The current evidence is strong that AI has materially advanced mathematics, and limited but real that it has solved some previously open problems. The key distinction is between:
- proved, community-checked advances in open mathematics, and
- highly public claims that are still awaiting broad independent verification.
What is clearly established
1) AI has produced genuine new mathematical results, not just benchmark solutions
The most solid evidence comes from systems that found new constructions or improved bounds on longstanding problems:
- FunSearch produced new constructions in the cap-set problem and improved results in bin packing. This is a real mathematical advance, even though it did not fully solve the underlying open problem.
- AlphaEvolve similarly found better algorithms and improved known results in a range of technical problems.
These are important because they show AI can contribute new mathematics, not merely reproduce known proofs.
2) AI has achieved major formal reasoning results
DeepMind’s AlphaProof / AlphaGeometry 2 reached silver-medal level on IMO 2024, and later systems such as Aristotle reached gold-equivalent performance on IMO 2025-style problem sets. This is not “open research” in the strict sense, but it is strong evidence that AI can reason about highly nontrivial mathematics.
3) AI has helped humans solve long-open problems
There are credible examples where AI materially helped with a long-open problem, but the human mathematician still played a central role in framing and validating the result. A good example is the reported GPT-5-assisted work on a 40-year-old optimization problem. That counts as real progress, but not yet as fully autonomous AI discovery.
What is promising but still provisional
4) Claims of outright solutions to open research problems are emerging
There are recent, high-profile claims that AI has solved or disproved problems that were previously open, including:
- an open convex optimization bound improvement,
- a result in enumerative geometry,
- a claim about the unit-distance problem in discrete geometry,
- and most dramatically, a claimed solution to a Navier–Stokes Millennium Prize Problem formulation.
These claims are notable because they come with formal artifacts, proof-assistant checking, or public technical writeups. But the level of confidence varies:
- Some are well-supported but still awaiting publication or broad independent verification.
- The Navier–Stokes claim, while extraordinary, should still be treated as provisional until the broader mathematical community has had time to inspect and validate it.
What the evidence does not yet show
Even with these advances, there is still not strong evidence that AI has broadly solved major frontier open problems in the way human mathematicians mean that phrase. In particular:
- The most dramatic claims are not yet universally accepted.
- Many results are still best described as AI-generated candidate proofs or AI-assisted discoveries.
- Formal proof checking helps a lot, but it does not by itself guarantee that a result is historically, conceptually, and community-wise established as a breakthrough.
Bottom line
The evidence now supports three conclusions:
- AI has clearly made material advances in mathematics.
- AI has sometimes produced genuinely new results on problems that were previously open.
- The strongest “AI solved a famous open problem” claims are still too recent to treat as fully settled without independent verification.
So the honest summary is:
AI has moved beyond toy examples and begun contributing real new mathematics, but the claim that it has broadly and definitively solved major long-standing open problems is still only partially established.
