Terence Tao Warns AI May Exhaust Mathematics' Supply of Fruitful Open Problems
- Terence Tao says AI has flattened problem difficulty in many mathematical areas, while rapid model changes and companies' undisclosed failures leave no clear boundary between AI-feasible and AI-hard questions.
- Tao argues that a good open problem is scarce because its value depends on judgment about whether it can expose new connections, rather than merely having an answer; he contrasts this with arbitrary tasks such as computing the $10^{10^{10}}$th digit of pi.
- He says even rumors that someone is pursuing a promising problem can draw large-scale AI-powered effort to solve it before the original research has matured.
- Tao warns that this incentive could push researchers to withhold promising directions, reversing open-science practice and weakening the research ecosystem needed for later progress and for interpreting results.
- Hacker News commenters debate whether AI proofs can still generate insight through reverse engineering, versus whether proof volume, opaque derivations, and reduced credit will damage mathematical training and careers.
Hacker News opinions
If proofs are tropes, explanations are stories. There will not be an end to stories.
I disagree. You only reach real understanding and appreciation after doing the hard work yourself, and AI may make that economically infeasible. The story analogy misses that.
I read Tao's thread as a response to the Navier-Stokes results from the last 24 hours. If mathematics gets levelled this fast, what is left, and how do you protect a field over the next six months?
Why protect a field from AI? If mathematics is solved, move to an area that is not.
The timing is striking. An article already argued that mathematics is becoming the next job of the "human calculator."
Could mathematicians reverse-engineer AI proofs for new insight, as chess players learn concepts from engine games?
Maybe, but LLM approaches are often verbose and strange. People often use them to get an answer, then reconstruct a more human and shareable path. In mathematics, how someone got there is often the valuable part.
The larger problem is the shock to the system that trains mathematicians and assigns merit. Perelman's Poincare proof took years to digest; a Navier-Stokes proof may too, while systems generate more proofs than people can absorb.
Pure mathematics depends heavily on intellectual satisfaction and recognition from a small peer group. If the work becomes interpreting "Astra's theorem #18398" instead of making a human contribution, fewer people may want to do it.
I think current incentives will favor short-term extraction. Tao says solution-extraction tools can solve the immediate problem while damaging the ecosystem needed for later progress and for understanding results.
If an AI solution is symbolically verified but yields no insight, it is still not very interesting to the profession. Navier-Stokes is unusual because the prize makes being first matter.
Mathematicians will be less likely to work on a problem once a solution exists, even if the solution is incomprehensible.
An AI solution still tells us that a solution exists and gives something to work backward from. Even an inscrutable proof is usually better than nothing.