British mathematician Timothy Gowers, a distinguished Fields Medalist, has recently revealed a groundbreaking achievement: ChatGPT 5.5 Pro independently conducted PhD-level mathematical research in number theory in under two hours, with absolutely no human intervention. Gowers explicitly stated in his blog that his own mathematical contribution was zero, and he didn't even employ any particularly clever prompts.
Gowers, who holds the Combinatorics Chair at the Collège de France and is a Fellow at Trinity College Cambridge, presented ChatGPT 5.5 Pro with open problems from a paper by number theorist Mel Nathanson. These problems explore the possible sizes of certain sets of integer sums and the efficiency with which sets possessing prescribed properties can be constructed.
ChatGPT 5.5 Pro Solves Open Math Problem in 17 Minutes
Nathanson had previously proven an exponential bound for one of these problems and posed the question of whether it could be improved. According to Gowers, ChatGPT 5.5 Pro "thought" for 17 minutes and 5 seconds before delivering the best possible construction, achieving a quadratic bound. The core idea involved the model swapping out a component in Nathanson's proof for a more efficient variant, which is well-known in combinatorics but had not been obviously applied to this specific problem before.
Upon request, ChatGPT then rewrote the entire argument as a LaTeX preprint in just 2 minutes and 23 seconds. Gowers verified its correctness and subsequently had the model solve a related variant, which it handled flawlessly. Both results are now available as a preprint.
Generalised Problem: From Exponential to Polynomial Breakthrough
A generalized version of the problem proved significantly more challenging. Prior work by Isaac Rajagopal, an MIT student, had established an exponential dependency for this problem. Gowers provided ChatGPT with Rajagopal's paper and tasked it with finding an improvement.
What followed was a gradual escalation of the model's capabilities: after 16 minutes and 41 seconds, the model presented a first improvement. Rajagopal deemed this step correct but characterized it as a routine modification of his own work. Gowers then, as he put it, "got greedy" and prompted ChatGPT to aim for a much stronger bound.
After another 13 minutes and 33 seconds, the model reported optimism but noted that two technical statements still required checking. Nine minutes and 12 seconds later, the checks were complete. The final preprint was ready in 31 minutes and 40 seconds. The model had successfully improved the bound from exponential to polynomial.
Gowers reported Rajagopal's assessment that the results are "almost certainly correct," both regarding individual proof steps and the underlying ideas. Rajagopal’s nuanced judgment indicated that while the initial improvement was a "routine modification," the subsequent improvement to a polynomial bound was "quite impressive." He specifically called the model's key idea "quite ingenious" for discovering a counterintuitive approach.
