The AI maths breakthroughs everyone quotes are counterexamples, not proofs
A counterexample and a proof are not the same kind of achievement. A proof shows that something is always true. A counterexample shows that something claimed to be always true is not, by producing one object where it fails.
Both settle a question. They ask different things of whoever finds them. One demands an argument that covers every case. The other demands a single object, and permission to keep guessing until you have it.
That distinction is the subject of a blog post the Cambridge mathematician Timothy Gowers published on 12 August. Gowers won the Fields Medal in 1998. He has also read the papers, which most people commenting on AI and mathematics have not.
He is not dismissive. He calls the results “extraordinarily impressive” and says plainly that models can prove hard things too.
“LLMs are not just good at finding counterexamples: they can find proofs of difficult statements...
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