Terence Tao, the UCLA mathematician and Fields Medalist often described as one of the finest living mathematicians, has issued a warning about what artificial intelligence is doing to mathematical research: the stock of good open problems is being "mined in a non-renewable fashion," and the identification of worthwhile problems — not their solution — is becoming the field's scarcest resource. Writing in a four-part thread on Mathstodon on Monday, Tao laid out why he believes the AI era may push mathematicians toward secrecy, reversing centuries of open scientific exchange. For more on the research front, follow the latest AI research coverage on our homepage.

An Ocean of Problems, a Shortage of Drinking Water

Tao's argument starts with a paradox. The set of possible math problems is infinite, so scarcity sounds absurd. But quantity is not the issue — quality is. Anyone can generate endless open problems at will, Tao noted, such as computing the 10^10^10th digit of pi. The vast majority are worthless: they "show no particular propensity to reveal any further insights or connections to other questions."

"A country or region can suffer a critical shortage of drinking water while simultaneously being surrounded by a massive ocean," he wrote.

Deciding which problems deserve attention, he argued, is "a lengthy, deliberate, and subjective process," informed by historical experience with what earlier work on similar problems actually produced. Central to that judgment is what Tao calls the "difficulty landscape" — knowing which questions current methods can answer easily, which take real effort, and which are impossible, because the interesting problems tend to live at the boundaries.

AI Is Flattening the Difficulty Landscape

That landscape is exactly what AI is erasing. AI tools have "flattened the difficulty landscape now in many areas of the subject," Tao wrote, "thus destroying the ability to locate promising new problems in that area." Worse, there is no stable frontier marking where AI competence ends: the technology changes too quickly, and — in a pointed jab — Tao blamed the boundary's obscurity in part on "the refusal of AI companies to disclose their negative results, or reveal the process towards obtaining their solutions."

The result, in Tao's telling, is a race dynamic he has directly witnessed: "even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential."

The Open-Science Incentive Problem

That is where the warning turns structural. If announcing a research direction invites an AI swarm to strip-mine it, mathematicians may simply stop announcing anything. "The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community," Tao wrote — an outcome he noted would reverse centuries of tradition in which mathematics advanced through open problem-sharing in journals, seminars and preprint servers.

Indiscriminate AI use, he argued, delivers short-term wins at a long-term cost: it solves "problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained."

Tao's Proposal: Designate Problems Worth Solving Carefully

Tao does not propose banning AI from mathematics — he concedes that is probably infeasible. Instead he suggests communities designate classes of problems where the solution process itself matters, so that a raw answer without analysis of the techniques used, and without what it reveals about nearby problems, would be treated as "of negligible or even negative value."

His analogy is modern food banks, which no longer accept arbitrary donations just because they are technically edible, instead maintaining explicit standards for what contributions are actually useful.

In a reply to a commenter, Tao added a related observation: traditional automated theorem provers "aren't very good at proving theorems," a field dominated instead by what he called "automated theorem verifiers" — the difference with LLMs is "largely their effectiveness."

A Crowded Week for AI and Mathematics

The thread lands at a charged moment. It came days after OpenAI announced that an internal model had produced a Lean-verified proof that Navier-Stokes fluids can blow up in finite time — a claimed milestone toward the Millennium Prize Problem that NYU mathematicians whose work underpinned the effort say unfolded without proper credit, a dispute covered by Science magazine and here on AI Buzz Wire. Tao has been a careful chronicler of this transition all year, publishing a widely read essay on mathematics in the age of AI.

His new post sharpens that argument from a new angle: the risk is not that AI solves everything, but that it consumes, unearned and unanalyzed, the finite catalog of problems worth solving — leaving the next generation of mathematicians with an ocean of the worthless kind.

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