An 80-Minute Solution to a Hard Problem

OpenAI's GPT-5.4 Pro found a solution to Erdős problem #1196 in about 80 minutes, then spent 30 minutes writing it up as a LaTeX paper. Formal verification is currently underway.

Terence Tao noted on the Erdős problems forum that this work reveals a previously unknown connection between the structure of integers and Markov process theory. He suggested the result could be a meaningful contribution to number theory beyond just solving that one problem.

Kevin Barreto, who announced he will soon join OpenAI's AI for Science team, also commented on the same forum that the Markov chain technique used by the model was a creative step that human mathematicians had long overlooked.

Key points are as follows.

• Solution found in 80 minutes
• LaTeX paper draft produced in 30 minutes
• Formal verification in progress
• Sparks debate over whether new mathematical knowledge may be hidden within already-known data, rather than outside the training data