Terence Tao on open problems as a scarce resource
Tao reframes AI theorem-proving progress as an ecosystem problem: the scarce resource is not arbitrary questions, but well-chosen open problems whose difficulty landscape can still guide future research.
Links: Original source
Logged at IST: 2026-09-09 18:24 IST
What it is: Terence Tao's four-part Mathstodon thread on AI, open problems, and the danger of indiscriminate solution extraction.
Gist: Tao argues that good open problems are scarce even though possible questions are infinite. A useful problem is not just unanswered; it sits in a difficulty landscape where solving it may reveal techniques, connections, and nearby structure. Random questions can be generated endlessly, but most are either uninteresting, too easy, or too far beyond current methods to teach the field much.
His AI concern is that powerful systems flatten parts of this difficulty landscape. That is often good: new tools make more mathematics reachable. But if a tool flattens a region without revealing a new frontier, mathematicians lose the ability to see which nearby problems are promising and why. AI companies' reluctance to disclose negative results or solution process makes that boundary even harder to map.
The sharp claim is that identifying promising problems is now the scarce resource. If merely hearing that someone is working on a problem can trigger large-scale AI-powered effort to solve it first, researchers may become less willing to share directions openly. Tao thinks that would damage centuries of open-science practice.
His proposed norm is to value careful analysis, not just raw answers: for many classes of problems, the desired contribution should explain the solution, extract insight, and map the nearby difficulty landscape. A bare solution can be technically correct while still having negligible or negative value for the research ecosystem.
Newsletter angle: Useful counterweight to AI-progress headlines: the question is not only "can agents solve harder problems?" but whether solution extraction destroys the shared problem-selection process that makes fields cumulatively intelligent.