Tech

OpenAI Claims Progress on a Decades Old Math Puzzle

May 22, 2026 · From the archive, written in the Professor's voice before our October 2026 redesign from theguardian.com

What happened

OpenAI researchers applied large language models to the Paul Erdős planar unit distance problem. They combined chain of thought prompting with formal verification tools to generate candidate solutions. The models produced new lower bounds on the chromatic number of the plane.

Why it matters

This shows that AI systems can now assist with abstract mathematical reasoning rather than only pattern matching. Readers should treat models as collaborators that test hypotheses and verify results. The workflow shifts from asking quick questions to structuring multi step verification loops.

Who's doing it

OpenAI published internal benchmarks showing their system reached 4.987 chromatic number candidates on the planar unit distance problem. The team released partial proofs for community review on their research blog.

Try it

1. Open ChatGPT and paste the Erdős problem statement.
2. Use the prompt 'Walk through every assumption and check against known bounds using formal logic.'
3. Copy promising outputs into Lean or Coq for verification and iterate until contradictions appear. Expected outcome: clearer candidate bounds after three refinement rounds.

Read the original at theguardian.com