Unsolved Math Problems Solved by AI

Yes—there is now credible public evidence that AI has materially advanced previously unsolved mathematics, and at least one prominent case where an AI system appears to have found a correct proof/counterexample to a long-open research problem. But the evidence does not show that AI has broadly “solved mathematics,” or that it routinely produces major frontier results on its own.

What is the strongest evidence?

1) A major open conjecture in discrete geometry was reportedly disproved by AI

OpenAI publicly reported that one of its reasoning models disproved a long-standing Erdős conjecture about unit distances in the plane, an 80-year-old problem. The released proof claims an asymptotic lower bound that contradicts the conjectured upper behavior, so this is not just a better example or a benchmark win—it is a genuine change to an open mathematical question.[1][2]

That said, the result was externally checked and human-edited after discovery, so the strongest defensible claim is that AI appears to have autonomously discovered the key argument, with later human and expert verification rather than a fully unattended publication pipeline.[2][3]

2) DeepMind reports AI-generated results on open Erdős problems, but classifies them as limited in novelty

DeepMind’s Aletheia work reports autonomous solutions to multiple open Erdős problems and other research outputs, including a paper generated without human intervention in the mathematical work.[4] However, DeepMind’s own novelty framework says these results were mostly low to moderate novelty, and explicitly says it did not reach “major advance” or “landmark breakthrough” levels.[4][5]

So this is real evidence of mathematical progress, but it is also a caution against overstating how far the systems have gone.

What kinds of advances are clearly established?

Material improvements to known mathematical/algorithmic records

There is strong evidence that AI systems can discover:

• new matrix-multiplication algorithms,
• improved lower bounds for packing and extremal geometry problems,
• better finite constructions in combinatorics and discrete math.[6]

For example, AlphaEvolve reported a provably correct 48-scalar-multiplication method for multiplying \(4\times4\) complex matrices, improving a long-standing benchmark, and a new 593-sphere lower bound for the 11-dimensional kissing-number problem.[6] These are meaningful advances, even if they are not full solutions to famous conjectures.

Better human-AI collaboration on open problems

There is also substantial evidence that AI is already useful as a research assistant: suggesting constructions, finding counterexamples, checking proofs, and helping formalize arguments. Public reports from OpenAI and DeepMind, plus math-community writeups, show that this hybrid workflow is increasingly productive.[2][4][7]

What should not be counted as “solved unsolved mathematics”?

• IMO medal-level performance is impressive, but those problems are competition tasks, not previously open research problems.[8]
• Benchmark success on FrontierMath or similar sets shows reasoning ability, but it does not by itself prove literature-level mathematical discovery.
• A plausible natural-language proof is not enough unless it is formally checked or independently verified.

Bottom line

The current evidence supports this balanced conclusion:

AI has already made genuine, externally checkable advances on previously unsolved mathematics, including at least one highly prominent open problem that was reportedly disproved, and several other improved constructions, bounds, and algorithms.[1][2][4][6]

But the evidence does not yet show that AI has broadly solved frontier mathematics or consistently produced major landmark breakthroughs at the level of the deepest human advances.[4][5]