GPT-5.4 Pro and an Amateur Solve a 60-Year-Old Mystery

A 23-year-old amateur has managed to solve a mathematical problem that remained unanswered for 60 years, the famous Erdős problem #1196, thanks to the assistance of GPT-5.4 Pro. This problem concerns primitive sets of integers, where no number can be exactly divided by another from the same set. The question posed by Erdős was about a specific sum involving the formula 1/(a log a) and its tendency to reach a precise limit of 1.

Liam Price, without formal mathematical training, collaborated with his friend Kevin Barreto to implement a method they call "vibe mathing." This approach involves formulating the problem in natural language, allowing the AI to generate creative solutions. The prompt used was strictly formatted in LaTeX and prohibited internet access, thus encouraging the AI to demonstrate originality.

The GPT-5.4 Pro model responded with a solution that immediately addressed the question of the limit approaching 1. By using mathematical concepts typically applied to other types of problems, the AI was able to circumvent the obstacles that had blocked mathematicians for decades.

After the generation of this solution, mathematicians Jared Lichtman and Terence Tao reviewed the document produced by the AI. Although adjustments were necessary to clarify certain aspects of the proof, the main idea remained intact. Terence Tao noted that the problem seemed simpler than initially perceived, suggesting that human researchers had been on the wrong track from the beginning.

This case demonstrates how artificial intelligence can avoid biases and traditional academic reflexes, thus opening new avenues for thinking and solving mathematical problems.