OpenAI Model Disproves 80-Year Erdős Conjecture

Summary

An internal OpenAI general-purpose reasoning model autonomously disproved a central conjecture in discrete geometry posed by Paul Erdős in 1946 — the unit distance problem’s square grid optimality. The model produced a 125-page proof identifying an infinite family of counterexamples providing a polynomial improvement. The proof connected the problem to algebraic number theory, a link mathematicians hadn’t explored. Externally verified by independent mathematicians.

Implications

• Capability signal: The model was general-purpose, not math-specialized or scaffolded for this problem. This is the strongest autonomous mathematical reasoning demonstration from any vendor.
• IPO timing: Published May 20, two days before the confidential S-1 filing. Whether deliberate or not, this is a capability proof landing in the investor narrative window.
• Competition framing: Positions OpenAI’s reasoning models as producing novel mathematical results, not just solving existing benchmarks. Different competitive axis than SWE-Bench or Terminal-Bench.
• Feeds threads: token economics competition (capability justification for pricing premium), GPT-5.5 thread (reasoning model family demonstration).