Fourier transform (any kind of transform, really) is at the same time so simple and so mind-boggling. The math to produce it just fits together super neatly: ap

Fourier transform (any kind of transform, really) is at the same time so simple and so mind-boggling. The math to produce it just fits together super neatly: applying algebra principles (basis change, dot products, etc.) to functions, and seeing that it works really is a stunning achievement of mathematics. I sometimes wonder if analysis could have been discovered the other way around, that functions could have first been described as a sum of harmonics, and that we would have stumbled upon "time-defined" functions as the inverse fourier of harmonics. If you don't know about the FT, you should really dig into it. It's way simpler that number theory, cryptography or complexity theory, yet it is incredibly useful and frankly beautiful.