OpenAI internal model solves 3 Erdős problems

This is more interesting than another benchmark win because the output is a set of checkable proofs, not a score on a test set. If the claims hold up, it suggests internal reasoning systems are starting to contribute real mathematical knowledge, not just imitate it.

• –The paper reports three Erdős problems resolved by proofs generated entirely by an OpenAI internal model.
• –The work spans combinatorics and number theory, which is a harder test of structured reasoning than standard coding or chat tasks.
• –This kind of result matters because proof generation is one of the clearest ways to measure whether a model can discover new facts, not just retrieve known ones.
• –The practical caveat: this is still a research paper, so the key question is whether the approach is reproducible and extensible beyond carefully chosen math problems.