Several of the mathematical results OpenAI announced in August 2026 involved constructing examples that mathematicians had long sought. In an essay published on August 12, Timothy Gowers asked whether LLMs might be especially good at this kind of search.
The results included the first construction of a non-sofic group and a proof concerning how multicolour Ramsey numbers grow. The former settled an open question in group theory; the latter addressed a major Ramsey-theory problem.
A possible pattern is that language models are good at finding examples or counterexamples. Gowers spends much of his essay questioning even that description. The same mathematical result can look like a proof or a counterexample depending on how the problem is stated. LLMs have also proved difficult general theorems.
Gowers considers another possibility: models can draw on a large collection of known techniques and try many approaches quickly. Humans may have an advantage in recognizing which directions need a deeper conceptual insight. He suggests this could explain some differences between their mathematical work, but says he has no scientific answer yet.