I fucking love Fourier Fast Transforms.

I'm a biochemist, and at undergrad, the way we learned about how protein structure is determined via X-ray crystallography was basically "We crystallise the proteins like this, then we shoot some X-rays at it, and obtain a diffraction pattern, which we then do some mathememagic on, and voila! You have a 3d structure of a protein"

It frustrated me that we basically just handwaved the process of how we go from the diffraction pattern to a 3d structure (biochemists don't really need to understand the nitty gritty of how this works, tbf). It took me quite a few months to go digging deeper in my quest to independently learn how this mathememagic worked — it took so long because although questing in the tomes of chemistry helped, I then had to turn to physics books if I wanted to actually understand stuff.

So glad I did though. FFT is very cool.