Unsolved Math Problems Solved by AI

As of now, the evidence is strong that AI has materially advanced some previously open mathematical problems, and there are a few credible cases where AI appears to have produced genuinely new, externally checked mathematical results. But the evidence is not strong enough to say AI has broadly “solved mathematics,” or that it has cracked canonical grand challenges like the Riemann Hypothesis or \(P\neq NP\).

What is clearly supported

1) A major new result in discrete geometry

OpenAI reported that an internal reasoning model found a new family of point configurations that disproves a long-standing conjectural picture around the Erdős unit-distance problem, using an unexpected connection to algebraic number theory.[1] The company published the proof, companion materials, and expert commentary, making this one of the strongest public examples of AI-originated mathematical discovery.[1]

This is best described as a real advance on a famous open problem—and in some formulations, a disproof of a central conjecture—not merely a benchmark win.[1]

2) Lean-verified solutions to some open Erdős problems

There are now several examples where AI systems, paired with proof assistants like Lean, produced machine-checked proofs of previously open statements in the Erdős problem collection, including problems such as #281, #728, and #729.[4][5][6][7][8] These are important because formal verification gives unusually strong correctness evidence.

That said, these cases vary in depth. Some are genuinely open research problems; others involve ambiguities in the original problem statements or are not comparable in difficulty to the hardest famous conjectures.[5][6]

3) Material progress on research problems, not just theorem proving

OpenAI also described GPT-5 helping solve a 40-year-old open problem in optimization: the stability of Nesterov’s accelerated gradient method.[2] In that case, the model contributed key ideas and exploration, while the human mathematician did substantial correction and proof work.[2] This is good evidence that AI can accelerate research, even when it is not the sole author of the proof.

A similar pattern appears in robust statistical estimation, where AI-assisted work helped establish a sharp minimax rate for a previously unresolved problem.[3]

4) Better bounds and new constructions

DeepMind’s AlphaEvolve reports include improvements to known mathematical and algorithmic objects, such as a new algorithmic improvement for \(4\times 4\) complex matrix multiplication and improved lower bounds for the 11-dimensional kissing-number problem.[9] These are material advances, even when they do not amount to a complete solution of a famous open conjecture.

What this means overall

The best current summary is:

• Yes: AI has solved some previously open mathematical statements, especially when paired with formal proof systems.
• Yes: AI has materially advanced several open problems by finding new constructions, sharper bounds, or key proof ideas.
• No: There is not yet evidence that AI has broadly replaced human mathematicians, or that it has solved the most iconic open problems of modern mathematics.

Important nuance

A lot depends on what you mean by “solved”:

• Autonomous discovery of a new proof or counterexample: rarer, but now documented in a few cases.[1]
• Human-AI collaboration leading to a publishable theorem: increasingly common.[2][3]
• Formal proof of a previously open problem: strong evidence of correctness, but not always of deep novelty or broad importance.[4][5][6]

Bottom line

The current evidence says AI has crossed a real threshold: it is no longer limited to contest-style math. It can now generate new proofs, counterexamples, and improved bounds on open research problems, sometimes in ways that experts regard as mathematically serious.[1][2][3][9] But the field is still at an early stage, and the strongest results so far are concentrated in carefully scaffolded settings, often with formal verification and human oversight.[4][5][6]