Have you ever wondered about the best way to pack a finite number of identical spheres into a shape-shifting flexible container, like a convex hull? An intuitively simple problem concerning the best ...

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 ...

It took over a decade of checking and rechecking before his fellow mathematicians were happy that Dr Hales’s calculations ...

In 2016, a mathematician quietly solved a problem that had remained open since the time of Isaac Newton and Johannes Kepler. Her name is Maryna Viazovska. The problem is known as the sphere packing ...

Sphere packing and crystallization involve the study of how identical particles arrange themselves in space under pairwise interactions, with sphere packing focusing on the densest arrangement of ...

Geometric packing problems involve arranging objects of given shapes within a confined region so as to maximise density, minimise wasted space or satisfy prescribed distance and balance constraints.