OpenAI Claims Progress on an 80-Year Math Puzzle Using AI Reasoning
OpenAI applied large language models to the Paul Erdős planar unit distance problem, which asks for the minimum number of distinct distances among points in a plane. The system generated candidate configurations and verified constraints through symbolic checking and numerical simulation. The company reported new upper and lower bounds that narrow the known range for the chromatic number of the plane.
The case shows how AI can serve as a hypothesis generator rather than a calculator. Readers learn to treat model outputs as starting points that require formal verification. This shifts workflows toward hybrid loops of generation followed by proof or measurement.
OpenAI published internal logs showing the model produced 47 candidate graphs, of which three survived human review and computer algebra checks. The work appeared in a May 2026 Guardian report citing company statements.
Step 1: Go to chat.openai.com and paste the Erdős problem statement plus the instruction 'Generate 10 distinct point configurations that minimize repeated distances.' Step 2: Export the coordinate lists and run them through a Python script using SciPy's distance_matrix function to count unique distances. Step 3: Compare the resulting counts against published bounds at erdosproblems.com; any reduction becomes a candidate for further proof.