New Scientist · Global
Established mathematical ideas open a new path through an 80-year-old problem
Recap published
Paul Erdős conjectured that points arranged in a grid give the most equal-length connections. The problem resisted mathematicians for 80 years, and its last improvement came more than 40 years ago. A model built by OpenAI found that he was significantly wrong, using a technique from algebraic number theory. Kevin Buzzard says the ideas were "already in the literature". Will Sawin was at first disbelieving, then convinced himself it works, and has since used the technique to improve the result slightly.
Why it matters
Experts could read and test a machine-found argument, and one has already built on it. Samuel Mansfield notes that few geometry specialists would have known enough number theory to try it.
Read the original at New Scientist
Origins, evidence and credits
Original headline: Mathematicians stunned by AI's biggest breakthrough in mathematics yet
Original reporting: New Scientist ·
- Origins and holders
- The conjecture comes from Paul Erdős. The article connects the result to existing ideas in algebraic number theory.
- What was checked
- The article reports that Will Sawin examined the argument, convinced himself it worked and used the technique to improve the result. This is not described here as a formal verification.
- Limits reported
- The article says OpenAI has not disclosed how the model was trained. The recap follows the article as amended on 10 June 2026.
People and institutions credited
Paul Erdős (20th-century mathematician, the conjecture); Will Sawin (Princeton University); Kevin Buzzard (Imperial College London); Tim Gowers (University of Cambridge); Misha Rudnev (University of Bristol); Samuel Mansfield (University of Manchester); OpenAI (the model; the article says OpenAI hasn't said how it was trained).