Terence Tao: AI is mining mathematics' open problems non-renewably

Mathematician Terence Tao warns that mathematics' stock of good, fruitful open problems is being "mined in a non-renewable fashion", risking scarcity of promising questions. He laid out the argument in a four-part thread on Mathstodon on September 8, 2026.

The ocean and the drinking water

Tao concedes the warning seems counterintuitive: the set of possible problems is infinite. His analogy is a country suffering a critical shortage of drinking water while surrounded by a massive ocean. Any number of open problems can be generated at will — such as working out the 10^10^10th digit of pi — but the vast majority are not worth attention: they reveal no further insights or connections, or are too easy, or too impossible relative to known techniques.

Judging whether a question is worth highlighting is a lengthy, deliberate, subjective process, informed by historical experience of the mathematics similar problems generated. It depends on knowing a field's "difficulty landscape": which questions are easy with known methods, which yield with effort, and which are impossible.

Flattening the difficulty landscape

Every advance — in technique, technology or infrastructure such as access to libraries of past literature — lowers the difficulty of solving problems. That is generally good, but it flattens the landscape until a field's geometry can no longer be discerned and promising questions extracted.

The AI era differs in one respect: there are no definitive such boundaries. AI tools have flattened the landscape in many areas, yet no clear frontier separates "AI-feasible" from "AI-hard" problems — which still exist, since difficulty is unbounded and some problems are undecidable. Tao attributes this partly to fast-changing technology, partly to AI companies' refusal to disclose negative results or their path to solutions.

The scarce resource

The identification of a promising problem has therefore itself become the scarce and precious resource. Tao notes that even the rumour of someone working on a problem can trigger massive AI-powered effort to flatten it before the original project reaches full potential. Incentives may now point towards not sharing promising research directions with the broader community — which, he warns, would reverse centuries of open-science tradition and do serious long-term damage to the field.

Standards, not prohibition

In the final post, Tao argues that indiscriminate use of powerful solution-extraction tools meets the short-term goal of solving the problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress. Prohibiting automated tools outright may be technically infeasible, he accepts, but many classes of problems can still be designated as desiring careful analysis: work that not only solves the problem but identifies insights from the solution process. He compares this to a modern food donation drive, which no longer accepts arbitrary contributions even when verified to be technically edible, but maintains socially accepted standards about what is actually sought.