How do you best arrange oranges in a box to make the most of the available space? It's a problem that already exercised Johannes Kepler back in the 17th century, and that wasn't fully solved until 1998. In 2016 the mathematician Maryna Viazovska made a further breakthrough in the theory of sphere packings. She explained her results at the Royal Society's celebration of the legendary mathematician Srinivasa Ramanujan, who was elected a fellow of the Society 100 years ago. During a coffee break she gave us a condensed description of sphere packing problems and her work.

You can also read an article based on our interview with Viazovska – https://plus.maths.org/content/packing-spheres