Of all the concepts I learned in my undergraduate math and physics courses that I no longer have any grasp on today, Fourier series and transforms may be the biggest lacuna. I remember one of my professors explaining that Fourier was just trying to explain heat transfer and assumed his equations would work, but that it took Mathematicians decades to prove that they indeed do. I also remember that Fourier series are insanely useful; enter today's article, which is exhibit 809 in the usefulness of Fourier series. A mathematician used Fourier analysis to figure out what goes into the opening chord of "A Hard Day's Night." Since Beatles music is tightly controlled on the internet, I wasn't expecting to be able to post what the opening chord actually sounds like, since any cover wouldn't actually have it as it was played on the recording, since nobody knew what it was. There's a pretty good tautology for you. But it looks like some enterprising youtuber found a way to post a video containing the music. Enjoy.
The chord and mathematician are discussed here:
http://www.noiseaddicts.com/
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