Unsolved Math Problems Solved by AI

As of mid-2026, the evidence is strong that AI has materially advanced previously unsolved mathematical problems, and in a few cases has produced genuinely new, checkable mathematical results. But it is not evidence that AI has broadly “solved mathematics,” or that it has resolved the biggest open problems of the field.

Bottom line

The clearest current evidence falls into three buckets:

1. AI has disproved or materially advanced some long-open conjectures.
2. AI has generated formal, machine-checkable proofs and new constructions.
3. AI still relies heavily on human verification, problem selection, and interpretation.

Strongest evidence so far

1) A counterexample to a long-standing discrete-geometry conjecture

OpenAI reported that one of its reasoning models found a counterexample to the planar unit-distance conjecture, a problem associated with Erdős. The result was not just a numerical pattern: it produced an infinite family of point sets with more than the conjectured \(n^{1+o(1)}\) unit-distance behavior, and OpenAI said the proof was externally checked by mathematicians.openai A companion paper by leading mathematicians gives a human-verified version of the argument and explains the result in standard mathematical terms.openai

This is the best public example of AI-originated work that appears to have changed the status of a previously open mathematical question.

2) Semi-autonomous solutions to smaller research problems

DeepMind’s Aletheia/Gemini work reports large-scale exploration of open Erdős problems and related research tasks, including cases where the system found previously open problems already solved in the literature, as well as some apparent novel solutions.deepmindopenai One published example concerns an Erdős–Graham irrationality problem, where the authors describe the original problem as being autonomously solved by the AI system, with the final paper developed through human–AI interaction.deepmind

This is meaningful evidence that AI can now contribute to real research-level mathematics, but the results vary in autonomy and scope.

3) Formal proof-search systems are now resolving open problems at scale

A more technical line of work uses systems that combine language models, search, and proof assistants such as Lean. One reported framework solved a number of open Erdős and OEIS problems and produced machine-checked proofs.deepmind The important point here is not just that the model “sounds right,” but that the outputs can be formally verified by a proof checker.

That said, these are still often special-purpose, scaffolded systems, not unconstrained autonomous mathematicians.

4) AI has produced publishable-level mathematical research outputs

There are also AI-assisted or AI-generated papers in arithmetic geometry and related areas, including work reported by DeepMind on eigenweights in arithmetic Hirzebruch proportionality.deepmind These show that AI is starting to operate inside genuine research workflows, not only contest-style benchmarks.

What this does and does not mean

It does mean:

• AI can now find new mathematical constructions.
• AI can sometimes disprove conjectures or improve known bounds.
• AI can produce machine-checkable proofs in formal systems.
• AI is no longer limited to olympiad-style or textbook mathematics.deepmindopenaideepmind

It does not yet mean:

• AI has solved the hardest famous open problems, such as the Millennium Prize problems.
• AI can reliably do open-ended mathematical research without human guidance.
• AI has replaced mathematicians in framing problems, judging significance, or turning raw discoveries into accepted theory.

Best current summary

The current evidence supports this statement:

AI has begun to make genuine mathematical discoveries, including some that resolve or overturn previously open conjectures, but it has not yet demonstrated broad autonomous mastery of frontier mathematics.

If you want, I can also give you a short table of the strongest examples, ranked by how convincing the evidence is.