Gowers, 62, winner of the 1998 Fields Medal, often known as the "Nobel Prize of Mathematics", and a professor at the College de France, said on his blog recently that he gave the AI open number theory problems from a paper by mathematician Mel Nathanson, and it improved existing results with what he described as "zero" contribution from himself.

"I didn’t even do anything clever with the prompts," Gowers wrote.

One problem asked whether an existing mathematical bound, or limit, could be improved.

After thinking for 17 minutes, the model identified a better method by replacing part of the original proof with a more efficient approach already known in combinatorics, a branch of mathematics focused on patterns and arrangements, but not previously applied to that specific problem, according to The Decoder.

When asked, the AI then rewrote the proof as a full academic preprint in just over two minutes.

1998 Fields Medalist Timothy Gowers. Photo courtesy of College de France

He then gave the AI a more general version of the problem involving previous work by Isaac Rajagopal, a student from U.S.'s Massachusetts Institute of Technology, who had earlier found an exponential result for a similar problem, and asked for an improvement.

After reviewing Rajagopal’s paper, ChatGPT first made what Rajagopal described as a routine improvement. Gowers then asked it to attempt a much stronger result. Less than an hour later, the model had improved the result from exponential to polynomial, producing another complete preprint.

Rajagopal said the first improvement was expected, but called the stronger result "quite impressive." He described the AI’s key idea as "quite ingenious," saying it found a new way to compress complex mathematical structures while preserving their most important properties.

"It is the sort of idea I would be very proud to come up with after a week or two of pondering, and it took ChatGPT less than an hour to find and prove, using similar methods to those in my own proof," he said, adding that the idea appeared "completely original."

Gowers said the work was comparable to "a perfectly reasonable chapter in a combinatorics PhD," noting that while it was not a groundbreaking discovery, it was a meaningful and non-trivial extension of existing research.

He said the rise of advanced language models could change the future of mathematics. "The lower bound for contributing to mathematics will now be to prove something that LLMs can’t prove," he wrote.

Gowers said future researchers may need to focus less on routine proof-building and more on asking better questions, guiding AI systems, and finding problems machines still cannot solve. He predicted that by 2029, mathematical research could be transformed "out of all recognition."