Erdős problems

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a geometry conjecture first posed by Paul Erdős in 1946. The company says this is the first time AI has autonomously solved a prominent open problem central to a field of mathematics, with verification from mathematicians including Thomas Bloom and Noga Alon.

OpenAI's GPT-5.4 Pro model has reportedly solved Erdős open problem #1196 in approximately 80 minutes, with another 30 minutes to format the solution as a LaTeX paper. Mathematician Terence Tao notes the solution reveals a previously undescribed connection between integer anatomy and Markov process theory.