How AI Is Reviving Erdős’s Unsolved Math Puzzles and Advancing Pure Mathematics

Erdős problems and recent progress

Paul Erdős posed over a thousand problems, many in number theory, combinatorics, and graph theory, that appear simple but have resisted solution for decades.

Thomas Bloom curated an online list of these problems. Between 2024 and early 2025, the status of 111 entries changed from “unsolved” to “solved.” In October 2025, Wouter van Doorn posted a comment on problem 1102 and supplied a non‑AI proof the following month.

AI‑assisted attempts

Kevin Barreto and Liam Price used large language models (LLMs) to attack problem 333. Their generated solution was later found to duplicate an existing proof, but the experiment motivated further exploration.

On 4 January 2026, the team employed GPT‑5.2 Pro to produce a proof for problem 728. The logical steps of that proof were independently validated by another AI tool named Aristotle.

Price described a repeatable workflow: query a chatbot for a candidate solution, feed that solution to a fresh chatbot instance for verification, and iterate until the output satisfies the verification step.

The concentration of Erdős problems in number theory, combinatorics, and graph theory makes them comparatively tractable for current LLMs, which handle symbolic reasoning in these domains better than in other areas of mathematics.

Institutional breakthroughs

On 20 May 2026 OpenAI announced that an internal, non‑public model solved a 1946 Erdős problem (the unit‑distance conjecture). The announcement included a blog post, a peer‑reviewed paper, and an evaluation by nine world‑class mathematicians who assessed the proof’s correctness and significance. The counterexample is shown in the image below.

In January 2026 a DeepMind team of 24 researchers published a paper solving four Erdős problems and uncovering nine previously forgotten solutions. In May 2026 another DeepMind group reported that its most capable autonomous agents solved nine of 353 unsolved Erdős problems, each at a cost of only a few hundred dollars.

These results illustrate a new research mode: AI systems can explore vast mathematical spaces, propose novel connections, and generate candidate proofs that human mathematicians can inspect and refine.

Key artifacts

https://arxiv.org/abs/2605.22763

https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf