sphere packing

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries.

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

Improvements in how densely spheres and other shapes can be packed together could lead to advances in materials science, deep space communication and theoretical physics.