Sphere packing

The sunlight-collecting organelles known as chloroplasts solve a packing problem: how to optimize photosynthesis without sustaining damage from dangerously intense rays.

After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.

A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

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.