Three Years Ago, AI Struggled with Basic Arithmetic. Now It's Solving Problems That Stumped Humans for 80 Years.

To understand the tension at the conference, consider the slope of this curve: three years ago, the best models couldn't reliably do arithmetic. Last year, they matched the world's top high school students at math competitions. This year, they're starting to crack open problems that have resisted humans for decades.

Three developments anchor that last claim:

May: An unreleased internal OpenAI model falsified the Erdős unit distance conjecture, posed in 1946 and open for 80 years. Princeton mathematician Noga Alon called it "probably the best-known problem in this subfield of discrete geometry."

July: A mathematician working at Anthropic posted that Claude Fable had found a counterexample to the Jacobian conjecture in higher dimensions.

August 1: OpenAI announced that an internal version of its next-generation model family, Astra, had "solved ten major open problems," several of which "have broad significance across mathematics." As of this writing, these results had not yet undergone peer review.

Of the 20+ Mathematicians Interviewed, Most Aren't Panicking

A significant number said AI does help their research, but only in a limited way; they expect AI to keep complementing human weaknesses, not replacing humans outright.

To be clear: this was a series of 20+ face-to-face conversations, not a statistical survey. So all we can say is "a significant number," not a percentage.

More importantly, there's a second layer. Even those who believe AI will eventually surpass humans on all mathematical tasks bristle at the phrase "math is solved." Their reasoning: mathematics has a whole spectrum of goals and values, and "solving open problems" is just one of them. AI will change which goals humans should pursue, but it won't change why humans wanted to do mathematics in the first place.

Why They're Not Panicking: Every Time a Machine Masters Something, Mathematicians Just Rename It "Computation"

This composure doesn't come out of nowhere. At the press conference, a high-school student reporter asked the assembled medalists a question: if a student worries AI will push them out of mathematics, what would you say?

Tsimerman's answer: keep learning, keep improving, because you don't know what the world will look like; also, engage with AI proactively, because it's bound to be a big part of the future. But he added: "I don't think this profession will exist in its current form."

Yu Deng, a University of Chicago professor and a fellow Fields Medalist, disagreed. Describing himself as "on the more optimistic side," he predicted that "AI will come to help mathematicians, not replace them." His vision: future mathematicians propose new theories, new ideas, new frameworks, while AI handles part of the technical details.

The key is his next sentence: "AI will get stronger, but by then we will redefine what counts as technical details. I believe the way we do mathematics will change, but the joy we get from it will not."

In other words, the boundary of "technical details" is itself movable. This is precisely how mathematics has coped with automation for decades: once computers make multiplication or algebraic simplification trivially easy, humans move up a rung to new problems computers can't tackle; each chunk that gets eaten is reclassified as "not really mathematics anymore."

Jordan Ellenberg captured this mindset best in his 2014 book How Not to Be Wrong:

After all, mathematics has been computer-assisted for decades. Many computations that were once considered "research" are now viewed the way we view adding a bunch of ten-digit numbers — nothing creative, nothing praiseworthy. Once your laptop can do it, it stops being mathematics.

But that hasn't put mathematicians out of work. We've always managed to stay just ahead of the expanding frontier of what machines can do, like an action hero sprinting in front of a fireball. And if future machine intelligence can take over much of what we now call research? Then we'll reclassify that research as "computation."

Jordan Ellenberg, How Not to Be Wrong, 2014

This playbook has worked every time. The open question is whether it will work one more time.

The Most Common Way Mathematicians Use AI Now? As a Guide Into Unfamiliar Subfields

Attitudes only go so far. Here's how mathematicians actually use AI — three levels of engagement, from lightest to heaviest.

Level 1 is the most common because it feels safest. Carnegie Mellon's Jeremy Avigad has noticed the pattern: people are fine with "AI as a powerful search engine," but balk at "AI proving theorems." Same model, different role — finding is fine, concluding makes people uneasy.

Neckrasov added a detail: before, with that 500-page textbook, he might spend weeks reading before realizing it didn't even match his project. Now that AI points him to the right pages, he reads "more focused, more motivated," because "those are exactly the results I need."

And even at the heaviest level of use, he still treats AI as a tool:

Even when I have AI prove something, I already have a picture in my head of what the project looks like, what it's about, what methods should be used.

What I want is for it to do the work on my idea — to help me process my own ideas faster — not to have it think for me.

Vasiliy Neckrasov, graduate student, Brandeis University

Who's Actually Worried: Early-Career Mathematicians — Because the Problems Grad Students Train On Are Exactly What AI Is Best At

The established crowd can afford to stay calm. One level down, the anxiety is sharper — Avigad's blunt take: the earlier you are in your career, the more you have to lose. Two mechanisms explain why.

First, the training pipeline. Grad students learn by grinding through problems that are hard but doable — exactly the tier AI now handles best. AI isn't taking students' work away. It's taking their practice away.

Second, money. If the public decides AI can replace mathematicians, funding dries up. Two interviewees — Columbia's Michael Harris and Leiden's Rodrigo Ochigame — pointed to a July White House report as the narrative in action. The report argues for shifting resources away from "legacy" research institutions and explicitly cites "AI doing mathematics" as a case study.

Harris and Ochigame are both members of the "Leiden Declaration" working group, which we'll get to.

Our reporter's own assessment: if AI progress in mathematics stopped right now, the basic structure of the field would hold. Human mathematicians would gravitate toward the side AI is weak at — proposing new ideas — while using AI to accelerate the routine parts.

Does "AI Can't Do Theory-Building" Actually Hold Up?

That brings us to the final defense. Mathematicians' last claim to irreplaceability: AI can't do theory-building — inventing new definitions and frameworks that make previously unaskable questions possible. Solving a problem is navigating an existing map; theory-building is drawing a map that didn't exist.

Our reporter put this to Tsimerman. He wasn't buying it, citing a familiar pattern of moving goalposts:

First it was: it can talk, but it'll never do math. Then: it can do contest math, but it'll never do research math.

Jacob Tsimerman

The direction of the goalpost movement, he said, is predictable.

Greg Burnham, a researcher at Epoch AI who does long-term capability evaluation, framed the same issue differently: "Sometimes I hear mathematicians talk about AI and they fall into a trap that many of us fall into — commenting only on current capabilities without grasping where the trajectory of capability growth leads."

But Burnham's own stance isn't "AI will definitely break through." In his view, AI could hit a ceiling and never produce genuinely original ideas or theories; it's equally easy to imagine that as training scales up, models will develop genuinely original mathematical abilities. Both scenarios are consistent with the current evidence.

Tsimerman's camp believes AI could surpass humans on every mathematical task — not just solving posed problems, but posing the interesting questions in the first place, and clearly articulating the path to the answer.

Terence Tao: Mathematics Has Seven Goals. AI Has Accelerated Only One.

But following this thread leads to an entirely different level of discussion. Suppose Tsimerman is right — that AI will soon exceed humans on every cognition-related mathematical task. Does that make human mathematicians useless?

On July 25, Terence Tao gave a public lecture in Philadelphia titled "Mathematics in the age of AI." He put up a slide with a simple question: "What are our goals?"

"I don't think anyone has made a complete list," Tao said.

His core argument follows. For a long time, a fuzzy list didn't matter, because these goals were aligned: solving a hard problem helped you understand the world, and brought together a community working on the same problem. Chase one, the others follow automatically. So everyone talked about just one or two goals, and nothing went wrong.

What AI breaks is precisely that alignment. It races ahead on one particular item — "solving open problems" — while the others don't keep pace. So pursuing one sub-goal begins to come at the expense of the others.

Later in the lecture, he gave a concrete example:

We are very, very close to a situation where a major result is proven and verified to be correct, but no human can understand it or explain it.

Terence Tao, July 25, 2026, Philadelphia

This pushes the goal of "solving research problems" forward by a huge margin, while simultaneously dragging "human understanding of the discipline" backward. Tao's conclusion: mathematicians now need to articulate "what mathematics should be for" far more clearly than before, in order to mount a real response to this shock.

Thurston's 1994 Record: He Proved His Theorems Too Well, and It Killed the Field

What happens when a proof is too hard for anyone to understand? It actually happened thirty years ago. In 1994, Fields Medalist William Thurston published an article in the Bulletin of the American Mathematical Society titled "On Proof and Progress in Mathematics," where he recorded a true story.

His central claim: what mathematicians are really doing is finding "ways for people to understand and think about mathematics" — especially as members of a social community.

He used his own career as an example. Early on, he worked in a field called "foliations" (don't worry about what it is; Thurston himself wrote "it doesn't matter"). At the time, several groups were actively working on it, and he quickly proved a string of major theorems, including a classification theorem giving necessary and sufficient conditions for a manifold to admit a foliation.

Then the field was emptied. Thurston breaks the cause into two parts, which he calls two "ecological effects."

The first is the barrier. His papers were written in the conventional, intimidating style of a mathematician, heavily relying on readers already sharing certain background and insights. But foliations was a young, opportunistic new field; there was no standardized background at all. He would casually invoke whatever mathematics he'd learned from elsewhere, with no room to explain it in the paper. He'd also toss out extremely condensed, almost mystical insights — his example: "the Godbillon-Vey invariant measures the spiraling of a foliation" — which read like Greek to most readers at the time. The barrier to entry was thus raised enormously high, and many grad students and mathematicians retreated as soon as they couldn't even follow the proofs of the key theorems.

The second is what's left for others.

When I started doing foliations, I thought everyone wanted the answers. I thought they wanted a powerful set of proven theorems they could use to answer more mathematical questions. But that was only part of the story. More than knowledge, people want understanding that is their own.

William Thurston, "On Proof and Progress in Mathematics," Bulletin of the American Mathematical Society, Vol. 30, No. 2, April 1994

And in a system that credits people by name, they also need the credit that comes with theorems.

The consequences came quickly: within a few years, he heard mathematicians telling each other, "Don't go into foliations; Thurston has cleaned it out." Someone even told him as a compliment that he'd killed the field. Graduate students stopped learning it, and before long, he himself moved on to other things. Thurston stresses this wasn't because the territory was mined out — there were plenty of interesting questions then, and still are. Today, very few mathematicians can understand the state of the art in foliations as it was back then.

Now translate that story into AI terms. The mechanism is identical — and stronger. If AI proves a batch of important open problems in ways completely impenetrable to humans, the motivation for people to think deeply about mathematics is pulled out. There are fewer frontiers for young mathematicians to pioneer, the field struggles to train the next generation, and human understanding of existing mathematical theory slowly erodes.

Fields Medalist Timothy Gowers spelled out this endgame in a July 26 blog post:

We might end up in a situation where the mathematical literature has expanded enormously in some form, but there is no corresponding community of human experts with a shared understanding of any part of it. Almost all of mathematics would become like the fields we have largely forgotten: papers sitting on shelves for decades, read by no one.

Timothy Gowers, July 26, 2026

Another Mathematician Disagrees: Even With All the Answers Available, People Would Still Do Math

But there's a completely opposite way to read the same situation. University of Toronto professor Daniel Litt wrote a blog post in February 2026 titled "Mathematics in the Library of Babel," which imagines an extreme scenario leaning the other way:

Imagine a library containing a proof of every theorem, complemented by excellent guides. You ask a question; it leads you to the answer and explains it to you. What would mathematicians do in such a library?

Asked that way, the answer is clear: they'd be thrilled and get to work immediately. They'd start asking questions right away: How is the Riemann Hypothesis proved? How is the Hodge Conjecture proved? And that one thing they've always wondered about (for me, the Grothendieck-Katz p-curvature conjecture)? Then they'd keep working until they actually understood the answer. That work is nowhere near done. Not even close.

Daniel Litt, "Mathematics in the Library of Babel," February 2026

Litt added a note after this: he isn't saying humans are inherently better at asking interesting mathematical questions. "I'm just saying this is why we got into math in the first place: we want to understand. That's the point."

Here's a relevant context: that optimistic blog post is itself a self-correction, a record of "I underestimated." Litt originally expected AI wouldn't produce research rivaling top human mathematicians until 2040, and was unlikely to do so before 2030. In March 2025, he made a bet with Tamay Besiroglu, co-founder of Mechanize, wagering that AI wouldn't manage it by 2030 — at 3:1 odds, giving himself the longer odds. By the time he wrote the blog post, he said he expected to lose that bet.

An even more direct data point comes from "First Proof": a group of top mathematicians pulled 10 lemmas from their own unpublished work to test the models. Litt expected 2 to 3, optimistically 4 to 5. Across all attempts combined, the result was 6 to 8.

So his optimism has nothing to do with "AI being weak." He's optimistic because even if AI is strong, there's still work for humans to do.

The Leiden Declaration: 3,000+ Signatures. Gowers Helped Draft It but Didn't Sign.

Positions alone aren't enough; the mathematical community has already tried to codify them. The most formal collective response so far is the "Leiden Declaration," which grew out of a September 2025 workshop at the Lorentz Center in Leiden, Netherlands. Participants included historians, philosophers, computer scientists, AI researchers, and mathematicians from several subfields.

Its structure is tripartite: a preamble, then a list of "the characteristic values of mathematical research that we have a shared interest in preserving," followed by the threats to each value, and finally recommendations to individuals, mathematical organizations, policymakers, and AI companies. Michael Harris and Rodrigo Ochigame, both mentioned earlier, are members of the declaration's working group.

Putting values and threats side by side makes the conflicts immediately visible:

One recommendation to policymakers has a headline that says it all: "Don't believe the hype." The tech industry has strong commercial incentives to exaggerate its products' abilities; consult experts, including mathematicians, when making policy, rather than relying on press releases and popular coverage of mathematical results.

Our reporter's assessment of the declaration is measured: it reads more like a starting point than a complete picture. It doesn't say what the future of mathematics should look like in a world that has already been profoundly changed.

Gowers Attended That Workshop but Didn't Sign

The declaration now has over 3,000 signatures. Gowers' reason isn't opposition. As he put it: "It makes confident assertions and recommendations in several places where I don't have confidence."

The point he's least sure about is "results are attributed to specific authors." His thought experiment: if, in the future, AI is autonomous enough to read the literature itself, solve problems it finds, and its solutions are automatically formally verified — so correctness is beyond doubt — then there is simply no human to take credit or responsibility. Would that be a bad thing threatening mathematical values? His analogy: if mathematical theorems no longer bear the names of mathematicians, perhaps that's no more problematic than "stars aren't named after astronomers; most stars don't have names at all."

His own alternative is the most concrete proposal in this entire discussion: shift the credit from "the one who solved it" to "the one who explained it."

If A solves a major open problem in one shot using a large model, with the result formally verified and correctness beyond doubt; and B spends the effort digesting that solution and writing it in a form other mathematicians can read and learn from — then B should get most of the credit. This kind of credit doesn't work like today's. Today's credit is admiration for brilliance, insight, speed, and hard grind; this kind of credit is closer to the gratitude we feel for someone who "wrote a great textbook, making a whole field coherent and readable." He even imagines that the job of a "research mathematician" in the future might be: picking out a slice of the vast output AI produces, and writing it into a book that gives other mathematicians the satisfying sense of "truly mastering a field."

But Gowers immediately douses this with cold water: whenever someone says "the future role of humans is X," his pessimistic inner voice asks — why do you think AI can't do X? Take this very proposal: why couldn't ChatGPT 8.2 chat with you for a bit about your mathematical taste and background, then produce a perfect textbook customized just for you?

The Last Interviewee: The Old Way of Doing Math Won't Survive, but Something Else Will Grow

What grows out of a dead-end path? Mathematician and author David Bessis put both sides on the table.

"I don't think the old way of doing mathematics has much of a chance of surviving." But, he says, "something else will grow" to take its place. He doesn't know exactly what it will look like, but he believes there are fundamental reasons people will keep doing something that looks like mathematics.

"We still want to understand the world. We still want to understand mathematics."

The gloom the reporter expected never came. A significant number said AI does help them, but only in limited ways. Same-cohort Fields Medalist Yu Deng of the University of Chicago: mathematicians propose new theories and frameworks; AI handles technical details. "AI will get stronger, but by then we'll redefine what counts as technical details."

Look at the same line from the other direction and you get Tsimerman's rebuttal. The last line of defense is that AI can't propose genuinely new definitions and frameworks (making previously unaskable questions askable). His answer: there's a record of moving goalposts. First it was "it can talk, but it'll never do math." Then "it can do contest math, but never research math." Greg Burnham, who evaluates AI capabilities at Epoch AI, added a measured note: AI could hit a ceiling and never produce original theory, or it could develop genuinely original capabilities as training scales — both are consistent with the current evidence.

Let's look at what they actually do with AI. The most common use is as a guide into an unfamiliar subfield. Brandeis grad student Vasiliy Neckrasov put it most concretely.

Carnegie Mellon's Jeremy Avigad identified the mechanism: people are far more comfortable with "AI as a really powerful search engine" than "AI proving results directly." Same model — when it's finding the path, people accept it; when it's producing conclusions, people get nervous. Two more levels of use: letting AI solve a piece of a larger project; and paying $200/month for Codex to search literature, fill proof gaps, and review drafts — Neckrasov's premise being that he has the whole picture in his head first, then has AI work on his ideas.

On July 25, Terence Tao gave a public lecture in Philadelphia, showing a slide titled "What are our goals?" with a list of reasons for doing mathematical research. He said himself: no one has made a complete list.

Tao's example: we're very, very close to a situation where a major result is proven and verified to be correct, but no human can understand it or explain it.

What happens when a proof is too hard for anyone to understand happened once before, thirty years ago. Fields Medalist William Thurston recorded it in the Bulletin of the American Mathematical Society: early in his career, he quickly proved a string of major theorems in "foliations," and then the field was emptied out.

The opposite reading exists too. University of Toronto's Daniel Litt imagined a library with a proof of every theorem and excellent guides: mathematicians would be thrilled and get to work immediately, working until they truly understood the answer. He's optimistic because even if AI is strong, there's still work for humans. When he wrote it, he had just revised his own timeline — he'd originally bet AI couldn't match top human mathematicians by 2030; he now expected to lose that bet.