Monumental Proof Settles Geometric Langlands Conjecture | Quanta Magazine
In classical signal processing, sound waves get built up out of sine waves whose frequencies correspond to the pitches contained in the sound. It’s not enough to know which pitches the sound contains — you must also know how loud each pitch is. That information allows you to write your sound as a combination of sine waves: just start with the sine waves of amplitude 1, then multiply each sine wave by an appropriate loudness factor before adding the sine waves together. The sum of all the differe...
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