Fun fact. Spoiler alert, though -> the number of people for which the blog post will clarify this mysterious fact is also less than 9.8x10^42https://twitter.com/johncarlosbaez/status/1043161440545267713 …
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True! Fourier analysis is one of those pieces of math that springs to vivid life in its applications.
But even pure mathematicians should think about the Fourier transform of the characteristic function of an interval. You're not excused, you purists out there! 
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