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What Is the Fourier Transform?
Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, decomposes any function into its parts.
The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure waves of many different frequencies. 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. “It’s known that if you have a whole lot of tuning forks, and you set them perfectly, they can produce Beethoven’s Ninth Symphony.” The process only fails for the most bizarre functions, like those that oscillate wildly no matter how much you zoom in on them.
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