments; they are expert assessments of how the tools behave in real mathematical work.
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