OpenAI Model Overturns 80-Year-Old Erdős Conjecture, Achieving n^(1+δ) Unit Distance Pairs

According to Beating, OpenAI's general reasoning model has overturned the unit distance conjecture proposed by Erdős in 1946. The classical conjecture held that the number of point pairs at unit distance on a plane would not significantly exceed n^(1+o(1)); however, the model's new point set construction achieves n^(1+δ) pairs, where δ is a positive constant, breaking the upper bound maintained for nearly 80 years.

The model completed this proof without specialized mathematics systems or customized tools. External mathematicians including Noga Alon, Tim Gowers, and Arul Shankar verified the original proof and published a supporting paper on arXiv, confirming the derivation employs advanced techniques from algebraic number theory.