Unsolved Math Problems Solved by AI

The current evidence supports a qualified yes: AI has solved some previously open mathematical problems and has materially advanced others, but the strongest claims still mostly come from a small number of highly publicized cases and often involve human checking, formal verification, or collaboration.

What is most convincing right now

1) A long-standing open conjecture in discrete geometry was reportedly disproved

OpenAI announced that an internal reasoning model disproved the Erdős unit-distance conjecture in planar discrete geometry, by constructing configurations with asymptotically more unit distances than the conjecture allowed.openai This is one of the clearest public examples of AI contributing a genuine new result on a recognized open problem.

Why it matters:

• it was a real research problem, not a benchmark;
• the result is a disproof, not just a better heuristic;
• the company published supporting material and said external mathematicians checked it.openai

A small but important caveat is that the final write-up and validation involved humans, so this is best described as AI-driven discovery with human verification, rather than purely autonomous mathematics.

2) A batch of additional open problems was claimed solved or substantially advanced

OpenAI later announced ten advances in mathematics and theoretical computer science generated by its internal model, spanning geometry, coding theory, group theory, operator algebras, quantum complexity, lattice cryptography, Ehrhart theory, Ramsey theory, and extremal graph theory.openai The announcement says the outputs include both complete resolutions and substantial progress.

This is strong evidence that AI can now contribute across several research areas, but the exact weight of each item still varies:

• some results are full solutions,
• some are progress results rather than final closures,
• and independent community assessment is still in progress for parts of the set.openai

3) Formal proof search has produced verified solutions to some open problems

A preprint on AI-driven formal proof search reported that LLM-based agents, paired with Lean verification, resolved 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures, along with other improvements and bug-finding in formalizations.deepmind Because the proofs are machine-checked in Lean, this is particularly strong evidence that the systems can produce correct formal mathematics, not just plausible prose.

The limitation is that these are a heterogeneous collection of problems, and not every solved item is a major landmark theorem. Still, it is solid evidence of genuine mathematical discovery in an automated workflow.deepmind

4) DeepMind has shown meaningful research-level progress, but is more cautious in its own claims

Google DeepMind has reported systems that can solve olympiad-style problems at very high levels and can contribute to research-level work, including open Erdős problems and other mathematical tasks.openai It also distinguishes between autonomous and collaborative results and explicitly says it is not claiming major landmark breakthroughs in its own internal taxonomy.openai

That caution is important: DeepMind’s results are real evidence of capability, but they do not yet amount to a claim that AI has broadly solved the deepest open problems in mathematics.

Where AI is clearly making a difference, even when it does not “solve” the whole problem

The best-established broader effect is material acceleration of human mathematics:

• AI helps explore candidate proofs faster,
• imports ideas from neighboring fields,
• searches through large problem spaces,
• and catches errors or formalization gaps.

Examples include GPT-5 assisting a mathematician on a decades-old optimization question,deepmind and GPT-assisted work in robust density estimation that sharpened previously non-optimal bounds.deepmind These are not autonomous AI breakthroughs, but they are genuine research accelerations.

What the evidence does not yet show

There is still no solid public evidence that AI has:

• solved the biggest headline problems of mathematics at a stable, repeatable level;
• routinely produced major landmark theorems without human steering; or
• replaced mathematicians in the research loop.

In other words, AI has crossed from “good at math problems” into “capable of producing real research results,” but it has not yet become a general-purpose independent mathematician.

Bottom line

If “solved or materially advanced” means any credible new result on an open problem, then the answer is yes. If it means regularly and autonomously breaking major frontier problems, the evidence is still limited.

The best-supported current conclusion is:

AI has already produced some genuine mathematical discoveries, including at least one high-profile disproof and several formally verified or research-level advances, but these results remain selective, heavily validated, and often human-guided.openaiopenaideepmindopenai