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.[1][2]
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.[1][2]
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.[5] This did not solve the cap-set problem in full, but it did produce genuinely new mathematical objects that improved on known constructions.[5]
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.[3] It also found a faster algorithm for multiplying \(4\times 4\) complex matrices.[3] These are clear examples of AI moving the frontier, even when they do not settle the underlying problem completely.[3]
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,[1] and a later Gemini Deep Think system reached gold-medal standard in 2025.[2] 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.[1][2]
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.[1] 
OpenAI also published companion remarks describing the result as settling the relevant Erdős problem.[2]
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.[1][2]
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.[10]
- 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.[6][7][8][9]
These are legitimate advances, but most are best characterized as AI-assisted research rather than fully autonomous theorem proving.[6][7][8][9][10]
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.[6] DeepMind has also been careful in its own taxonomy not to claim “landmark breakthrough” status for its math results.[6]
Bottom line
The best current evidence says:
- AI has clearly and repeatedly advanced open mathematics by finding new constructions, better bounds, and stronger algorithmic ideas.[3][5]
- 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.[1][2]
- Most other impressive results are still hybrid human–AI achievements or improvements on partial results, not full autonomous solutions of the hardest famous problems.[6][10]
