Unsolved Math Problems Solved by AI

Answer from Sep 23See the current answer

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Which open math problems has AI actually solved so far?

The current evidence is that AI has materially advanced several previously unsolved mathematical problems, and in a few cases has produced results that appear to solve or refute open problems in a way that is machine-checkable or externally verified. But the strength of the evidence varies a lot by problem type.

What is well supported

1) AI has solved very hard Olympiad-level problems

The strongest, most solid evidence comes from formal theorem proving on International Mathematical Olympiad problems.

DeepMind’s AlphaProof + AlphaGeometry 2 solved 4 of 6 problems from IMO 2024, reaching silver-medal level, including the hardest problem on the exam.
This is verified through formal proof infrastructure, so it is much stronger evidence than a natural-language “AI answer.”

This is a major advance in mathematical reasoning, but it is not quite the same as solving a frontier research problem, because IMO problems are designed for a competition and have known human solutions.

What is strong evidence of genuine mathematical discovery

2) AI has found new constructions and improved bounds in open problems

This is the clearest evidence that AI has gone beyond imitation.

Examples include:

FunSearch: found new constructions related to the cap set problem and improved bin-packing heuristics.
AlphaEvolve: reportedly improved known results in areas such as the 11-dimensional kissing-number lower bound and 4×4 complex matrix multiplication.
These are not full solutions to the underlying open problems, but they are real advances: the AI found better objects, constructions, or algorithms than were previously known.

This category is the most convincing evidence that AI is contributing original mathematical content.

What is possible but should be read cautiously

3) Claims of AI solving famous open problems

There are public claims that AI systems have produced major results on problems such as:

Navier–Stokes
Connes’s rigidity conjecture
discrete geometry conjectures
Fermat’s Last Theorem formalization

The key distinction is this:

A formalized proof or externally checked proof is strong evidence.
A company announcement without independent mathematical validation is weaker, even if technically impressive.

So the evidence is strongest when the result is:

formally checked by a proof assistant like Lean, or
independently verified by human mathematicians and published.

The best overall summary

AI has clearly moved from merely solving benchmark problems to doing things that look like real mathematical research assistance, including:

discovering new constructions,
improving known bounds,
finding formally verified proofs,
and solving very hard competition problems.

However, the evidence for AI having generally solved major open problems in mathematics is still limited. The most defensible statement is:

AI has already materially advanced previously unsolved mathematics in narrow but important areas, and it has achieved some fully verified breakthroughs, but it has not yet demonstrated broad, autonomous mastery of frontier mathematical research.

Sources

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History

Checked 28 times since Jul 25

How strongly the models agree, per check. Amber points mark checks that changed the answer.

Oct 22
The answer changed

The new answer adds the KLS conjecture as a major AI-assisted problem reportedly proved in 2026, supported by a newly surfaced Microsoft Research source. It also names additional specific results from OpenAI’s mathematics release.
- Solving a 31-year-old grand challenge in mathematics – the KLS conjecture - Microsoft Research
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Oct 14 – Oct 15 3 checks, no change
- Oct 15same answer, new wording Read this version
- Oct 14sources did not come up, answer stands Read this version
- Oct 14a different reading, set aside Read this version
Oct 7
The answer changed

The new answer adds documented AI-generated/formally checked resolutions of open Erdős problems, including a public writeup and broader proof-search results. This strengthens the evidence beyond the standing answer’s framing of outright open-problem solutions as mostly recent claims awaiting broad verification.
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Sep 30 Checked, no change
- Sep 30same answer, new wording Read this version
Sep 23
The answer changed

The consensus shifted from claiming AI has actively resolved major open problems (like Erdős problems, Navier-Stokes, and Fermat's Last Theorem) to a much more cautious stance that AI has only achieved silver-medal Olympiad levels and improved bounds/constructions, while claims of solving famous open problems lack sufficient independent validation.
Shown above
Sep 16
The answer changed

The new consensus substantially strengthens the conclusion, asserting that AI has settled major open problems, including a Navier–Stokes result, and resolved numerous Erdős and other conjectures. The old consensus treated such claims as tentative, unverified, and not community-accepted, while affirming only material advances and possible machine-checkable results.
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Jul 27 – Sep 9 19 checks, no change
- Sep 9same answer, new wording Read this version
- Sep 2 Read this version
- Aug 26 Read this version
- Aug 19same answer, new wording Read this version
- Aug 11 Read this version
- Aug 10same answer, new wording Read this version
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- Aug 8same answer, new wording Read this version
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- Aug 5same answer, new wording Read this version
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- Aug 3same answer, new wording Read this version
- Aug 2same answer, new wording Read this version
- Aug 1same answer, new wording Read this version
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- Jul 30same answer, new wording Read this version
- Jul 29same answer, new wording Read this version
- Jul 27 Read this version
Jul 25, 2026
Topic started

The first answer. Every later check is compared with it.
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How the 4 models compared · 2 contradictions

OpenAI gpt-5.6-luna · Google Gemini gemini-3.5-flash-lite · DeepSeek deepseek-v4-flash · Grok grok-4.3-no-reasoning

Contradiction · critical

AI systems have solved or produced proofs for major open problems such as the Navier–Stokes existence and smoothness problem.

Model A states that an AI system produced a proof showing a singularity in 3D Navier-Stokes equations, verified using Lean.

Gemini

Model B argues there is no evidence AI has produced a complete, accepted solution to the Navier–Stokes existence problem.

OpenAI

“There is much less evidence that AI has independently produced a complete, accepted solution to a major famous problem such as the Riemann hypothesis, P versus NP, or the Navier–Stokes existence problem.”

Model C asserts that AI has not produced a breakthrough on any Millennium Prize problem, including Navier-Stokes.

DeepSeek

“AI has not yet produced a breakthrough on a major unsolved conjecture** (e.g., Riemann Hypothesis, P vs NP, or any Millennium Prize problem).”

Model D claims an internal OpenAI system produced an analytical proof and Lean formalization resolving the Navier-Stokes Millennium Prize Problem.

Grok

“produced an analytical proof and Lean formalization showing that smooth three-dimensional fluid motion can develop a singularity in finite time, resolving statement “C””

How to verify: Check official announcements from research institutions and independent mathematics experts regarding whether a verified solution to the Navier-Stokes problem has been achieved by AI.

Contradiction · critical

AI has successfully produced a complete, computer-checked formalization and proof of Fermat’s Last Theorem.

Model D claims that an AI multi-agent system produced the first end-to-end, computer-checked proof of Fermat’s Last Theorem in Lean.

Grok

“a multi-agent system built around Claude produced the first end-to-end, computer-checked proof of Fermat’s Last Theorem in Lean.”

How to verify: Check Anthropic's official research publications and the Lean theorem prover community repositories to verify if a full proof of Fermat's Last Theorem was generated and checked.