Tim Gowers used ChatGPT 5.5 Pro to produce PhD-level additive number theory results in under an hour, with zero mathematical input from himself.
Key Takeaways
ChatGPT 5.5 Pro solved an open problem from Nathanson’s additive number theory paper, constructing a quadratic upper bound after 17 minutes of reasoning – verified correct by MIT student Isaac Rajagopal.
It then improved Rajagopal’s exponential bound to polynomial in k, using what Rajagopal called a clever, original idea he would have been proud to find after weeks of work.
The LLM’s edge came from recognizing that Nathanson’s inductive construction implicitly used a Sidon set, then substituting a more efficient Sidon set of quadratic diameter.
Gowers flags a structural problem for math research culture: “gentle” open problems, traditionally used to onboard PhD students, are now solvable by LLM in under an hour.
No clear publication venue exists for AI-produced correct mathematics; Gowers proposes a moderated repository requiring human certification or proof-assistant formalization.
Hacker News Comment Review
Commenters broadly agree expert human oversight remains necessary: LLMs still make conceptual errors only domain experts catch, making deep human knowledge a prerequisite for reliable use.
A recurring thread debates credit and analogy: commenters compare the human-LLM dynamic to F1 drivers and cars – the human who directs and certifies the work still contributes meaningfully, even if the LLM does the technical lifting.
Access inequality surfaced as a concrete concern: frontier long-thinking models like GPT-5.5 Pro are unaffordable under typical Eastern European academic budgets, creating a two-tier research environment.
Notable Comments
@vthallam: OpenAI employee publicly offered a free Pro account to the academic commenter who raised the access-cost barrier.
