What does Gauß have to do with the nuclear arms race?

Veritasium: How An Algorithm Could Have Stopped The Nuclear Arms Race. (YouTube, 26:32min)

“The Fast Fourier Transform is used everywhere but it has a fascinating origin story that could have ended the nuclear arms race. […]
Thanks to Grant Sanderson of 3Blue1Brown for his helpful feedback on the script. His great video on the Fourier Transform is here”

3Blue1Brown: But what is the Fourier Transform? A visual introduction. (YouTube, 21min)

It blew my mind that Carl Friedrich Gauß found the discrete Fourier transform – 150 years earlier that Fourier.