OpenAI Claims It Solved an 80‑Year‑Old Geometry Conjecture

AI Summary

OpenAI says its new reasoning model has autonomously disproved the 1946 geometry conjecture posed by Paul Erdős, ending an 80‑year‑old open problem. Backed by mathematicians Noga Alon, Melanie Wood and Thomas Bloom, the claim follows earlier, premature GPT‑5 assertions and could reshape AI‑driven scientific discovery.

The Lead

OpenAI says its new general‑purpose reasoning model has produced an original proof that disproves the famous geometry conjecture posed by Paul Erdős in 1946, ending an 80‑year open problem.

OpenAI Announces Disproof of Erdős’s 1946 Geometry Conjecture

The company released a pre‑print and companion remarks signed by mathematicians Noga Alon, Melanie Wood and Thomas Bloom. The proof introduces a completely new family of constructions that outperform the long‑standing “square‑grid” belief.

Timeline of Claims and Corrections

July 2025: Former VP Kevil Weil tweeted that “GPT‑5 found solutions to 10 unsolved Erdős problems”.
Later 2025: Critics including Yann LeCun and Demis Hassabis called the claim a misrepresentation; Weil removed the post.
May 20, 2026: OpenAI publishes the new disproof, backed by external experts.

Why This Disproof Could Redefine AI‑Driven Research

The breakthrough demonstrates that an AI system can autonomously manage long, intricate chains of reasoning and synthesize ideas across mathematical sub‑fields, a capability that researchers argue could translate to breakthroughs in biology, physics, engineering and medicine.

What Comes Next for AI in Fundamental Science

Experts anticipate a surge in AI‑assisted exploration of other long‑standing conjectures. If the model’s reasoning can be generalized, we may see a new era where AI acts as a co‑discoverer rather than a tool.