Why the Legendary Erdős Problems Are Falling to AI

In a series of breakthroughs beginning in May 2026, artificial intelligence models started solving legendary mathematical problems from Paul Erdős. These advances, starting with a counterexample to the 1946 “unit distance” problem, signal a ‘phase transition’ in AI’s abilities. The meeting of a curated online list of Erdős problems and powerful new AI models formed a unique proving ground for this technological leap.

Key takeaways

• An OpenAI AI model produced the first historically significant proof by an AI in May 2026, solving Erdős’s “unit distance” problem.
• By August 2026, an unreleased model named Astra had made 10 additional advances, including solutions to three more Erdős problems.
• Mathematicians describe these events as a dramatic change, or “phase transition,” in how mathematical research is done.
• The website erdosproblems.com, curated by mathematician Thomas Bloom, provided a clear benchmark that helped catalyze this AI-driven research.
• Paul Erdős’s problems are famously simple to state but mathematically deep, making them an ideal and ironic testing ground for corporate AI.

AI’s Breakthroughs on Erdős Conjectures

On May 20, 2026, an internal AI model at OpenAI produced a counterexample to Paul Erdős’s 1946 “unit distance” problem. This marked the first historically significant proof to come from an AI model. The AI’s approach was innovative, applying ideas from a distant branch of mathematics previously unused for this problem. While human mathematicians would substantially improve on the result within weeks, the breakthrough was influential, with related techniques soon used to solve other important problems.

Rapid Expansion

Then on August 1, OpenAI announced that an unreleased model named Astra had made 10 additional mathematical advances, including solutions to three more problems posed by Erdős. Mathematicians have described these developments as a “phase transition” in AI’s mathematical capability. Noga Alon of Princeton University stated these models are “changing dramatically the way mathematical research is being done.”

The Enduring Legacy and Idiosyncrasy of Paul Erdős

Paul Erdős was a prolific, itinerant Hungarian mathematician who posed thousands of questions, often attaching prize money from his own pocket for their solutions. The rewards ranged from a token $10 or $25 to thousands of dollars for problems he considered important or difficult. Since his death in 1996, a nonprofit foundation based in Iowa has promised to honor these financial bounties.

He was a deeply whimsical and cynical figure. Erdős traveled constantly, living out of a suitcase for years at a time and owning almost nothing. He only wore silk, avoided physical contact, and gave away most of his money. He fueled his incessant output of mathematical ideas with a steady diet of amphetamines and referred to God as the “Supreme Fascist.”

His problems are famously simple to explain yet mathematically deep. It is a historical irony that these conjectures have now become a central proving ground and, in effect, a series of PR coups for major technology companies like OpenAI, which has used internal AI models to solve several Erdős problems.

Thomas Bloom’s Curatorial Role and the erdosproblems.com Website

English mathematician Thomas Bloom, a rising star in arithmetic combinatorics, created erdosproblems.com in early 2023. He intended the site as a personal resource to catalog problems posed by Paul Erdős, gathering a couple hundred entries to track which remained unsolved. As a fellow mathematician drawn to Erdős’s style, Bloom aimed to apply modern mathematical techniques, often unknown to Erdős himself, to resolve obscure problems. His goal was to identify a core of truly difficult problems that would “demonstrate the limits of our knowledge.”

Curating the Conjectures

A crucial part of Bloom’s work involved curating the list itself. Erdős often stated problems in ambiguous or unclear ways. Bloom took on the task of determining the most sensible version of each problem for the website, clarifying these statements for a modern audience.

Building the Site with AI

To build the website, Bloom used ChatGPT to write the Python code that ran it. At the time, this was seen as a remarkable demonstration of a large language model’s capabilities. However, the idea of using AI to collaborate on solving the mathematics itself still seemed like only a distant possibility in early 2023.

The Website as a Catalyst and the Changing Landscape

Thomas Bloom’s website, erdosproblems.com, launched in early 2023, became a central home for tracking these mathematical problems. Bloom curated the list, clarifying ambiguous statements from Erdős to create sensible versions of each problem. The site’s audience grew gradually over time.

Between 2024 and the first eight months of 2025, the status of 111 problems on the list changed from ‘open’ to ‘solved’, though some had been solved years earlier but were only recorded then. The website’s existence and its structured list provided a clear, organized benchmark and target for research efforts.

A Unique Testing Ground

This convergence of Bloom’s curated list and advancing AI capabilities created a unique testing ground. The result was the rapid AI-driven solutions announced in 2026, beginning with OpenAI’s counterexample to the “unit distance” problem in May and followed by further advances from a model named Astra in August. These events were hailed by mathematicians as a dramatic change in how mathematical research is conducted.