My favorite physics crank was the guy who convinced himself that curves don’t exist; they’re merely lots of line segments pasted together. He proceeded to derive a whole lot of remarkable nonsense about astrodynamics, and maybe relativity? It’s been a while.

Maybe ironically, the idea that curves don't exist hasn't gone away, it's still a serious idea: spacetime could be discrete, in which case curves really are a series of discrete line segments. Loop quantum gravity is one such theory, and I would hardly say it's crackpot physics.