Unsolved Math Problems Solved by AI

The current evidence says yes, AI has materially advanced some previously unsolved mathematical problems, and in a few cases appears to have solved them outright, but the strongest evidence is still for specific, narrow open problems rather than broad “general mathematical genius.” The most credible public cases are:

1) AI has likely solved at least one prominent open problem

The clearest public example is OpenAI’s report that an internal reasoning model disproved a longstanding conjecture in discrete geometry related to the Erdős unit-distance problem, with a proof checked by external mathematicians and a companion write-up released publicly.openai This is stronger than benchmark performance because it concerns a genuinely open research question, not a contest problem. Independent follow-on mathematical work has already used the construction.deepmind

A second notable case is an AI-assisted counterexample to the Jacobian conjecture in dimension > 2, reported publicly in 2026 and said to have been quickly verified by mathematicians. That would also count as a real resolution of an open problem in the “counterexample” direction, though the public documentation is thinner than for the OpenAI discrete-geometry result.

2) AI has made real progress on open research problems, especially via formal proof and search

Google DeepMind and others have released systems that combine language models with Lean or other theorem provers to generate machine-checkable proofs. One public result reports 9 of 353 open Erdős problems solved in one campaign, plus additional results on OEIS conjectures and related topics.deepmind DeepMind’s own published taxonomy is cautious: it reports results at lower levels of novelty and explicitly does not claim a major “landmark breakthrough” yet.deepmind

This matters because it shows AI can do more than imitate proofs: it can participate in a research loop of proposing, checking, revising, and sometimes completing formal proofs.

3) AI has improved bounds and constructions, even when not fully “solving” the problem

Some of the strongest evidence is in improved constructions rather than final solutions:

• FunSearch found new constructions for the cap-set problem, improving known bounds.deepmind
• AlphaEvolve improved bounds and constructions on several problems, including a new lower bound for a kissing-number problem in 11 dimensions.openai

These are genuine mathematical advances, even though the underlying problems remain open.

4) AI is also helping humans solve research problems faster

There are public examples where AI helped a mathematician or research team close a problem, but the human still framed the question and validated the argument. That is still meaningful progress, but it is better described as AI-assisted research than autonomous AI mathematics.deepmindgithub

Bottom line

The best current evidence supports this summary:

• Confirmed: AI can now produce real, verifiable mathematical advances on open problems.
• Likely/partly confirmed: AI has solved at least one prominent previously open problem and possibly more via counterexamples.
• Not supported yet: the claim that AI routinely performs deep, independent frontier mathematics at the level of the biggest unresolved problems, such as the Millennium Prize Problems.

So the right reading is: AI has moved from contest math into genuine research mathematics, but its strongest successes are still concentrated in problems that are amenable to search, formal verification, counterexample construction, or tight bound improvement.deepmindopenaideepmindopenai