© Ivan Pierre Aguirre for The New York Times
This story first appeared as the cover story in Issue 4 of The Atlas, a new global publication by Coda Story and The Continent. Sign up to the newspaper here.
In late July, at the International Congress of Mathematicians (ICM) in Philadelphia, the mathematician Jacob Tsimerman was awarded one of four Fields Medals – the highest honour in mathematics.
A few hours later, Tsimerman announced that he was joining OpenAI.
Tsimerman’s departure from theoretical mathematics, while at the absolute peak of his powers, highlights the fault line in a debate that is upending the normally quiet world of higher mathematics. “What a dick move,” said one mathematics professor, speaking to The Atlas off the record.
Tsimerman, who has written extensively about his fear of “omnicidal futures involving artificial intelligence” – a fear that AI could wipe out humanity, closely associated with the AI “doomer” community – has said he will work on OpenAI’s safety team.
Tsimerman and OpenAI did not respond to a request for comment.
In recent months, OpenAI has announced proofs of various longstanding mathematical problems, solved with one of the company’s latest large language models. Other companies have also made advancements: RedNote, a Chinese AI model, obtained a perfect score at the International Mathematical Olympiad in Shanghai in July.
Human mathematicians, at all levels of the profession, are reeling from the implications. Tim Gowers, a professor at the University of Cambridge who helped to verify one of OpenAI’s proofs, has written that even if AI models fail to progress further, “we have still probably entered an era where it will become very difficult for humans to compete with AI at solving mathematical problems”.
This is a startling assessment – and a marketing coup for the likes of OpenAI.
“Mathematicians actually have a special role in this,” said Joshua Grochow, an associate professor in Computer Science and (by courtesy)Mathematics at the University of Colorado Boulder. “The AI companies’ PR pitch is essentially to say, ‘Look, we have solved math. the intellectually hardest thing ever, therefore we can solve everything.’ ”
LLMs have not solved math – far from it. Nonetheless, Grochow added, recently some capabilities have improved. “They are legitimately able to produce real math, new math that they had not produced before. So you can’t deny that utility. You can deny the extent of that utility, but you can’t say it’s all BS.”
Miek Messerschmidt, a senior lecturer in mathematics at the University of the Witwatersrand in Johannesburg, recently used Anthropic’s Claude to take a crack at a problem that had stumped him. Claude solved it within 30 minutes. “How did I feel? You mean emotionally? I was relieved, because I didn’t have to go down this dead end any more. But I was also disconcerted by what this entity could do in such a short amount of time.”
Mathematics has been disrupted by technological leaps before. The abacus. The mechanical calculator. The blackboard, even, which played an instrumental role in standardising training and mathematical notation (“It’s hard to research, because most of what’s written on blackboards doesn’t stay there very long,” said mathematics historian Michael Barany).
But AI is a different kind of disruption. Where previous advances helped mathematicians expand the frontiers of their knowledge, large language models threaten the livelihoods, and purpose, of mathematicians themselves.
“Our place in society at developing new ideas has been quite unthreatened for quite some time,” said Tim Chartier, a Professor in the Department of Mathematics and Computer Science at Davidson College. “For a long time, the frontier of mathematics could only be expired by the mathematicians themselves. There were no tools that could push into that boundary, except the research mathematician…At this current time, it’s not like we don’t need research mathematicians – but the landscape has changed so quickly, it’s hard to know what that will look like a year from now, two years from now.”
This matters for everyone: for thousands of years, mathematics has been considered to be the foundation of scientific knowledge. There is no physics without mathematics. No astronomy without mathematics. And there is no computer science – or AI – without mathematics. What happens if there are cracks in the foundation?
“I think that LLMs pose an existential threat to the mathematical community,” wrote Tasmin Chu, a PhD student at the California Institute of Technology, in an essay published on 2 August – the day after OpenAI released a set of ten new mathematical results, resolving or making progress on various problems.
“This is a polemic, not a press release,” Chu continued. “I know that others feel the same way; I have spent today crashing out and learning that top mathematicians I know are crashing out.”
Some of what mathematicians are worried about is the same as what everyone else is worried about: that AI will take their jobs; that AI companies have absorbed everyone’s work, and are reproducing it without attribution or compensation; that students aren’t learning properly any more; and that there won’t be jobs for them when they graduate.
But some worries are more specific to the field. Like the fear that, if mathematics becomes too reliant on particular AI models, then AI companies will have the power to restrict access to a select few – or make it prohibitively expensive. That promising young mathematicians, instead of turning to research, will use their talents instead to refine proprietary algorithms, which may or may not be used for the common good. That there will be no one left to understand, let alone vouch for, the mathematics produced by the machines. That objective truth, or anything close to it, is going to be much harder to prove – a fear shared with journalists, incidentally, who find it increasingly difficult to verify whether a photograph is real or fake.
After speaking with more than a dozen leading mathematicians from around the world, The Atlas can confirm that Chu is not alone with her fears: it’s all anyone is talking about. The crisis is existential – and mathematicians are looking to one man in particular to guide them through it.
There are no working mathematicians who are truly famous. The closest anyone gets is Terence Tao, a professor at UCLA, who is often referred to as the world’s greatest living mathematician. A prodigy, Tao skipped five grades of school, receiving his masters degree at age 16. By 21, he had earned a PhD from Princeton, and was awarded the Fields Medal just ten years later, in 2006, for his pioneering work with Ben Green on prime number theory.
But what sets Tao apart, in a field infamously incomprehensible to outsiders, is his ability to communicate to both mathematicians and laypeople alike. This has made him a de facto spokesperson for the mathematics community – and extremely influential in setting its norms. “From all accounts he’s a lovely man,” said one researcher, speaking anonymously.
“But the social pressure to agree with Terry Tao is really strong.”
On July 24, the day after Jacob Tsimerman joined OpenAI, Tao gave a public lecture at the ICM titled “Mathematics in the Age of AI”. In it, he presents his “working hypothesis”: that AI tools for mathematics, which he already uses in his own research, will keep getting better. This will allow for collaboration on a vastly greater scale than has ever been possible before, Tao argues, and speed up the pace of research – revealing new, previously unimagined frontiers.
But it will also change, fundamentally, the role of human mathematicians. There will be little point in problem-solving – the computers will handle that. But the humans will still have to do the really hard work: understanding why AI-generated proofs are correct, and explaining this to others. The sooner they embrace this and plan accordingly, Tao concludes, the better.
The Atlas reached out to Terence Tao to request an interview. His human assistant, UCLA media relations officer Holly Ober, declined the request, making a referral instead to a “living document” which is maintained by Tao’s Claude AI assistant, on his website. This document synthesises Tao’s current thinking on AI, based on his public writings and talks, even “interviewing” Tao with follow-up questions.
As per his AI assistant, Tao believes that the topic of AI in mathematics is too important to be left to just a small number of spokespeople – and that his own “influence on this discussion should diminish as the rest of the community steps up.”
Not everyone believes in the inevitability of AI defining the future of mathematics. According to several sources, both organisers and funders were disappointed with the turnout at the ICM in Philadelphia. Despite the gravity of the occasion, the congress was not at capacity.
Ila Varma and Tarik Aougab, associate professors at the University of Toronto and Haverford College respectively, may have had something to do with that. In March, they launched a petition to boycott the ICM due to the ongoing war in Iran, increasing authoritarianism in the United States and the risks faced by visiting academics – if they were even allowed in. “AI companies were invited, but most African mathematicians who tried to attend couldn’t get visas,” Varma said.
More than 2,600 people signed the petition. For Varma, this is evidence that mathematicians may yet use their status to resist the influence – and the cash – of the big AI companies.
“There’s an idea that the positionality of mathematics in society is to decide who’s smart, who’s worthy of the most lucrative career opportunities and the privileges that go along with it. And now we are being asked to take this technology that is likely to be extremely unhealthy for users, that’s bad for the environment, this thing built on unethical labour, and our discipline is being used against many of our wishes to tell society that this thing is intelligent, and that you should let it do your thinking for you.”
Michael Harris, a professor at the Institut de Mathématiques de Jussieu in Paris, was at the ICM in Philadelphia. “The talks I attended on AI, starting with Tao’s public lecture, took pains to insist on the need for human mathematicians to make sense of anything produced in the name of the discipline, by machines or by humans,” he said. “There is a growing resistance to any use of AI whatsoever in mathematics, especially among young people, and this will become evident over the next few months.”
One of the clearest voices of dissent belongs to Max Weinreich, Assistant Professor of Mathematics at the City University of New York.
In an essay published earlier this month, Weinreich makes the case against what he describes as “artificial mathematics”: “Mathematicians do not need to use AI, nor should we use AI; soon, I argue, you will not want to have your name associated with AI. Instead, we should use our intellectual authority to oppose its development.”
His opposition is about more than mathematics, he told The Atlas. In his view, the environmental and financial implications of the AI boom pose major societal risks – and mathematicians, given their privileged position, are one of the few groups of people who can do anything about it.
As John Fletcher, a theoretical physicist and mathematician, observed: “There is a lot of power in being perceived as the smartest people in the world.”
Po-Shen Loh, a professor at Carnegie Mellon and former coach of the US International Mathematical Olympiad team, backs mathematicians to figure it out – by treating it like a maths problem. “AI is making mathematicians engage with the real world. They are smart enough to realise they have an existential crisis. They’re quickly racing down to discover all the dead ends, to see what works and what doesn’t.”
And when they figure it out, maybe they’ll let the rest of us know.
A version of this story, edited for length, first appeared in The Atlas newspaper. Additional reporting by: Shougat Dasgupta, Masho Lomashvilli, Irina Matchavariani.
Simon Allison
Isobel Cockerell
Isobel Cockerell
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