OpenAI Model Solves 80-Year-Old Erdős Problem with Original Proof
OpenAI revealed that its latest general-purpose reasoning model has successfully generated an original mathematical proof that refutes a well-known unsolved geometric conjecture introduced by Paul Erdős in 1946. This achievement represents the first instance of an AI independently addressing a significant unresolved issue in mathematics. Accompanying the announcement, mathematicians Noga Alon, Melanie Wood, and Thomas Bloom, who oversees the Erdős Problems website, provided supportive comments regarding the disproof. Bloom had previously criticized a hasty claim made by former OpenAI VP Kevin Weil about GPT-5 resolving ten Erdős problems, labeling it "a dramatic misrepresentation." Following backlash from Yann LeCun and Google DeepMind CEO Demis Hassabis, Weil's post was retracted. OpenAI asserts that the new model has identified a completely new family of constructions that outperform the square grids mathematicians had deemed optimal for nearly 80 years, showcasing AI's capacity for extensive reasoning and interdisciplinary connections, with potential applications in biology, physics, engineering, and medicine.
Key facts
- OpenAI's new reasoning model produced an original mathematical proof disproving a geometry conjecture posed by Paul Erdős in 1946.
- This is the first time AI has autonomously solved a prominent open problem central to a field of mathematics.
- Mathematicians Noga Alon, Melanie Wood, and Thomas Bloom supported the disproof.
- Thomas Bloom previously called a post by former OpenAI VP Kevil Weil a 'dramatic misrepresentation.'
- Weil's post claimed GPT-5 solved 10 unsolved Erdős problems, but it only found existing solutions.
- Criticism from Yann LeCun and Demis Hassabis led to Weil taking down his post.
- The model is a general-purpose reasoning model, not specifically designed for math.
- OpenAI says the proof has implications for biology, physics, engineering, and medicine.
Entities
Institutions
- OpenAI
- Google DeepMind
- Erdos Problems website