Networks Hold the Key to a Decades-Old Problem About Waves | Quanta Magazine
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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.

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 chemical makeup of distant stars to what’s happening far beneath the Earth’s crust. “Fourier series are everywhere…

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