Why the Legendary Erdős Problems Are Falling to AI

On May 20, 2026, OpenAI made a startling announcement that rocked the mathematical community. An internal AI model, not accessible to the public, had generated a counterexample to the century-old "unit distance" problem, a conjecture introduced by the legendary mathematician Paul Erdős in 1946. Erdős posed countless questions throughout his career, but this one stood out for its simplicity and profound complexity.

It marked the first major breakthrough from an AI model in mathematical history. Although the initial result required refinement from human mathematicians, it introduced innovative techniques from a different mathematical domain that had never been applied to this problem before. Furthermore, the AI's findings sparked immediate interest, prompting related methods to solve several other significant mathematical challenges.

In August 2025, OpenAI revealed that another unreleased model, dubbed Astra, had made ten additional groundbreaking mathematical contributions, including solutions to three more of Erdős' problems. These developments have been hailed as a watershed moment in AI's role in mathematical research. Noga Alon, a Princeton University mathematician who has tackled numerous Erdős problems, described the impact as "dramatically changing the way mathematical research is being done."

Erdős was a nomadic figure, traversing the globe and sharing problems with mathematicians worldwide, often offering monetary rewards for solutions. He passed away in 1996, but a foundation in Iowa has pledged to fulfill his unsolved bounties. Despite his eccentricities, such as wearing silk and avoiding physical contact, Erdős was deeply respected.

His problems, many of which pertain to number theory and combinatorics, have now become a focal point for major tech companies' research endeavors. However, the journey began with Thomas Bloom, an English mathematician with a keen interest in arithmetic combinatorics, an area bridging number theory and combinatorics. Bloom recognized the need to organize Erdős' problems to avoid redundancy and confusion.

In early 2023, he compiled a list of around 200 problems on erdosproblems.com, a platform he initially created for personal use but eventually shared with the world. Bloom's initiative inadvertently became a catalyst for AI-driven mathematical discoveries. By 2025, nearly 1,000 problems had been cataloged on his website, with a significant portion solved through AI's assistance.

Bloom's efforts to refine Erdős' ambiguous statements and foster a community of mathematicians discussing these problems have proven instrumental. Many commentators on his site, including someone from a customer service background, have reported transformative effects on their mathematical pursuits.