Neat. I wrote a tool that shows interactive examples of how you can actually do the calculations for multiplications with Fourier transforms:

https://blog.robertelder.org/fast-multiplication-using-fouri...

The trick is really just about realizing that you can re-write a number like 1234 as a polynomial like 1 * 10^3 + 2 * 10^2 + 3 * 10^1 + 4 * 10^0.