Unsolved Math Problems Solved by AI

The current evidence is that AI has materially advanced several previously open mathematical problems, and in a few cases may have solved them in a credible, externally checkable way—but the strongest claims still depend on what counts as “solved” and on how much human verification or cleanup followed the model’s output.

Bottom line

The best-supported examples are:

1. A genuine disproof of a long-open conjecture in discrete geometry: OpenAI reported that an internal model found a counterexample to Erdős’s planar unit-distance conjecture, and mathematicians later produced a human-checked version of the argument.openaiopenai
2. Lean-checked proofs of open problems: systems combining LLMs with formal proof assistants have produced machine-verified proofs of some open Erdős problems and related conjectures.deepminddeepmind
3. Broader but less final research progress: AI systems have improved bounds, constructions, and algorithms in combinatorics and theoretical computer science, even when they did not fully settle the underlying question.deepminddeepmind

What is strongest right now

1) Erdős’s planar unit-distance conjecture

This is the clearest high-profile case. OpenAI announced in May 2026 that an internal model produced a construction violating the conjectured near-linear growth of unit distances among \(n\) planar points, yielding a lower bound of the form \(u(n)\ge n^{1+\delta}\) for some \(\delta>0\).openai A companion mathematical write-up and expert commentary make the argument publicly checkable, and later refinements made the exponent explicit.openai

This is strong evidence that AI can do more than spot patterns: it produced a mathematically substantive counterexample to a long-standing open problem. The remaining caveat is provenance: the final proof is robust, but outsiders cannot fully audit the model’s internal search process.

2) Formal proofs of open problems

A separate, very important line of evidence is formal theorem proving. A preprint on Aristotle/GPT-style proof search reports a Lean formalization of an Erdős problem (problem #728) and describes it as autonomously resolved by an AI system.deepmind Another large-scale effort reported solving a meaningful fraction of formalized open Erdős problems and OEIS conjectures, with Lean proofs and released code.deepmind

These results are especially persuasive because Lean checks the proof mechanically. That said, they are strongest as evidence for AI-assisted formal mathematics rather than for unconstrained “human-style” discovery.

3) Research-level challenge benchmarks

The First Proof benchmark showed that current systems can sometimes produce correct research-level proofs for unpublished problems, including cases judged essentially correct by expert referees.deepmind This is good evidence that AI can now contribute at the level of real research mathematics, not just contest geometry or olympiad-style tasks.

But these benchmarks are not the same as independently discovering a new theorem from scratch: they test performance on problems already selected and formalized by humans, with varying amounts of scaffolding.

What AI has clearly not done yet

There is no solid evidence that AI has broadly solved the hardest open problems in mathematics, such as the major Millennium Prize problems, on its own. Current successes are impressive but still concentrated in areas where:

• the statement is crisp and formalizable;
• the problem can be attacked by search;
• the answer can be checked mechanically or by expert verification;
• existing libraries and formal tools already cover much of the needed ground.

Best overall assessment

AI has definitely materially advanced previously open mathematical problems, and in a few notable cases it has likely resolved them in the mathematical sense. The strongest evidence comes from:

• a counterexample to the Erdős unit-distance conjecture,openaiopenai
• Lean-verified proof search on open Erdős-style problems,deepminddeepmind
• and research-level benchmark successes on unpublished problems.deepmind

So the honest summary is: AI is now a real contributor to frontier mathematics, but not yet a general autonomous solver of open mathematical research.