趋势解读：Fields Medalist says ChatGPT 5.5 Pro delivered "PhD-level"，聚焦形式化数学证明能力

British mathematician Timothy Gowers used OpenAI's ChatGPT 5.5 Pro model to tackle open problems in number theory, with the AI producing complete scientific papers in under two hours, without any mathematical guidance from Gowers himself. According to Gowers, the AI's output reached "PhD-level" and managed to improve upon existing mathematical bounds, demonstrating a remarkable degree of independent mathematical reasoning. Isaac Rajagopal, a young researcher involved in the work, called the model's key idea "completely original," an achievement he said a human mathematician would be proud of after weeks of deliberation. British mathematician Timothy Gowers had ChatGPT 5.5 Pro tackle open problems in number theory. The model significantly improved an existing mathematical bound. One of the junior researchers involved calls the model's key idea "completely original." Fields Medalist Timothy Gowers writes in his blog that ChatGPT 5.5 Pro has produced a piece of doctoral-level mathematical research, and that his own mathematical contribution was zero. The model did all the work in under two hours. "I didn't even do anything clever with the prompts," Gowers writes. The mathematician, who holds the Combinatorics Chair at the College de France and is a Fellow at Trinity College Cambridge, fed the model open problems from a paper by number theorist Mel Nathanson. The paper investigates the possible sizes of certain sets of integer sums and how efficiently sets with prescribed properties can be constructed. Ad Nathanson had proved an exponential bound for one of the problems and asked whether it could be improved. According to Gowers, ChatGPT 5.5 Pro thought for 17 minutes and 5 seconds, then delivered the best possible construction with a quadratic bound. The core idea: the model swapped out a component in Nathanson's proof for a more efficient variant that's well known in combinatorics but whose application to this particular problem wasn't obvious. Ad DEC_D_Incontent-1 When asked, ChatGPT rewrote the argument as a LaTeX preprint in 2 minutes and 23 seconds. Gowers checked it for correctness, then had the model solve a related variant, which it handled without any issues. Both results are available as a preprint . A generalized version of the problem proved much harder. Here, there was prior work by Isaac Rajagopal, an MIT student who had proven an exponential dependency. Gowers gave ChatGPT Rajagopal's paper and asked for an improvement. Ad What followed was a gradual escalation: after 16 minutes and 41 seconds, the model delivered a first improvement. Rajagopal judged this step correct but called it a routine modification of his own work. Gowers then got, as he puts it, "greedy" and asked ChatGPT to try for a much stronger bound. After 13 minutes and 33 seconds, the model reported optimism but said two technical statements still needed checking. Another 9 minutes and 12 seconds later, the check was done. The finished preprint was ready in 31 minutes and 40 seconds. The model had improved the bound from exponential to polynomial. Ad DEC_D_Incontent-2 According to Gowers, Rajagopal declared the results are "almost certainly correct," both at the level of individual proof steps and the underlying ideas. Ad