OpenAI says its latest model has solved close to 400 landmark open problems in mathematics, and the claim has left working mathematicians uneasy about the future of their field. In an October 6 report, the company said the model took about three hours of computation on average to crack each one. Those problems had been sitting unsolved for decades, serving as benchmarks that generations of researchers had tried to crack.

The company had made a bigger splash weeks earlier. In early September, OpenAI claimed that an internal model had solved the Navier-Stokes Millennium Prize problem. The effort reportedly unleashed about 10,000 agents that ran for 88 hours straight.

At Cornell, the reaction was swift. The entire math department, from faculty to staff to students, was called to a town-hall meeting the day before a lunch that one professor later described in a widely read essay. The meeting was meant to offer support, but it also raised hard questions. How should the department evaluate future job candidates? What should a Ph.D. student expect when an AI can solve a dissertation problem and even draft the thesis?

A race to the remaining problems

Not everyone sees the news as a crisis. Alex Townsend, a younger colleague who has been working on a book about computers and mathematics, said he had gathered roughly 200 important unsolved problems in his subfield, numerical linear algebra. Rather than let OpenAI or Anthropic reach them first, he decided to publish the list himself, in the hope that friends and colleagues could tackle them, possibly with AI help, before the big companies did.

Townsend told the author he was releasing another 600 long-standing problems across applied mathematics. He argues that resisting AI is futile and that mathematicians need to adapt quickly. His colleagues did not all agree. Some were excited by the plan. Others were angry, saying it helped speed up the solving of problems that should have been left for students and could undermine the pipeline for training young researchers.

The disagreement also reached the department in more personal ways. Justin Moore, a logician who works on set theory, told colleagues at the town hall about a problem he had followed for 19 years. In 2010, he bought a bottle of XO cognac in Luminy, outside Marseille, and planned to open it when the problem was solved. Then an AI proof of that problem appeared. When someone asked what he thought of it, Moore said he didn’t know, because he hadn’t read the paper yet. He said he had been “too busy.”

In an email afterward, Moore said he still planned to open the bottle once a group of trusted peers agreed the proof was correct and they collectively understood it. He also wrote that he had “a feeling that the cognac tasting will feel more like a wake than a celebration.”

Knowing versus understanding

Much of the split comes down to what mathematicians value. Applied mathematicians will use any available tool, including physical intuition, computers, experiments and data, to find an answer and make sense of it. Pure mathematicians care most about why an answer is true. For them, knowing the right answer without the reasoning can feel empty.

That tension is hard for the public to grasp. Curtis McMullen, a professor at Harvard and a Fields Medalist, put it bluntly in an email to the author: “Mathematics is not radiology. It is more like art or philosophy, and in fact, human understanding is what it is all about.”

Some students are asking the same question. Aria Beaupré, a graduate student, asked at the town hall what the point of pure mathematics is now. The author said he has since come to think the answer may lie partly in human connection. An undergraduate who wrote to him after a radio interview said that the ideas and math they shared brought meaning to their lives, and that AI could not replicate that.

Whether that is enough depends on what mathematics is. If mathematical truths exist independently of people, then AI’s discoveries are worth celebrating no matter who makes them. If mathematics is mainly a human creative pursuit, something may be lost when machines take over the search. Moore put it this way: “AI is separating those two things in an uncomfortable way and making us look in the mirror at ourselves.”

Prizes test the limits

Literary awards are facing similar questions. Some prizes have explicitly accepted AI-assisted work, including a Japanese short story prize that has honored entries developed with ChatGPT. Others have stripped awards after detector software flagged entries as machine-written. The Caine Prize for African Writing opened a review after Pangram, an AI-detection tool, flagged almost all of a winning story, according to The Atlantic. The author denied using AI, and no final finding had been announced as of October 21.

Those cases show how unsettled the rules remain. Detection tools can be wrong, and some writers have said they relied on speech-to-text software or other assistance. The question of what counts as the writer’s own work is still being worked out in both literature and mathematics.

This article was written with the assistance of AI.
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