Definition
Plain language
A classic math problem about fitting as many circles as possible into a region without overlapping.
As stated in the literature
A canonical computational-geometry optimization problem (e.g., packing equal circles in a unit square), used as a benchmark for LLM-driven optimization systems like AlphaEvolve and optimize-anything.
Why it matters: It's a clean, well-studied benchmark for testing whether AI systems can match or beat decades of human mathematical optimization.
For example, an LLM-driven optimizer is asked to place 30 equal circles inside a unit square so the smallest one is as large as possible, and its solution is compared against known records.
Heard on the show
“But circle packing in a square?”Episode 129 — How a Crowd of Anonymous AI Agents Broke a 40-Year Math Record