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
“On circle packing and an autocorrelation task, it matches or exceeds every baseline.”Episode 046 — When the AI Optimizer Edits the Grade Book: Why Harnessing Evolution Needs a Wall