Unsolved Math Problems Solved by AI

Short answer: Yes—there is now solid evidence that AI has materially advanced previously unsolved mathematical problems, and a smaller but important set of cases where AI-generated results have been judged mathematically valid as solutions or counterexamples to open conjectures. The strongest evidence comes from official lab announcements, arXiv papers, and peer-checked results rather than press hype.openaiopenai

What counts as “materially advanced” vs. “solved”

A useful distinction is:

• Materially advanced: AI finds new constructions, better lower/upper bounds, faster algorithms, or plausible proof ideas that humans can verify and extend.
• Solved: AI produces a correct proof or counterexample for an open problem, and the result is accepted by mathematicians or appears in a research paper with verifiable arguments.

By this standard, the evidence is strongest for new bounds and constructions, and somewhat weaker—but real—for actual solutions/counterexamples to open research problems.openaiopenai

Strongest evidence of genuine progress

1) FunSearch: new constructions for the cap-set problem

DeepMind’s FunSearch combined a language model with automated evaluation and discovered new constructions for the cap-set problem, a long-standing open problem in extremal combinatorics.deepmind This did not solve the cap-set problem in full, but it did produce genuinely new mathematical objects that improved on known constructions.deepmind

2) AlphaEvolve: repeated improvements to open bounds and records

DeepMind’s AlphaEvolve reported improvements on a range of open problems, including a new lower bound for the 11-dimensional kissing number and improved solutions in combinatorics, geometry, and number theory.deepmind It also found a faster algorithm for multiplying \(4\times 4\) complex matrices.deepmind These are clear examples of AI moving the frontier, even when they do not settle the underlying problem completely.deepmind

3) Olympiad-level theorem proving

AI systems have reached very high performance on IMO-style problems. DeepMind reported silver-medal-level performance in 2024 with AlphaProof + AlphaGeometry 2,openai and a later Gemini Deep Think system reached gold-medal standard in 2025.openai This is important evidence of mathematical reasoning ability, but it is not the same as solving long-open research problems, because IMO problems are newly written contest problems, not decades-old conjectures.openaiopenai

Strongest evidence of AI actually solving or refuting open problems

4) Disproof of the Erdős unit-distance conjecture

The clearest public example is OpenAI’s 2026 announcement that an internal model disproved a long-standing conjecture in discrete geometry by producing a counterexample construction that external mathematicians reviewed and judged valid.openai OpenAI also published companion remarks describing the result as settling the relevant Erdős problem.openai

This is notable because it is not just a benchmark win: it is a mathematical counterexample to an open conjecture, and the result was externally scrutinized.openaiopenai
That said, it is best described as disproving a key conjecture rather than completely solving the broader unit-distance problem.

5) Human–AI papers on open research questions

There are also several examples where AI contributed to proofs of open questions that appeared in research papers:

• A GPT-5-assisted result on the Nesterov accelerated-gradient question, where the AI helped suggest structure but the human mathematician produced the rigorous proof.deepmind
• DeepMind reports and arXiv papers describing AI-assisted results in arithmetic geometry, representation theory, and number theory, including an autonomously solved Erdős–Graham series problem in one paper and broader human–AI collaboration in others.deepmindopenaiopenaideepmind

These are legitimate advances, but most are best characterized as AI-assisted research rather than fully autonomous theorem proving.deepmindopenaiopenaideepminddeepmind

What the evidence does not show

The current record does not support the claim that AI has solved the field’s most famous open problems—such as the Riemann Hypothesis, P vs NP, or Navier–Stokes existence and smoothness—in a verified way.deepmind DeepMind has also been careful in its own taxonomy not to claim “landmark breakthrough” status for its math results.deepmind

Bottom line

The best current evidence says:

1. AI has clearly and repeatedly advanced open mathematics by finding new constructions, better bounds, and stronger algorithmic ideas.deepminddeepmind
2. AI has at least one high-profile, externally reviewed success in solving/disproving a longstanding open conjecture—the Erdős unit-distance conjecture result is the clearest example.openaiopenai
3. Most other impressive results are still hybrid human–AI achievements or improvements on partial results, not full autonomous solutions of the hardest famous problems.deepminddeepmind

If you want, I can also turn this into a table of specific problems, what AI did, and how strong the evidence is.