As of October 2026, the evidence is strong that AI has materially advanced previously unsolved mathematical problems, and there is also credible evidence that it has fully solved some genuinely open problems. What is not yet established is that AI has broadly or routinely cracked the biggest famous open conjectures in mathematics.
What the evidence shows
1) AI has clearly made real advances on open problems
The most solid evidence comes from systems that produce checkable new constructions, bounds, or proofs rather than just fluent mathematical text.
Examples include:
- FunSearch: found new constructions for the cap-set problem, which is a longstanding open problem in combinatorics, though it did not solve the whole problem.
- AlphaEvolve: extended this style of search to larger program spaces and reportedly improved bounds / found new constructions across several mathematical and algorithmic problems.
- Formal proof search systems: recent AI+Lean work has reportedly solved multiple open problems in curated collections such as Erdős problems and OEIS conjectures, with machine-checked proofs.
These are meaningful advances because they go beyond benchmark-style reasoning and produce outputs that can be formally or computationally verified.
2) There is credible evidence of some outright open-problem solutions
The strongest recent claims are:
- An
OpenAI internal model reportedly disproved a longstanding Erdős conjecture in discrete geometry about unit distances. The result was externally verified and accompanied by a paper and formal artifacts.
- A 2026 formal-proof-search paper reports solving 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures using Lean-based verification.
- Some of these results were described as open for decades, which makes them especially notable if the formalization and novelty claims hold up.
This is the best current evidence that AI has moved from “helpful assistant” to a system capable of contributing new, correct mathematics on previously open questions.
3) AI has also reached a high level on competition mathematics
DeepMind’s AlphaProof and AlphaGeometry 2 achieved silver-medal level on the 2024 International Mathematical Olympiad, solving 4 of 6 problems with machine-checked proofs. That is not an open research problem, but it is important evidence that AI can now do sophisticated proof search at a level once thought far away.
How strong is the evidence?
The evidence is strongest when the result has one or more of these features:
- a Lean/formal proof
- an independently checkable counterexample
- an executable construction or algorithm with a clear scoring rule
- external mathematical verification and a public paper or repository
The evidence is weaker when the claim is only a company announcement without enough public detail, or when the result is an “advance” rather than a full solution.
Bottom line
The current evidence supports this careful conclusion:
AI has already materially advanced several previously open mathematical problems, and it has likely solved some genuine open problems in specific, formally checkable settings.
But it is not yet justified to say that AI has generally solved the major famous open problems of mathematics. The field is moving fast, though, and the gap between “advancing” and “solving” is now much smaller than it was a few years ago.
