The unit distance problem asks: given *n* points on a plane, how many pairs can be exactly distance 1 apart? For 80 years it was assumed that the square grid was the maximum. With 4 points: ``` A---B | | D---C ``` → 4 pairs at distance 1. OpenAI's AI proved that configurations based on algebraic number theory systematically beat any grid for large values of *n* — the improvement in the exponent is small (≥0.014) but **polynomial**, which over time makes a huge difference in the pair count. The curious part: it's not that the AI knows more math — it's that it doesn't have 80 years of wrong intuitions to overcome.