Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal. Introduction Two centuries ago, Joseph Fourier gave mathematicians a magical technique. He conjectured that it’s possible to write almost any function as a sum of simple waves, a trick now called the Fourier transform. These days, the Fourier transform is used to understand everything from the chem...