Unsolved Math Problems Solved by AI

The current evidence is that AI has definitely advanced previously unsolved mathematics, and in a few cases has appeared to resolve or overturn longstanding conjectures—but the strongest results are still limited to problems where outputs can be externally checked, formally verified, or digested by mathematicians.

What is clearly established

1) AI has produced new results on open problems

A major example is DeepMind’s FunSearch, which found new constructions for the cap set problem and improved known lower bounds rather than merely reproducing existing answers.openaiopenai This is real mathematical progress on a long-open problem, even though it does not fully solve the problem.

2) AI has improved bounds and constructions across several research-level problems

DeepMind’s later AlphaEvolve work reports improvements on a range of mathematical and algorithmic tasks, including the 11-dimensional kissing number and other open problems, with a public repository of problems and verification materials.githubarxivdeepmind These are material advances, but mostly in the form of better constructions, tighter bounds, or rediscovered known optima—not full resolutions of major open conjectures.

3) AI can solve very hard formalized problems

DeepMind’s AlphaProof/AlphaGeometry system reached silver-medal level on IMO 2024 problems, showing strong formal reasoning and proof search.ieee That is impressive evidence of mathematical competence, but IMO problems are not the same as unresolved research conjectures.

The strongest “AI solved an open problem” case so far

The most prominent recent example is OpenAI’s public announcement that an internal model disproved a conjecture in discrete geometry related to the Erdős unit-distance problem.research OpenAI released a proof manuscript and companion remarks from mathematicians, which is unusually strong evidence for a genuine new result.deepmind The important nuance is that this is best described as disproving a longstanding conjectured upper bound, not fully solving every aspect of the unit-distance problem.

That makes it the clearest public case that AI has moved beyond toy or competition settings into research-level discovery.

What has not been shown

Despite these advances, there is no solid evidence that AI has resolved the major remaining Millennium Prize problems or become a generally reliable autonomous mathematician. Current systems still struggle with:

• deciding whether a problem is truly open,
• avoiding plausible but invalid proofs,
• choosing fruitful abstractions,
• and producing results that stand up without substantial human checking.

Bottom line

The best-supported conclusion is:

AI has materially advanced several previously unsolved mathematical problems and has at least one strong public case of disproving a longstanding open conjecture, but it has not broadly solved major open mathematics in the way humans would usually mean by “solved.”

If you want, I can also give you a short timeline of the key breakthroughs or a table separating “competition success,” “new bounds,” and “genuine open-problem advances.”