Shalma Wegsman in Quanta:
In the early 1800s, the French mathematician Jean-Baptiste Joseph Fourier discovered a way to take any function and decompose it into a set of fundamental waves, or frequencies. Add these constituent frequencies back together, and you’ll get your original function. The technique, today called the Fourier transform, allowed the mathematician — previously an ardent proponent of the French revolution — to spur a mathematical revolution as well.
Out of the Fourier transform grew an entire field of mathematics, called harmonic analysis, which studies the components of functions. Soon enough, mathematicians began to discover deep connections between harmonic analysis and other areas of math and physics, from number theory to differential equations to quantum mechanics. You can also find the Fourier transform at work in your computer, allowing you to compress files, enhance audio signals and more.
“It’s hard to overestimate the influence of Fourier analysis in math,” said Leslie Greengard(opens a new tab) of New York University and the Flatiron Institute.
More here.
Enjoying the content on 3QD? Help keep us going by donating now.