Artificial intelligence has formally verified the prizewinning proof that solved the sphere packing problem in eight dimensions, a result closely tied to Maryna Viazovska’s Fields Medal. The ...

Circle packing encapsulates the challenge of optimally arranging a set of circles within a given container without overlap, a process that has profound implications in both theoretical mathematics and ...

What is the most space-efficient way to pack tennis balls or oranges? Mathematicians have studied this “sphere-packing” problem for centuries, but surprisingly little attention has been paid to ...