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On the last morning of a weeklong national holiday in China, a mathematician checked his phone and found one email after another with the same PDF. It was a list of unsolved math problems, and OpenAI had just claimed answers to many of them.
In a post on the Proofs and Prompts blog that collected more than a hundred reactions from mathematicians around the world, Fudan University professor Xiaolei Wu, who works in group theory, described reading the list of solved problems. “It looked unreal,” he wrote. “These were almost all the major open problems in my field!”
OpenAI posted the 722 papers to GitHub on the night of October 6, all written by an unreleased AI model that had been pointed at roughly 4,000 open problems. Mathematicians have spent the time since deciding whether to cheer or grieve, and some, like Wu, seemed to do a little of both.
A flood of proofs, a few retractions
This was not the first shot across the math bow from OpenAI. On September 8, the company said an internal model had cracked the Navier-Stokes problem, a longstanding question about how fluids like water and air move. The problem carries a $1 million Millennium Prize, one of seven offered for solving some of math’s most intractable problems (one had been solved by a human in the early 2000s). OpenAI said as many as 10,000 AI agents worked on it at a computing cost in the millions of dollars.
A credit fight followed. NYU's Tristan Buckmaster and Anthropic's Levent Alpöge had posted related work a day earlier, and Buckmaster accused OpenAI of racing ahead after learning about it. OpenAI said it never saw their work, and Sam Altman defended his team.
The October dump was bigger. None of the five remaining Millennium Prize problems fell outright, but the papers claimed advances on three of them, including the Riemann hypothesis, the famous puzzle about prime numbers.
Mathematicians who reviewed the batch said many results were strong enough to anchor an academic career. Even a researcher at rival Anthropic called the release the most significant moment in mathematical history.
OpenAI said an average result took computing resources equivalent to about three hours of ChatGPT Pro thinking time, a fraction of the computing power behind the Navier-Stokes push.
But OpenAI also had to pull three papers within days after finding errors. It also wasn’t clear how many of the papers had been thoroughly checked. OpenAI said that the results are “at different stages of verification” and that “many, but not all, of the manuscripts have been formalized.”
Weeks earlier, 25 Fields medalists, Terence Tao among them had warned that rushing out AI solutions could hurt math itself. After the dump, a group letter called the release "not a demonstration of scholarship, but a demonstration of power."
OpenAI did not share its prompts or which model it used, which went against the advice of an advisory group of mathematicians it helped form, and said it planned to keep testing its models on open problems.
Proofs without people
Some researchers saw their lifetime work upended overnight, whether it was only planned or already in progress. Open problems that anchored dissertations, grant proposals and careers were suddenly answered.
But math had not been solved. The answers arrived before the understanding, flipping the usual order. Not all of the results will necessarily hold up, but the work of checking them, explaining them and connecting them to the rest of the field could take years.
The new danger was the newly opened up easy road. With answers arriving ready-made, it was tempting to skip the slow work that built understanding in the first place, and the field could pay for that later. Tao wrote that none of the humans behind the new proofs were around to answer questions, give talks or train students. He likened it to hearing a movie spoiler or a crossword clue.
“One cannot explore a problem as profitably and richly once one is aware of an existing solution,” he wrote on the Proofs and Prompts blog post.
Math is not the only field facing that trade. Classrooms, offices and labs are all trying to work out how to use these tools without letting them do the thinking, and few had settled on the balance. In effect, people are having to learn a new way of learning.
Or, as a mathematician put quite poetically, “Some of our favourite mountains have been conquered,” University of Oxford professor Martin Bridson wrote, “but behind them are bigger mountains that we can tackle with new equipment.”