I've never been great in math, although I'm learning it largely by accident in learning to program in Ruby and Crystal. Cryptography has challenged a lot of my preconceptions about myself. In my efforts, I've have a couple of realizations that might seem initially unrelated, but have a huge impact:
A two square cipher is basically a Keyed Ceasar drawn as two squares. As well, for a regular Ceasar Cipher:
If 7, then 19 if mod 26. Meaning that if one shifts a cipher seven spaces, they can keep encrypting it until they reach the original plaintext at nineteen shifts.
Specifically, this means classical ciphers like Polyalphabetic Ciphers can be split into key pairs, given a large amount of time and effort.
I'm not sure if this was intended by Julius Ceasar or not.