Timothy Gowers · 2026-05-08 · major
Tim Gowers: A Recent Experience With ChatGPT 5.5 Pro — Fields Medalist Watches GPT Solve Open Number-Theory Problems Polynomially in Two Hours
Fields Medallist Tim Gowers documents handing Mel Nathanson's open additive-combinatorics questions to ChatGPT 5.5 Pro and watching it improve exponential bounds to polynomial ones in roughly two hours, with what Gowers calls completely original constructions.
A Fields Medallist hands an open math problem to ChatGPT 5.5 Pro and gets a polynomial bound back in two hours, with what he calls a completely original argument.
What is it?
A long blog post from Sir Timothy Gowers — Cambridge research professor, 1998 Fields Medallist, and combinatorics chair at the Collège de France — describing what happened when he gave ChatGPT 5.5 Pro the open questions in Mel Nathanson's recent additive-combinatorics paper on the diameter of sets with prescribed sumset sizes. Gowers notes upfront that his mathematical input was zero.
How does it work?
Gowers fed the model the questions cold. For the h=2 case, ChatGPT 5.5 Pro replaced the existing 2^k − 1 exponential upper bound with a quadratic bound that Gowers calls best possible, building the construction from Sidon sets and arithmetic progressions. For general h, a first attempt cut the bound from exponential in k to exponential in k^α for any α greater than 1/2 (16 minutes 41 seconds of thinking time); a second pass got it down to polynomial in k inside roughly two hours of total wall-clock. The key device — using h²-dissociated sets to control relations — was, in Gowers' view, completely original.
Why does it matter?
Gowers is exactly the audience that LLM-skeptical mathematicians have pointed to as the unfooled judge. His post lands a different conclusion: 'the lower bound for contributing to mathematics will now be to prove something that LLMs can't prove.' The piece is also concrete evidence for the GPT-5.5 Pro pricing tier — Gowers ran the long 30/180-per-million-token model, not the cheaper Instant default — and feeds directly into the open argument about whether AI mathematical research counts as research.
Who is it for?
mathematicians, AI researchers, anyone tracking the math-research bar
Try it
https://chatgpt.com — model picker → GPT-5.5 Pro