Soh Kam Yung"The “lonely runner” problem might seem simple and inconsequential, but it crops up in many guises throughout math. It’s equivalent to questions in number theory, geometry, graph theory, and more — about when it’s possible to get a clear line of sight in a field of obstacles, or where billiard balls might move on a table, or how to organize a network."
New Strides Made on Deceptively Simple ‘Lonely Runner’ Problem | Quanta Magazine
A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem in decades.