AI Tools Contribute to Solutions of Several Erdős Problems and Longstanding Conjectures in 2025–2026

OpenAI announced in May 2026 that an unreleased general-purpose model had solved the planar unit distance problem, an 80-year-old conjecture in geometry. 5 Pro. The problem asks for the maximum value of a quantity associated with restricted families of primitive sets; Erdős suspected the value was 1.

6. The AI solution used a Von Mangoldt function, an approach previous human attempts had not employed. Lichtman later adapted the technique, working with Price, Kevin Barreto and Terence Tao, to settle a related 60-year-old conjecture.

In January 2026, Ravi Vakil and colleagues posted a paper whose proof was generated with Google Gemini and related tools. The argument links sphere-like shapes to flag spaces, connecting topology and algebraic geometry. Vakil stated that the AI could not have produced the result alone because it would not have known the correct question.

In the same month, Tony Feng at the University of California, Berkeley, published work in which Google’s Aletheia AI generated the core mathematical content required to compute previously unknown numbers that bridge algebraic geometry and number theory for the Langlands programme.

Thomas Bloom at the University of Manchester first observed non-trivial AI-assisted solutions to Erdős problems in the final months of 2025, shortly after GPT-5 became available. Kevin Barreto, a second-year undergraduate at the University of Cambridge, and Liam Price, who has no formal mathematics training, have since solved numerous additional Erdős problems with the same tools.

In April 2026, mathematicians and AI researchers met in San Francisco to discuss how to measure further progress. ” Jeremy Avigad of Carnegie Mellon University wrote that researchers are “running out of places to hide” because AI will soon prove theorems better than humans can.