New Shapes Solve Infinite Pool-Table Problem

Strike a billiard ball on a frictionless table with no pockets so that it never stops bouncing off the table walls. If you returned years later, what would you find? Would the ball have settled into some repeating orbit, like a planet circling the sun, or would it be continually tracing new paths in a ceaseless exploration of its felt-covered plane?

These kinds of questions occurred to mathematical minds centuries ago, in relation to the long-term trajectories of real objects in outer space, and for nearly that long they’ve seemed impossible to determine exactly. What will a bouncing ball be up to a billion years from now? It’s as hard to answer as it sounds.

More recently, though, mathematicians, among them former Members Alex Eskin, Curtis T. McMullen, Maryam Mirzakhani, Amir Mohammadi, and Alexander Murray Wright, have achieved a succession of stunning breakthroughs.