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Gowers: LLMs' famous maths solutions are mostly counterexamples, not proofs
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In a blog post, Tim Gowers reflects on which mathematical problems LLMs handle well, observing that their most celebrated solutions are counterexamples rather than proofs, and discusses the difficulty of defining a counterexample.
For engineers building or using LLMs for mathematical reasoning, Gowers' analysis suggests that current models are particularly strong at finding counterexamples but not uniformly superior to humans. This informs expectations about where LLMs can be reliably applied in math-heavy workflows and where human oversight remains necessary.
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Gowers notes that LLMs have solved major problems like the non-sofic group and multicolour Ramsey number, but these are mostly counterexamples.
He argues that LLMs can also find proofs, but the most famous successes are counterexample-based.
He highlights that defining a counterexample is not straightforward, using Vinogradov's three-primes theorem as an example.
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