Yes—there is now credible live evidence that AI has materially advanced mathematics and, in a few cases, appears to have solved previously open research problems. The strongest evidence is still selective and often hybrid (AI + human verification), but it is no longer limited to olympiad-style benchmarks.
AI has clearly crossed three thresholds:
- Elite contest performance on problems like the IMO, showing strong mathematical reasoning.[1][3]
- Research-level contributions, including novel proofs and counterexamples on problems that were previously open.[2][4][5]
- Machine-checked correctness in some cases, especially where Lean formalization is available.[4][5]
What it has not yet demonstrated is reliable, fully autonomous resolution of the hardest famous open problems, such as the Millennium Prize problems.
The strongest current evidence
1) A long-standing discrete-geometry conjecture was disproved
OpenAI reported that an internal reasoning model produced a proof/disproof of a central Erdős unit-distance conjecture in discrete geometry.[2] This was an 80-year-old problem, and the result was externally checked by mathematicians; a companion paper then gave a human-readable account and sharpened the quantitative bound.[2][3]
Why this matters:
- it is not just solving a benchmark;
- it overturns a genuine open conjecture;
- and it appears to have been driven by AI-generated ideas rather than simple retrieval.[2][3]
This is the clearest current example of AI making a real research-level breakthrough.
2) Lean-verified solutions to open Erdős problems
There are also reports of AI systems generating proofs for open problems in the Erdős collection, with some formalized in Lean.[4] One example is Erdős Problem #728, where a paper describes an AI-generated proof that was formalized and checked in Lean.[4]
This is important because formal verification gives strong correctness evidence. The caveat is that some of these problems are less mathematically central than the unit-distance conjecture, so they are better described as genuine but modest open-problem resolutions.[4]
3) Additional research-level progress in commutative algebra and related areas
Recent preprints describe AI systems generating and verifying solutions to several open problems in commutative algebra and related fields, including at least one result formalized in Lean 4.[6][7] These are credible signs that AI can now contribute to actual research, not just classroom or contest mathematics.
4) Broader large-scale formal proof search
A separate line of work reports formal-proof agents solving multiple open Erdős problems and many OEIS conjectures in batch mode.[8] This suggests growing capability, but the headline counts should be interpreted cautiously because:
- “open” covers problems of very different difficulty,
- some may be low-hanging or ambiguously stated,
- and formal correctness does not automatically imply major mathematical significance.[8]
Important caveats
- Human checking still matters. In the strongest cases, mathematicians reviewed, clarified, or re-expressed the arguments.[2][3]
- Not all “open” problems are equally important. Some database-listed problems are obscure or lightly stated rather than deep frontier questions.[4][8]
- Contest success is not the same as research success. IMO-level performance is impressive, but it is a different category from resolving an open conjecture.[1][3]
- No evidence yet of a general theorem-solving machine. The successes are real but uneven, and they do not show that AI can consistently solve arbitrary hard mathematics.
Bottom line
The current evidence supports this conclusion:
AI has materially advanced mathematics and has likely solved a small number of previously open research problems, including at least one major open conjecture in discrete geometry.[2][3]
But these successes remain selective, heavily verified, and not yet broadly general.
