Fields Medalist Timothy Gowers tested ChatGPT 5.5 Pro on open problems in additive number theory and reported that the AI produced PhD-level research in approximately one hour. The system improved theoretical bounds from exponential to polynomial using a novel mathematical construction, with the work validated by MIT researcher Isaac Rajagopal whose prior research formed the foundation.
AI Discovers Novel Construction in Number Theory
Gowers tested the model on open problems from Mel Nathanson's paper regarding the diameter needed for sets with prescribed sumset sizes. With just a few prompts containing no mathematical input, ChatGPT 5.5 Pro discovered a novel construction using h²-dissociated sets, creating what Rajagopal described as "half a geometric series squeezed into a polynomial interval."
The improvement from exponential to polynomial bounds represents significant progress on the problem. Rajagopal noted that "the improvement to polynomial in k is quite impressive...the sort of idea I would be very proud to come up with after a week or two of pondering."
Mathematical Research Training Faces Fundamental Shift
Gowers documented the experience in a blog post on May 8, 2026, with a guest contribution from Rajagopal. He observed that research training faces a fundamental shift, stating: "It is no longer enough that somebody asks a problem: it needs to be hard enough for an LLM not to solve it."
Gowers suggests future mathematicians should focus less on seeking immortality through theorems and instead value "insight into the problem-solving process itself." The story reached the Hacker News front page with 460 points and 319 comments.
GPT-5.5 Released in April 2026
OpenAI released GPT-5.5 on April 23, 2026. The model's mathematical capabilities demonstrated in Gowers' test represent a significant advance in AI reasoning abilities, producing work that Gowers characterized as making "a perfectly reasonable chapter in a PhD thesis" in just a couple of hours.
The validation by Rajagopal, whose work provided the theoretical foundation, adds credibility to the assessment of the AI's mathematical contribution.
Key Takeaways
- Fields Medalist Timothy Gowers reported that ChatGPT 5.5 Pro produced PhD-level mathematical research in approximately one hour with minimal prompting
- The AI improved theoretical bounds on an additive number theory problem from exponential to polynomial using a novel construction with h²-dissociated sets
- MIT researcher Isaac Rajagopal validated the work, noting the improvement was "the sort of idea I would be very proud to come up with after a week or two of pondering"
- Gowers suggests mathematical research training must shift focus, as "it is no longer enough that somebody asks a problem: it needs to be hard enough for an LLM not to solve it"
- OpenAI released GPT-5.5 on April 23, 2026, demonstrating significant advances in mathematical reasoning capabilities