Terence Tao warns AI is depleting open math problems
Terence Tao, a professor of mathematics at UCLA, posted a four-part thread on Mastodon on September 8, 2026, arguing that mathematics faces a paradox: the set of possible open problems is infinite, yet good, fruitful problems are being used up in a non-renewable way. He compares it to a country surrounded by ocean but short of drinking water. Anyone can generate an open problem at will, such as asking for the 10^10^10th digit of pi, but the vast majority of such problems reveal no useful insights or connections and are either too easy or too hard to teach anything. Deciding which problems are actually worth pursuing is a slow, subjective judgment built on historical experience of what a field's 'difficulty landscape' looks like: which questions are trivial with known methods, which take real effort, and which are out of reach. Tao says every advance in technique, technology or infrastructure flattens that landscape, which is normally good but erodes the ability to see where the interesting, still-unsolved questions sit. He argues that AI tools have now flattened the landscape across many areas of mathematics without leaving any clear line between 'AI-feasible' and 'AI-hard' problems, the latter of which certainly still exist since difficulty is unbounded and can even be undecidable. That blurred boundary is worsened, in his view, by how fast the technology changes and by AI companies withholding both their negative results and their solution methods. The practical effect, he says, is that identifying a promising problem has become the scarce and precious resource, since even a rumor that someone is working on a problem can draw a wave of AI-driven effort that flattens it before the original researcher's project can reach its full potential. Tao warns this could push mathematicians to stop sharing promising research directions publicly, reversing centuries of open-science tradition and doing lasting damage to the field. His proposed partial fix is not to try to ban indiscriminate use of automated solution-extraction tools, which he thinks is not realistically enforceable, but to mark out certain classes of problems as requiring careful analysis rather than a raw answer: work that also extracts insight from the solution process and maps the difficulty of neighboring problems. He likens this to a modern food bank that no longer takes any donation just because it is technically edible, but sets explicit standards for what it actually wants.
Key facts
- Terence Tao, professor of mathematics at UCLA, posted a four-part Mastodon thread on September 8, 2026 on AI's effect on open math problems.
- He says good, fruitful open problems are being mined in a non-renewable way, even though the set of possible problems is infinite.
- AI tools have flattened the difficulty landscape in many areas of math, and Tao says there is no clear line separating 'AI-feasible' from 'AI-hard' problems.
- He says identifying a promising problem, not solving it, is now the scarce resource, since even a rumor of someone working on one can trigger AI-driven effort to flatten it first.
- Tao warns the incentives may now favor not sharing promising research directions publicly, and proposes marking some problem classes as requiring careful analysis rather than raw solutions.
Why it matters
Tao's claim inverts the usual assumption that mathematics can never run short of problems because the space of possible questions is infinite. He argues the actual bottleneck was never the supply of problems but the slow, experience-based judgment of which ones are worth pursuing, and that AI tools are consuming that judgment faster than the field can renew it by flattening difficulty landscapes without leaving visible frontiers behind.
Who it affects
The argument is aimed at mathematicians and the broader open-science culture in the field: researchers who currently post conjectures, partial results and promising directions publicly, and who Tao thinks may face growing incentives to stop doing so if AI-driven effort can flatten a shared problem before the original researcher finishes.
How to use it
Tao does not propose banning automated solution-extraction tools outright, since he considers that technically infeasible. Instead he suggests designating certain classes of problems as requiring careful analysis, meaning work that also surfaces the reasoning behind a solution and maps out the difficulty of nearby questions, rather than accepting a raw answer with no accompanying insight.
How solid is it
This is a personal, informal argument from one mathematician, posted as a four-part thread rather than a paper or study. Tao offers reasoning, an analogy about water scarcity and one about food donations, but no data, statistics or named examples of specific problems being 'flattened' by AI effort, and he does not name any AI tool, model or company.
Risks and caveats
The thread names no concrete instance of a problem being mined out, no timeframe for when this dynamic began, and no researcher who has actually stopped sharing work as a result; Tao presents that last point as a possible future incentive shift, not something that has already happened. The argument rests on Tao's own judgment about difficulty landscapes, which is not independently verifiable from the thread itself.
“In fact, it is now the identification of a promising problem which is the scarce and precious resource.”
— Terence Tao, mathematics professor at UCLA, on Mastodon