Refuted by proof: OpenAI solves math problem after 80 years

OpenAI claims to have achieved a breakthrough in mathematics: According to the company, a new AI model has, for the first time, independently found proof that refutes an assumption from geometry that has been known for decades.

This time it should be right too

The question goes back to the Hungarian mathematician Paul Erdős and has been considered unsolved since 1946. However, it remains to be seen whether this actually resulted in a result. OpenAI has made similar announcements in the past, but they later turned out to be exaggerated. Around seven months ago, the company’s then OpenAI manager, Kevin Weil, said that GPT-5 had found solutions to ten previously unsolved Erdős problems. However, it later turned out that the system had only identified solutions that were already known from the specialist literature. The statement sparked criticism, including from Yann LeCun and Demis Hassabis. The relevant post was subsequently deleted. OpenAI reports on the process of solving the Erdos problem

This time OpenAI is trying to underpin its scientific claim by supporting well-known mathematicians. Accompanying the publication, Noga Alon, Melanie Wood and Thomas Bloom, among others, commented positively on the new result. Bloom had criticized the earlier GPT-5 announcement as a “dramatic misinterpretation”.

No specialized AI model

OpenAI dealt with current case specifically with the question raised by Erdős as to how many pairs of points on a surface can have the same distance from each other. According to the company, for decades the mathematical community assumed that the best solutions to the underlying problem resembled structures that roughly correspond to square grids. The new AI model now uses a completely different family of mathematical constructions that deliver better results and thus refute the previous assumption. The company speaks of the first known situation in which an artificial intelligence independently solved a significant open problem that is central to a mathematical subfield. OpenAI particularly emphasizes that the proof does not come from a system specifically designed for mathematics, but from a general model for complex logical reasoning.

If the result is confirmed in the long term, it could have implications far beyond mathematics. OpenAI sees this as an indication that modern AI systems are increasingly able to understand long and sophisticated trains of thought and create new connections between different areas of knowledge. This would have consequences for research in biology, physics, engineering and medicine.