When you arrange cylindrical cans in a cabinet, you're solving a packing problem. Those pyramids of oranges you see in the produce sections of grocery stores settle an important 17th-century conjecture by the astronomer Johannes Kepler. At the start of the Covid-19 pandemic, everyone became extremely conscious of the challenges of social distancing when many people are packed into a room. Almost every packing problem is similarly simple to state and straightforward to visualize, especially compared to the abstract and abstruse concepts that populate other areas of math. But they're incredibly hard to solve ?" so much so that experts still haven't figured out how to answer some of the most obvious-seeming questions, like how best to arrange balls (albeit four-dimensional balls) in a box. This makes packing a nice entrée into Quanta's math section: The questions mathematicians ask aren't that different from the ones you might. What's New and Noteworthy