Situated on a hill above the ancient port city of Trieste, Italy, his office at the International School for Advanced Studies overlooks a broad bay at the northern tip of the Adriatic Sea. The rich menagerie of phenomena we see in the world’s oceans—tsunamis, whirlpools, riptides—are all solutions to Euler’s equations. Even one of the simplest and most common kinds of solutions—one that describes a steady train of gently rolling waves—is a mathematical nightmare to extract from Euler’s equations. Until about 30 years ago, the bulk of what we knew about these waves came only from a mix of real-world observations and guesswork. “Before starting math, I thought water waves were something very understood—not a problem at all,” said Paolo Ventura, a postdoctoral fellow at the Swiss Federal Institute of Technology Lausanne and Maspero’s former graduate student.