Recent AI Success for Thorough Advanced Research

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Mathematician Thomas Bloom, runs erdosproblems.com, explains that OpenAI surfaced erdos problem solutions that were not unsolved. OpenAI GPT-5 simply surfaced existing papers solving them that he had personally overlooked, mislabeling them as “open” on his site. No new mathematics was generated—GPT-5 acted as an advanced search tool.

OpenAI’s Mark Sellke and Sebastien Bubeck previously announced on X that, using thousands of GPT-5 queries, they found [on the web] solutions to problems numbered 223, 339, 494, 515, 621, 822, 883 (part 2/2), 903, 1043, and 1079, plus partial progress on 11 others.

The great mathematician Paul Erdős who posed many challenging questions that have served as a benchmark of progress in many diverse fields of mathematics, particularly combinatorics and number theory.

Erdős was very prolific and wrote over 1500 papers, many of which had open problems, and wrote many letters. Bloom aims to include all of the interesting Erdős problems. For example, sufficient (but not necessary) conditions for a problem being included are Erdős including it on a standalone published list of problems, or being on record as offering a monetary value for its solution. A usually necessary (but not sufficient) condition is that the problem be reasonably understandable and interesting as a stand-alone statement. Erdős often attached prizes to his problems. Often this is a reasonable measure of how interesting/difficult Erdős thought the problem was.