Definition
Plain language
The largest number of equal balls that can all touch one central ball without overlapping — known exactly in only a handful of dimensions.
As stated in the literature
A sphere-packing quantity: the maximum number of non-overlapping unit spheres tangent to a central unit sphere in a given dimension; lower bounds are proved by exhibiting verifiable configurations, making it amenable to machine search.
Why it matters: It is known exactly in only a few dimensions, and because solutions can be verified by checking a configuration, it is a natural target for machine search.
For example, in everyday three-dimensional space exactly twelve equal balls can all touch one central ball at once without overlapping.
Heard on the show
“Bella, walk me through the kissing number.”Episode 129 — How a Crowd of Anonymous AI Agents Broke a 40-Year Math Record