Unsolved Math Problems Solved by AI

As of mid-2026, the evidence is real but still narrow: AI has genuinely solved or materially advanced some previously open mathematical problems, but mainly in concrete, search-friendly areas such as combinatorics, discrete geometry, number theory, optimization, and formalized proof benchmarks. It has not yet solved any Millennium Prize–level problem.

What the strongest evidence shows

1) A major open discrete-geometry conjecture was disproved

The clearest case is OpenAI’s report that an internal reasoning model produced a proof disproving Erdős’s planar unit-distance conjecture. The result was released with a proof manuscript and a companion remarks paper, and external mathematicians examined it and treated it as a correct, nontrivial result.[1][3]

Why this matters:

• It is a previously open problem.
• The AI’s output was not just a heuristic suggestion; it produced a new infinite construction.
• The result was checked by human experts and publicly documented.[2][3]

This is the strongest public evidence that AI has independently generated a genuine solution to a research-level mathematical problem.[1][2]

2) AI systems have solved some other open Erdős-style problems

There is additional evidence that AI agents can solve smaller open problems from the Erdős database and similar collections. DeepMind reported a system that, in a large sweep over open Erdős problems, autonomously solved several of them and produced formal Lean proofs for some.[6][7] These are meaningful results, but they are generally framed as modest-to-moderate advances, not landmark breakthroughs.

3) AI has materially improved known bounds and constructions

Google DeepMind’s AlphaEvolve reported improvements on several open problems by discovering better constructions or lower bounds, including a new lower bound for the 11-dimensional kissing-number problem.[8] That is bona fide mathematical progress, even when it does not fully settle the problem.

4) AI is now useful in human-AI research collaborations

There are credible examples where AI contributed a key idea that humans then completed into a proof, such as in mathematical statistics and some Erdős problems.[4][5] This is important because it shows AI is not just solving toy benchmarks; it is sometimes accelerating real research.

What the evidence does not show

The current evidence does not support claiming that AI has broadly solved the deepest famous open problems of mathematics. In particular:

• no accepted solution to the Riemann hypothesis
• no accepted solution to P vs NP
• no accepted Millennium Prize breakthrough

So the right summary is:

AI has crossed the threshold from “math benchmark performer” to “occasional contributor of genuine new mathematics,” but only in selected domains and not yet at the level of the field’s most celebrated open problems.

How to interpret the evidence carefully

A few distinctions matter:

• Autonomous solution: AI produced the proof/construction with limited human guidance.
• Human-AI collaboration: AI suggested a key step, but humans finished and validated the argument.
• Material advance: AI improved a bound, construction, or sub-result without fully solving the main problem.

Most of the strongest evidence is in the first two categories for specific, well-structured problems [1][6][8], while the broader research frontier still relies heavily on human judgment and verification.

Bottom line

The current evidence is substantial and credible that AI has:

1. solved at least one prominent previously open mathematical problem [1][2][3],
2. solved some additional open problems in specialized areas [6][7],
3. materially advanced others by improving bounds or constructions [8],

but it has not yet achieved a broad general breakthrough in frontier pure mathematics.