OpenAI Claims Progress on an 80-Year-Old Geometry Puzzle
What happened
OpenAI applied its o3 reasoning model to the Erdős planar unit distance problem, which asks for the minimum number of distinct distances among n points in a plane. The system produced new lower-bound constructions and proof sketches that researchers had not previously recorded. The Guardian reports the work as evidence of improved multi-step mathematical reasoning rather than a full solution to the conjecture.
Why it matters
You can treat frontier reasoning models as research assistants that generate candidate proofs and counter-examples before you invest human time. The technique shifts the workflow from manual literature search to rapid hypothesis generation followed by targeted verification. Users should log every model-generated step so that later manual checks remain traceable.
Who's doing it
OpenAI's internal math research team ran the o3 model on the Erdős problem and surfaced previously unseen lower-bound constructions that the Guardian article cites as the first AI-generated candidates accepted for further review by human mathematicians.
Try it
- Open ChatGPT and select the o3 model.
- Paste the statement of the Erdős planar unit distance problem and request lower-bound constructions with step-by-step reasoning.
- Export each reasoning trace, then verify the geometry claims in Lean 4; a working example is at https://leanprover-community.github.io.
Read the original at theguardian.com
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