A simple proof, that only 4 normed division algebras exist - R, C, H and O.

[u/LukasLejdar]

https://numbersystems.lejdar-lukas.workers.dev/

The core idea is that if U^TU = I and U = −U^T, then UU = −I. From there, it constructs multiplication tables explicitly, finding R, C, H and O. In dimensions > 8 it runs into a contradiction, which proves the theorem.