Overview
- An unreleased OpenAI general‑purpose model generated a counterexample to Paul Erdős’s long‑standing planar unit distance conjecture using algebraic number theory to build high‑dimensional point arrangements.
- OpenAI says it has formalized the unit‑distance result in the Lean proof assistant and submitted a paper, but the model’s raw reasoning and full chain‑of‑thought remain unavailable and independent peer review is still pending.
- Human researchers rapidly adapted the AI’s technique: Will Sawin published an improved quantitative version of the unit‑distance construction and Thomas Bloom and colleagues used a similar method to report a disproof of Erdős’s 1976 sum‑product conjecture.
- Experts note limits to the new counterexamples because many rely on exotic number systems rather than ordinary integers, so integer‑only versions of some Erdős conjectures may still hold.
- The episode shows AI can produce substantial, publishable math and it is likely to change research practice, but it also creates a near‑term demand for clearer verification standards, public audits, and wider formal checking of machine‑found proofs.