Paul Erdős's Unsolved Problems Are Becoming AI's Favorite Benchmark

Artificial intelligence is making its mark on one of mathematics' most storied problem lists. On August 1, OpenAI announced that its unreleased Astra model had made 10 new mathematical advances, including solutions to three more problems posed by the prolific Hungarian mathematician Paul Erdős, Quanta Magazine reported.

The Erdős List

The problems come from erdosproblems.com, a website created in 2023 by University of Manchester mathematician Thomas Bloom to catalog Erdős's scattered questions. Bloom launched the site for personal use, but it grew into a community hub where amateurs, undergraduates, and world-class researchers collaborate. By this summer, the database contained 565 solved problems and 652 still open.

From Hobbyists to Corporate Labs

Earlier this year, undergraduates Kevin Barreto and Liam Price used GPT-5.2 to solve Erdős Problem 728 and posted the result on Bloom's site. In January, a 24-person Google DeepMind team used Gemini to systematically evaluate 700 open conjectures from the database. On May 20, OpenAI announced a counterexample to the 1946 "unit distance" conjecture — the first historically significant proof to come from an AI model, according to Quanta.

Why Erdős Problems?

Erdős's questions span number theory, combinatorics, and graph theory — areas that have proved unusually accessible to large language models. The problems also vary widely in difficulty, making them a natural benchmark for a technology whose abilities are still uneven. Mathematicians are now discussing solutions in terms of "per-problem cost," the price of the tokens needed to find a proof.

A Shift in Research Culture

Not everyone is cheering. Princeton mathematician Noga Alon, who has solved dozens of Erdős problems over his career, told Quanta he has stopped trying: "Once AI started to solve them, there is no point anymore." Terence Tao has also stepped back from the community to focus on other work. The field is grappling with what it means to prove something when machines can find answers faster than humans can digest them.

The Bottom Line

Erdős's playful, prize-backed questions have become an unlikely proving ground for the world's most powerful AI labs. Whether that accelerates mathematics or changes what mathematicians value is a question no algorithm can answer.