A Fields medallist set out what AI is genuinely good at in maths — and the one thing it has no nose for
Timothy Gowers published a long post today on which mathematical tasks large language models handle well and which they do not. His positive list is specific: finding examples and counterexamples to conjectures, applying standard arguments already present in the literature, and using sheer speed to search places a human would not bother to look. The gap he identifies is what he calls a nose — the sense that tells a mathematician a line of attack is going nowhere before weeks have been sunk into it. Models, he argues, chase dead ends and often reduce a problem to a narrower sub-problem without making any real progress. He draws on his own exchanges with GPT-5.6 Pro rather than on a formal benchmark.
Why it mattersThis lands in the middle of a noisy fortnight for AI and mathematics, and it is the most useful thing said in it, because it is neither a press release nor a dismissal. Gowers is describing a division of labour rather than a scoreboard: the machine covers ground, the human decides which ground is worth covering. It also explains why announcements of solved problems keep drawing objections from mathematicians. Search finds results that were already nearly within reach, which is a real contribution — but it is not the part of the work people mean when they call a problem hard.
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