AI Is Solving Math's Oldest Problems — and Mathematicians Are Asking What Their Profession Is For

In mid-May 2026, OpenAI announced that one of its frontier models had disproved the Erdős unit distance conjecture — an 80-year-old problem in discrete geometry that had resisted some of the sharpest minds in the field since Paul Erdős posed it in 1946. In August, the same company published ten new mathematical and theoretical computer science results from an unreleased model called Astra, including a construction of a non-sofic group, a disproof of Connes’ rigidity conjecture, and resolutions of several more Erdős problems. Anthropic, not to be outdone, published two AI-derived results in academic cryptanalysis in July and released Claude’s ambitious attempt on the 150-year-old Riemann hypothesis.

For a discipline that measures progress in decades, this has been a bewildering year. And now the mathematical community is doing something it rarely does in public: it is arguing about what it is actually for.

A summer of soul-searching

The debate spilled into the open this week. On August 25, The Guardian published an opinion piece by mathematician Kasra Rafi and security researcher Bruce Schneier titled “No, AI doesn’t mean the end of mathematics — at least not yet.” Two days later, the newspaper printed a reply from Dr. Henry Bradford, a fellow of mathematics at Christ’s College, University of Cambridge, that is being widely shared among researchers: “Surprising AI breakthroughs raise soul-searching questions for mathematicians.”

The context for both pieces is telling. Earlier in August, around 40 top mathematicians gathered at OpenAI’s offices to discuss the future of their profession. The meeting was off-the-record, but by most accounts the mood was, in Schneier and Rafi’s words, “mostly pretty glum. People fear for their jobs, their careers and the work they love.”

Bradford’s letter is unusually personal. He notes that a key problem in his own field — the existence of non-sofic groups, a question in group theory that had stood for two decades — was solved that same month by OpenAI’s Astra model. “Astra’s proof consists largely in a slight twist on theorems by my colleagues Gabor Kun and Andreas Thom,” he writes. “Even a few months ago I would have found the idea that AI was capable of such a breakthrough incredible, so it seems foolhardy now to bet against AIs achieving superhuman capabilities in all areas of mathematical thought in the coming years.”

What the machines actually did

Strip away the existential dread, and the technical record of 2026 is genuinely remarkable. Schneier and Rafi — who have studied the results closely — sort AI’s mathematical achievements into two categories.

The first is finding counterexamples. The disproof of the Jacobian conjecture is the standout: once the counterexample was found, verifying it was quick and straightforward. The hard part was locating it in an enormous space of possibilities, a task where the AI appears to have combined machine-learned intuition with brute computational search — exactly the kind of grinding exploration humans are bad at.

The second is cross-pollination. The unit distance conjecture, most mathematicians believed, was probably true; they were searching for proofs, not refutations. The counterexample that killed it imported ideas from algebraic number theory — a field with no natural constituency working on discrete geometry. As Schneier and Rafi put it, an expert with exactly that background would probably have found the disproof if they had deliberately set out to look. But no such expert had a reason to work on this problem. AI, because of its scope, simply doesn’t have those disciplinary blinders.

The pattern repeated in August. According to reporting by Quanta Magazine, Astra’s ten advances include solutions to Erdős problems 146 and 180, the long-asked non-sofic group construction, and the disproof of Connes’ rigidity conjecture — results spanning combinatorics, group theory, and operator algebras. Quanta’s August 3 piece, “Why the Legendary Erdős Problems Are Falling to AI,” notes that a growing number of the celebrated problems Erdős left behind — with cash bounties attached, in his famous tradition — have now been settled by machines rather than people.

The limits argument

Schneier and Rafi’s core claim is that these are, in a precise sense, low-hanging fruit. “Current AIs are very strong at searching and recombining existing ideas,” they write, “but they are weak at building any deep and sustained new theory.” None of the 2026 results required inventing a new mathematical framework — no Grothendieck-style reconstruction of the foundations, no novel theory built from scratch. The AI excelled at searching a vast space of known mathematics and recognizing an unexpected connection; it did not create the mathematics it was connecting.

They also point out a subtler point about verification: a counterexample or a short proof can be checked quickly, which is why these results landed so decisively. The deep, theory-building work that defines mathematics at its highest level — the kind that takes a Fields Medal committee a decade to fully appreciate — remains outside the reach of the current generation of models.

Bradford concedes all of this. His question is different: what happens if and when it changes?

Thurston’s answer

The most interesting move in Bradford’s letter is his appeal to Bill Thurston, the great American topologist. In his celebrated 1994 essay “On Proof and Progress in Mathematics,” Thurston argued that mathematicians “discover … that what they really want is usually not some collection of ‘answers’ — what they want is understanding.” On this view, mathematics does not primarily live in papers and theorems. It lives in human brains, and new theorems are markers of progress in understanding — understanding that only exists while there are humans to hold it.

This matters politically, Bradford argues, because the economics are about to get brutal. “If AI can churn out research papers faster and cheaper than humans, then administrators within cash-strapped universities will surely be tempted to regard their mathematical researchers as superfluous.” On Thurston’s view, that would be a category error: the value of a working mathematician is not the paper they publish this year but their role in “the preservation and furtherance of mathematical knowledge among people.”

His closing line reframes the entire debate: “Whether mathematics thrives or perishes in the age of AI is not merely a technical question about the capabilities of future machine intelligences. It is a collective decision that society makes about what it is in the human intellect that we choose to value.”

Why this goes beyond mathematics

The argument is a preview of one that every knowledge profession will soon have. Mathematics is simply the first to face it squarely, because it has the cleanest definition of “solved” — a proof is a proof — and therefore the least room to hide behind ambiguity about whether the AI really did the work.

The three-way split now visible in the community is instructive. The pessimists fear administrative logic: if papers can be generated, departments will be cut. The optimists, like Schneier and Rafi, note that theory-building — the actual engine of the field — remains untouched, and expect a productive decade of human-AI collaboration on exactly the kind of search-and-connect problems that have been falling. And a third camp, with Bradford, argues the entire framing is wrong: the output of mathematics was never really the product, and a civilization that lets machines do its understanding has lost something regardless of how many theorems get proved.

The next milestone is easy to name and hard to date: the first AI-produced result that genuinely creates new theory rather than recombining old ideas. Until then, mathematicians are in the strange position of watching their field’s most famous open problems fall one by one, while arguing about whether any of it was the point.