Without a dedicated toolchain, OpenAI's performance this time is a perfect score in a bare-bones test.

According to Beating monitoring data, OpenAI's general reasoning model has achieved a breakthrough in Erdős' plane unit distance conjecture for the first time.
By constructing new point sets, the model has increased the number of unit distance pairs to n^{1+δ}, breaking nearly 80 years of upper bound expectations.
The model did not use specialized toolchains but instead introduced interdisciplinary deep tools from algebraic number theory into Euclidean plane geometry.
External scholars issued statements pointing out that the derivation involves ideas from Ellenberg–Venkatesh, Golod–Shafarevich, and others.
This achievement is regarded as a milestone in AI mathematics, demonstrating that a general model can propose original ideas and advance proofs without dedicated tools.