Timothy Gowers reports ChatGPT 5.5 Pro produced PhD-level additive combinatorics results in under an hour, verified correct by MIT student Isaac Rajagopal.
Key Takeaways
ChatGPT 5.5 Pro solved an open problem from Nathanson’s additive number theory paper by improving a diameter bound to quadratic, confirmed best possible.
It then improved Rajagopal’s exponential upper bound on a related parameter from exponential-in-n to polynomial-in-n, using an idea Rajagopal called original and clever.
The model thought for 17 minutes per hard sub-problem and produced LaTeX preprints autonomously; Gowers contributed zero mathematical input.
Gowers flags a publishing gap: results are publishable quality but arXiv bans AI-written content, and no credentialed repository for human-verified AI math yet exists.
The training-pipeline implication is direct: “gentle” open problems used to onboard PhD students are now solvable by LLMs, raising the bar for what counts as a viable first research problem.
Hacker News Comment Review
Commenters split on framing: several argue Gowers is the solver using LLM as tool, similar to how F1 drivers get credit despite car performance, not that the LLM independently did research.
A recurring skeptical thread notes every new frontier model gets the same “this is the first one that really works” reaction, questioning whether 5.5 Pro is a step-change or a familiar pattern.
Deeper discussion via John Baez quote asks whether mathematical value derives from scarcity of insight or utility of results, with implications for whether AI-generated proofs deflate the field or simply change its economy.
Notable Comments
@YeGoblynQueenne: argues the framing inverts causality – mathematicians are solving problems with ChatGPT, not ChatGPT solving problems autonomously.
@zarzavat: distinguishes three mathematician archetypes – problem solvers, theory builders, applied users – and analyzes which are most threatened by LLM capability gains.
