A recent experience with ChatGPT 5.5 Pro
Mathematician Timothy Gowers watched ChatGPT 5.5 Pro produce PhD-level additive number theory results in under an hour, with zero mathematical input from him.
What Matters
- ChatGPT 5.5 Pro solved a problem from Mel Nathanson’s open problem paper in 17 min 5 sec, yielding a quadratic upper bound that is best possible.
- The key improvement over Nathanson’s known result: using a more efficient Sidon set of quadratic diameter instead of powers-of-2.
- In 16 min 41 sec it tightened Isaac Rajagopal’s (MIT) exponential bound from exp in k to exp in k^ε for any ε>0.
- In a further 31 min 40 sec it produced a preprint achieving polynomial bounds; Rajagopal called it almost certainly correct at the level of ideas.
- Gowers’ threshold has shifted: the bar for open problems is no longer “unanswered” but “hard enough that an LLM cannot solve it.”
- No clear publication path exists: arXiv bars AI-written content, journals seem pointless, and Gowers proposes a moderated repository requiring human or proof-assistant certification.
- Rajagopal notes the polynomial improvement required an idea he would be proud to find after a week or two of pondering.
