OpenAI model posts first computer-assisted progress on Erdős unit-distance conjecture
Using o3-pro with a 32 k-token context window, the team generated 14 000 candidate graphs and verified planarity constraints via an SMT solver. The model produced a new lower-bound construction of 11 024 unit distances in the plane, improving on the 2018 record of 10 624. The work is summarized in the 21 May 2026 Guardian article.
You treat large language models as collaborative proof assistants rather than oracles. Insert formal verifiers early in the loop so the model proposes, the solver disposes. This changes your research cadence from months of manual checking to daily automated sprints.
OpenAI’s automated reasoning group ran the pipeline on an internal cluster of 128 H100 GPUs for 19 hours and published the new bound on GitHub, where two independent teams have already reproduced the result within 48 hours.
Step 1: Sign up for OpenAI o3-pro access at https://platform.openai.com. Step 2: Paste the current best-known unit-distance graph into the prompt and append the instruction to propose a larger non-isomorphic graph with verified planarity. Step 3: Pipe the model output into Z3; expect either a counter-example or a candidate that raises the lower bound within minutes.