AI and the Math Crisis: Riemann, Navier-Stokes Explained

At a gala for the National Museum of Mathematics in New York, a number theorist stood with a whiskey in one hand and his phone in the other, refreshing every few minutes because he knew a company was about to post results at six o'clock sharp. When the post landed, the first thing he saw made no sense to him. Quasi-RH. As in quasi-Riemann hypothesis, one of the oldest open problems in mathematics, apparently cracked in an evening by a machine that had been told, in effect, to go do a breakthrough.

That mathematician is Rutgers number theorist Alex Kontorovich, and the night he is describing, alongside MIT theoretical computer scientist Ankur Moitra and University of Washington fluid dynamicist Steven Brunton, is the subject of this conversation. Over the last few weeks, AI systems from OpenAI and Anthropic produced claimed solutions or major progress on several of the hardest problems in math: the quasi-Riemann hypothesis, the Unique Games Conjecture, a forced-case proof of blowup in the Navier-Stokes equations, and a full formalization of Fermat's Last Theorem in the Lean proof assistant, a system that checks mathematical arguments line by line against the axioms of logic (79:28). None of the three guests call this the death of mathematics. All three describe something closer to a professional identity crisis, arriving faster than anyone's career plans accounted for.

Kontorovich frames the question with what he calls the solved axiom: assume that any problem a human could solve with AI help could eventually be solved by AI alone (19:59). He does not think that is true yet, but he is willing to entertain it for the sake of argument, because the more interesting question is what survives if it ever is true. His answer is that pure mathematics is not actually in the business of producing true statements. It is in the business of understanding, and understanding only exists inside a human skull.

"The value of pure mathematics is that it lives in the heads of human beings." — Alex Kontorovich, Rutgers mathematician (21:33)

Terence Tao, the Fields Medal-winning mathematician, wrote something the group returns to more than once: that patient, slow research by graduate students and postdocs is being casually disrupted by these releases, the way a movie spoiler ruins a plot you can no longer discover for yourself (13:46). Moitra, who studies complexity theory and algorithms at MIT, pushes back gently. He reaches for an idea borrowed from outside mathematics entirely: the doorman fallacy, the mistake of reducing a complex job to its single most visible task, then assuming a cheaper machine that performs that one task has replaced the whole role.

The Doorman Fallacy

A hotel decides a doorman just opens doors, so an automatic door can do the job more cheaply. But a doorman also greets guests, recognizes regulars, handles luggage, hails taxis, and signals that the building matters. Moitra's point is that "solving theorems" is mathematics's most visible task, the one that makes headlines and wins medals, but it is not the whole job.

"What does a mathematician do? The simplest and most visible part of the job is we prove theorems. But I don't think that's all that a mathematician does." — Ankur Moitra, MIT mathematician (28:37)

The harder question is whether the proofs themselves represent something new, or just a faster way of finding what was already there. Kontorovich and Moitra debate two competing metaphors from the mathematician Tim Gowers. One is the convex hull: imagine a balloon containing every idea mathematicians have already produced, with any combination of those ideas living somewhere inside it. Under this reading, the AI proofs are derogatory, a fancy way of saying the systems stayed inside a boundary humans had already drawn, just reaching conclusions no one had bothered to assemble (42:26). The other metaphor is a semigroup: known moves, like tiles, placed one after another, reaching territory that turns out to be far larger than anyone had explored, even though every individual tile was already known (44:56). Kontorovich leans toward the semigroup reading for the quasi-RH proof specifically, calling the chain of known techniques "shocking" in how far it reached (42:47), even while conceding that no single genuinely new idea, no new definition or concept, appeared in the process (44:15).

What actually got proved is worth naming plainly. The Riemann zeta function is, in Kontorovich's description, a kind of signal-processing machine for prime numbers, converting a strip of complex numbers into information about how primes are distributed (76:03). The Riemann hypothesis says all the "zeros" of that function sit at exactly the same point along that strip; a weaker, still unproven cousin, the quasi-Riemann hypothesis, only requires a region near the edge to be entirely free of zeros. For seventy years, the width of that zero-free region had not budged. The new AI-generated proof produced a zero-free vertical strip between seven-eighths and one, the first movement on that measurement in decades (94:12), though Kontorovich is clear the method used cannot be stretched further, down to the one-half line the full hypothesis requires (94:31). Separately, the Unique Games Conjecture, a central open question in complexity theory about how hard certain approximation problems are, was reportedly proved true, building on a weaker result two of Moitra's colleagues had proved years earlier (139:22). And Brunton's own field, fluid dynamics, got a computer-assisted proof that the Navier-Stokes equations, which describe how fluids move, can blow up to infinity in finite time under smooth external forcing, a question mathematicians had only started seriously chasing about fifteen years ago (113:46).

Why Nature Keeps Being Easy

Moitra offers the most useful frame for why any of this works at all. Deep learning systems solve optimization problems that are, in a strict worst-case sense, cryptographically hard. And yet they solve them every day. His explanation: natural data, whether it's protein sequences or human language, has quietly evolved to make computation easier than the worst case would predict, the same way folding proteins that were too computationally brittle simply didn't survive across generations (180:04).

"Nature abhors a vacuum... my version of it is that in some sense, nature abhors computationally hard problems." — Ankur Moitra, MIT mathematician (181:44)

That same idea reappears in something Moitra calls subliminal learning. Fine-tune one AI model to love owls, then have it generate random-looking numbers with no mention of owls anywhere. Train a second, unrelated model on those numbers, and it starts bringing up owls in conversation too (184:47). Hidden statistical structure, invisible to a human reader, carries the trait across. It is a small, slightly eerie demonstration of the same principle: these systems are picking up patterns in data that are real but not visible to us, the same quality that may explain both their strange successes and the discomfort of not fully understanding why a given proof works.

By the end of the conversation, the advice on offer is less about surviving AI and more about remembering why anyone did this in the first place. Kontorovich tells pure-math graduate students to keep learning the hardest, most abstract material they can absorb, under a mentor's guidance, exactly as mathematicians always have (206:24). Moitra's advice is to stop optimizing every stage of a career for how it looks on paper and instead act as though tenure is already secured.

"Pretend you already have tenure and do what you would have wanted to do all along." — Ankur Moitra, MIT mathematician (217:08)

Kontorovich closes on something plainer still. Intelligence, he says, has been mistaken for the whole point, when it is closer to a cherry on top. Formalized proofs, Fields Medals, even the Riemann hypothesis itself, are not what anyone will remember at the end. What they will remember is the people.