News · 2026-09-09

Terence Tao says AI is strip-mining mathematics' supply of good problems

Terence Tao, one of the most prominent living mathematicians, argued in a four-part post on 8 September 2026 that AI systems are consuming mathematics' stock of good open problems in a way that does not replenish. His sharpest claim is an inversion of how the field has always valued work: "it is now the identification of a promising problem which is the scarce and precious resource," not the solving of one. He warns the incentives now point toward mathematicians no longer sharing promising directions publicly, which "would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."

Key facts

• The core claim: identifying a promising problem, not solving it, is now mathematics' scarce resource.
• When: posted 8 September 2026, in a four-part thread.
• Who: Terence Tao, Fields Medallist, writing on Mathstodon.
• Primary source: Tao's thread on Mathstodon.

The obvious objection arrives immediately: mathematics cannot run out of problems, because you can always write down another one. Tao anticipates it and answers with an image that does the whole job. "A country or region can suffer a critical shortage of drinking water while simultaneously being surrounded by a massive ocean."

Anyone can manufacture open problems at will — his example is working out the ten-to-the-ten-to-the-tenth digit of pi. The vast majority are worthless. As he puts it, they "show no particular propensity to reveal any further insights or connections to other questions, or may either be too easy or too impossible relative to known techniques to learn anything from the exercise." The scarce thing was never problems. It was good problems, and knowing which ones they are.

That knowledge, in Tao's account, comes from something he calls the difficulty landscape — a field's collective feel for what is easy with current tools, what is hard but reachable, and what is hopeless. Mathematicians navigate by it. Judging whether a question is worth a year of your life is "a lengthy, deliberate, and subjective process, often informed by historical experience on what good mathematics was generated (or not generated) while working on earlier problems of this type."

Here is the mechanism of the depletion, and it is more interesting than "AI solves things too fast." Tao points out that every advance — new technique, new technology, better access to the literature — makes problems easier and therefore flattens the landscape. That is normally fine, because the same advance usually enlarges the reachable sphere and creates fresh boundaries to explore. Flattening plus a new frontier is just progress.

What he says is different now is the missing second half. "One notable feature of the current AI era is the absence of any definitive such boundaries. While AI tools have flattened the difficulty landscape now in many areas of the subject, thus destroying the ability to locate promising new problems in that area, there are no clear frontiers that are separating the 'AI-feasible' problems from the 'AI-hard' problems."

And he assigns part of the blame for that missing map to the labs. The absence of a visible frontier is "in part due to the rapidly changing nature of the technology, but also compounded by the refusal of AI companies to disclose their negative results, or reveal the process towards obtaining their solutions." Publishing your wins and burying your failures leaves the field unable to tell where the boundary is.

Then the part that should worry anyone who cares about how research works. "We have now seen that 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." That is not hypothetical; it describes a dispute Ground Truth covered this month, in which OpenAI announced an internal model had resolved a Navier–Stokes result days after hearing that a human team using AI assistance had made a breakthrough. Tao had earlier called that team's work a breakthrough, and one of the researchers said OpenAI asked him to drop his coauthor. This post is Tao arguing about the structural consequence rather than the individual episode.

His proposed remedy is a norm, not a ban. He accepts it is "technically infeasible to completely prohibit the use of automated tools," and suggests instead designating classes of problems as ones where the community expects a careful analysis — a solution that also yields insight and maps the difficulty of nearby questions — and where a raw answer without that would be "of negligible or even negative value." His analogy: a modern food bank does not accept arbitrary donations merely because they are technically edible.

The honest caveat is that this is an argument, not a measurement. Tao offers no quantification of how many fruitful problems have been consumed, and there is a credible counter-position that new tools have always been accused of hollowing out craft while in fact opening new territory — calculators, computer algebra systems and formal proof assistants all drew versions of this complaint. Tao is careful about this himself, flagging his pi-digit scenario as "incredibly unlikely" and purely illustrative. But the specific asymmetry he identifies — flattening without a visible frontier, worsened by labs publishing only successes — is a concrete, checkable claim, and the remedy for it is one the labs could act on tomorrow. Practitioner Simon Willison's read of the underlying dispute is a useful companion.

Primary source, verified: read the paper →

Ground Truth. (2026, September 9). Terence Tao says AI is strip-mining mathematics' supply of good problems. Ground Truth. https://groundtruth.day/news/terence-tao-says-good-math-problems-are-a-non-renewable-resource.html

@misc{groundtruth:terence-tao-says-good-math-problems-are-a-non-renewable-resource,
  title  = {Terence Tao says AI is strip-mining mathematics' supply of good problems},
  author = {{Ground Truth}},
  year   = {2026},
  month  = {sep},
  url    = {https://groundtruth.day/news/terence-tao-says-good-math-problems-are-a-non-renewable-resource.html}
}

Topics: mathematics · ai-research · terence-tao · open-science · debate