The summer AI ate math

PHILADELPHIA, PA.—On July 24, the math world’s only true celebrity walked onto its most illustrious stage, to speak to the unprecedented threat that he and his peers are now facing.

Terence Tao is not a dramatic man. He speaks in a soothing voice, often tipping his head down and closing his eyes as he plucks each word with care from some recess of his revered mind. But that evening, several of those words were uncharacteristically grave. His lecture, entitled “Mathematics in the Age of AI,” struck a more foreboding tone than any of his previous comments on the subject. “It is a very confusing mess right now.” Artificial intelligence’s rapid ascent in math research, he said, has created “a crisis in our mathematical values and practices.”

Tao’s address was planned as the centerpiece of the International Congress of Mathematicians, the field’s largest gathering held once every four years, this time in Philadelphia. But just days ahead of it, Anthropic’s Claude Fable AI had disproved a longstanding mathematical idea called the Jacobian conjecture with a devastating, tweet-length equation. This came right on the heels of ChatGPT solving two other titanic open problems. A few months prior, any one of these feats would have been enough to secure a young mathematician a high-profile publication and a coveted tenure-track job. Now, many in the packed convention center ballroom felt completely at sea.

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Since that evening, the pace has only accelerated. On Tuesday mathematicians used AI to solve the first “Millennium Prize Problem” in 20 years—the field’s greatest conceivable achievement.

The AI onslaught, Tao said to his tense audience, is a moment for circumspection. If mathematicians want to figure out what the human’s role will be in this evolving equation, they first need to step back and ask: Why do they do math in the first place?

Tao’s advice doesn’t just apply to mathematicians. As AI companies push their tech to surpass humans in every way possible, we’re all trying to figure out how we fit into the fast-approaching future. That means looking inward, asking why we do the things we do, and how we’re fulfilled by them. It’s a task we shouldn’t procrastinate on—as Andrew Sutherland of the Massachusetts Institute of Technology put it to me over coffee at the congress, “mathematicians may be the canary in the coal mine for a lot of other professions.”

For math, the stakes are existential. The AI industry is convinced that conquering the subject’s “objective” truth is how companies will persuade investors that they’re on the path to superintelligence. Multiple AI companies have made eating mathematics their top priority. As one of several new AI-for-math start-ups attests in its slogan, “Solve math, solve everything.”

For the past year, I’ve been watching the situation unfold, witnessing a passionate but cloistered community of artisan-scientists become collateral damage in the technological arms race. But in Philadelphia, I could sense the anxiety coming to a head. In conversations over catered cheesesteaks and crochet sculptures of hyperbolic geometries, the central question of our age lay just beneath the surface of every conversation: How do you preserve what you love doing most when a machine can suddenly do it better?

The congress opened, as always, with the announcement of the Fields Medals—math’s highest honor, awarded every four years to up to four mathematicians under age 40. At a press conference with the winners—whose names were leaked earlier in the week, after someone asked ChatGPT to scrape the event website—the unstated theme of the congress took the spotlight. Jacob Tsimerman, who won for groundbreaking work at the interface of number theory and geometry, responded to a question about AI by announcing that he was leaving mathematics to work on AI safety for OpenAI.

For anyone who knows Tsimerman well, the news was less of a surprise. He recently authored a “taxonomy” of all the ways the technology might precipitate the human race’s extinction. He aims to work within the industry to put up guardrails on the damage AI can cause. “I’ve been saying this for a while,” he said when we caught up later in the week. “People just haven’t been listening.”

Tsimerman’s solemn projections clash with his outgoing, sweetie-nerd aura—he has taught improv classes to mathematicians and attended the Fields ceremony in a sky-blue velvet tuxedo. AI is a threat that his community is taking too lightly, he says. “We are not doing a sustainable thing,” he told me. “AI is going to become better than mathematicians at research mathematics very shortly.” At OpenAI, he hopes to mitigate the worst version of that future.

But many in the community see Tsimerman’s choice as a betrayal. Throughout the congress, several mathematicians told me that they found his statements irresponsible, that he was stoking the younger generation’s worst fears about their professional prospects, and that he was naive for trying to effect change within OpenAI’s corporate confines. Some even said that awarding him a Fields Medal—meant to free up young prodigies for a lifetime of advancing mathematics—was a mistake, in light of his impending departure from research.

Tsimerman wasn’t hurt when I relayed these complaints, responding with characteristic ease. “I want to break what I view as a taboo,” he said. “The idea that one shouldn’t talk about true-but-scary things, because they’re scary, is wrong.”

And the future of AI-dominated math offers “so much to be excited about,” he said. Tsimerman looks forward to an era where far more is known and proven—where there will be an infinite library of AI-generated results that mathematicians will have the privilege of parsing.

Others agree that acceptance is the only option. Javier Gómez-Serrano, a Brown University mathematician, has worked with the Google AI team on his favorite open question: whether or not the math we use to describe the motion of fluids is intrinsically broken. He now begins his talks with a slide on the “five stages of AI grief,” a painful but necessary road he thinks every mathematician is on.

Gómez-Serrano agrees with Tsimerman that math will never be the same. There will be fewer jobs, and they will be different, but they will go to those who adapt. “The whole system is going to collapse,” he told me at the congress. “Better to do something now than wait until it’s too late.”

Tao’s Friday evening lecture called another speech to mind. In 1900, amid a different mathematical crisis, the great mathematician David Hilbert stood in front of the second ever International Congress of Mathematicians and charted a clear path that has guided the field ever since. I can’t be the only one in the audience who made the connection—it’s the most famous speech in math’s long history—and Tao seemed aware of this.

Tao spoke of that crisis, when mathematicians realized that a number of paradoxes sat at the core of their subject. The supposed edifice of objective truth they’d spent centuries constructing apparently sat on a shaky foundation. “It was traumatic,” he said, “but we came out at the end with something very valuable.”

It was Hilbert who laid out a program to repair the ground math stood on by constructing basic, self-evident truths called “axioms,” from which all others could be derived. Problems arose with that plan, Tao admitted, but it succeeded in getting the field through the crisis. Today, most mathematicians are confident that their proofs begin and end with true statements.

“We are now entering a similarly turbulent period,” Tao said. “We have to actually think about our culture and practices.” But in the end, he said, “our subject will be much healthier and much more resilient.”

Tao is the closest thing math has to a leader—a modern-day Hilbert—and he seems aware of that responsibility to chart a path forward. He’s been dishing long social media posts tracking AI’s progress since before most mathematicians considered it a threat. Now, he’s advising they get proactive.

According to Tao, this identity crisis, too, is an opportunity for mathematicians to clarify what matters to them—why they do math, and what it should look like. AI companies have different incentives, and without proper checks, they would run roughshod over math’s established academic norms. Mathematicians need to decide on new norms, and enforce them, to rein in AI’s worst impulses, he says, and make it the boon to math it has the potential to be.

“We should … set the rules on what types of AI use are acceptable and which ones are not,” he said, “and not let external actors define the rules for us.” Tao complimented the Leiden Declaration, an effort by mathematicians to come together and advance new norms for AI use. (One of those “norms”—that the authorship of proofs should not be attributed to an AI model—is already receiving pushback from AI companies and some mathematicians.)

Tao’s view is that mathematicians shouldn’t eschew the technology. It has the potential to advance their interests, he believes, if they can rein it in with clear safeguards.

The night after Tao’s lecture, at a reception of the American Mathematical Society, I caught up with its president, Ravi Vakil. He wanted to correct the narrative around a splashy recent AI result, the aforementioned counterexample to the long-believed Jacobian conjecture. Claude Fable hadn’t done the mathematicians’ job for them, he said—it had made it more fun. On a popular blog, a number of top mathematicians had come together to make sense of the counterexample—to understand why the conjecture was false—and had found the answer fascinating. “It’s only a happy story,” Vakil said, because human understanding of the mathematical world grew. “Somewhere in this room right now, someone is explaining it to someone else.”

This is the happy future Vakil sees: AI might solve problems, but mathematicians will still have the joy of making sense of it all. A result is important only if mathematicians find meaning in it. As long as that’s true, math will remain a human endeavor, he says.

Vakil sees an urgent need to convince young people that math is still open to them. “People are especially anxious who don’t understand,” he says. Vakil’s tenure as president has already seen massive funding cuts and pullback on the visas that math departments rely on to attract top talent. Math graduate programs are accepting fewer students than in years past, he says. The narrative that AI is eating math, he fears, will become another excuse to cut funding.

He also worries about a generation of mathematicians pampered by the AI shortcut. “There’s no royal road to mathematics,” he told me. “You need to struggle with hard problems for long periods of time and be stuck.” This concern, that “the kids are not all right,” was a theme mathematicians echoed again and again. Students have been “freaking out” for a while, “but now it is reaching a crescendo,” as Sutherland put it to me.

So I circled the reception in search of young faces, accosting the gaggles of math Ph.D. students as they nursed their ticketed free glass of wine. I went around asking: If you could push a button that would stop all this AI-doing-math business, would you?

In true mathematician form, they had lots of technical questions about how this magical button would work and what downstream consequences it would have. Among those I could convince that this wasn’t some kind of monkey’s paw scenario, my unscientific poll split more or less down the middle.

Everyone in this group agreed on one thing, at least, far more than their seniors: AI will keep getting better at math. As Ph.D. student Hami Mehrabi put it, “it will make becoming a mathematician harder.” The goal they’ve built their lives around, to secure a tenure-track academic job, has always been enormously competitive, but AI will make those scarce postings ever scarcer.

Most wouldn’t give me their names. Whether they were excited or frustrated over AI, they felt the debate was too fraught and that they might be professionally penalized for airing their opinion. “I wish none of it happened,” said one such anonymous student, who feels that using AI is no longer a choice. He’s paying for a Claude “Max” plan just to keep up. “You’re hurting yourself if you don’t have a subscription,” he said.

But I was surprised, with all I’d heard, how many students remained hopeful about the future. “I just want to know the truth,” said Denisse Escobar Parra, a Ph.D. student at the University of California, Santa Barbara. “AI is helping us do things faster—I don’t think that’s bad.” Escobar Parra conceded that there will be fewer jobs, but she was willing to bet on her own ability to earn one. The culture of math has always been to dissuade all who don’t believe themselves exceptional. About half the young people I talked to had internalized this mentality, to the extent that they welcomed any further raising of the bar.

But amid all this acceptance, a growing faction of mathematicians isn’t ready to concede that AI is the field’s only future—not without a fight.

As Michael Harris and I crossed 17th Street toward the towering liberty-green copper dome of Pennsylvania’s largest Catholic church, he pointed a few blocks west. “You know I actually grew up right over there.” I’d chased down the Columbia University mathematician and Philly native after a session on the mathematics of Bach. We were now walking to the Cathedral Basilica of Saints Peter and Paul to hear the lecturer play some Bach sonatas on its enormous pipe organ.

For five years, Harris has been putting out a popular Substack newsletter criticizing the “mechanization” of mathematics—the active effort to subsume the age-old discipline into the modern, computer-dominated world.

Harris thinks mathematicians should be responding to tech’s intrusion like graphic artists and screenwriters—who have more in common with mathematicians, spiritually, than software engineers do, he feels—and are fighting to forbid AI wherever possible. Rather than collaborating with purveyors of frontier models to solve more problems, Harris argues, they should resist through collective action.

We arrived at the church early for the performance and stood in the center aisle, under its great vaulted nave, speaking in hushed voices. Harris resented Tsimerman’s public warnings—“a Fields medalist saying, ‘There will be no human mathematicians in four years,’ is guaranteed to discourage people from going into mathematics”—and he criticized as naive mathematicians who hoped AI companies would ever willingly adhere to the field’s standards of research conduct. But Harris agreed with Terence Tao about his talk’s thesis—that now was the time to focus on “why we do mathematics.”

It’s actually a question that’s long obsessed mathematicians, who have explored it in multiple famous, ruminative essays that are now required reading. Harris himself wrote a long, discursive book about his “problematic vocation.” For him, he told me, “math is about human flourishing.” It’s a thing people do solely for the sake of passion—not because it will be useful, or even beautiful, to anyone else. In our utilitarian world, Harris said, this is actually an act of defiance. “The idea that someone can simply work for a living and like what they do is a problem for capitalist society,” he whispered as mathematicians filed past us, filling up the pews.

For centuries, mathematicians have made an uneasy arrangement with society to skirt this “problem.” Students of engineering and medicine need to learn math, so as long as mathematicians teach, they’re funded and can spend the rest of their time on proofs. AI and politics are challenging that arrangement, but it’s not likely to collapse soon. “I find it very difficult to believe that there’s going to be a significant drop in teaching positions,” mathematician Geordie Williamson said. If smartphones and Google didn’t devalue math education, why should AI?

What’s under threat is the other side of the arrangement—the research that mathematicians fund through teaching. Even if humans retain a role in explicating AI’s discoveries, will it still amount to flourishing? “There is still a lot of value to having an expert human in the loop,” Sutherland says. “But it’s not clear how long that will last. And it’s really not clear how we should be training the next generation of mathematicians to be that expert human in the loop, and whether they will even want to be.”

Even Tao shares this fear. “We are very, very close to a scenario in which a major result gets proved,” he said in his lecture, “and no human can understand and explain it.”

In just the few weeks since the congress, something in the discourse has begun to shift. “There are a lot of mathematicians who have critical views on AI, but for a while were only discussing them behind closed doors,” says Naomi Sweeting, who just started a tenure-track position as an assistant professor of math at M.I.T. Recently, she says, “some are taking that critical perspective a little more public.”

In a widely circulated essay posted on August 3, the mathematician Max Weinreich presents “the case for total opposition to the use of artificial intelligence in mathematics.” He calls for individual mathematicians to outright refuse to use AI, and even to “use our intellectual authority to oppose its development.” On August 9, California Institute of Technology Ph.D. student Tasmin Chu authored a blog post entitled “The AI Dissenter Viewpoint,” arguing that mathematicians have “moral obligations to avoid collaborating with AI companies.” (A new blog called Proofs and Prompts launched on August 7 and has become a repository of more critical writings, including essays by multiple Fields medalists.) Even an August 17 math preprint paper ostensibly unrelated to the debate fired shots in a stray footnote, proclaiming that “mathematicians are currently being instrumentalised in a large scale advertising campaign by AI companies competing for market monopoly.”

Indeed, much of the anger is directed at the industry. “Our field is being used as fodder for press releases for these corporations,” Sweeting said. “And their agendas really have nothing to do with our goals.” As mathematician Srikanth Iyengar put it to me at the conference in an outburst of frustration: “They don’t care about beauty; they don’t care about truth. They only care about money.”

Sweeting also spoke of a “class divide” AI is exposing in math. “There are some people at the very top who are really excited about this,” she told me. “And there’s also a large population of people with less job security who are really concerned.” Similarly, Emily Riehl noted during a panel that industry collaborations and access to frontier models seemed to flow mainly to well-connected, mostly male, mathematicians—that the AI era might restore the “old boy’s club” of mathematics’ past. “It’s a question I haven’t heard anyone ask,” Riehl told me afterward. “But it’s been on my mind a long time.”

The stages of grief presume that something is lost, that fighting to recover it is futile. But the last month shows that mathematicians don’t all agree. “Technology should be here to serve us and not the other way around,” said Sweeting, whose website clearly states a personal no-AI policy. “I want to send a signal to graduate students that it is okay not to use AI and to do math for yourself.”

Williamson—who has authored papers with AI companies and considers himself one of the more AI-excited voices in the community—expressed disappointment at Tsimerman’s departure from research. “It’s sad,” he says. “It feels like a harbinger of things to come.” He doesn’t hesitate to tell me he’d push the hypothetical button to make AI go away. “It’s all happening too fast.” Williamson’s talk opened with a quote from M.I.T. professor Zhiwei Yun. “As a mathematician, I care not just about the end results, but also the journey,” it read. “AI is destroying my journey.”

It’s this tension, between the path to a result and the quantity of them, that AI is heightening in many parts of life. Do we do things to do them, or because we want them done?

“I view math as part of a vast and beautiful human project,” Sweeting says. “It’s this huge endeavor that puts us in communication with thousands of years of human thinking.” The question mathematicians are asking—the one we’re all asking—is whether the human project will continue if the thinking ceases to be human, and whether accelerating the future’s arrival is worth that cost.