The simplest cipher is just a permutation of the alphabet, which can be easily broken from a (long enough) encrypted piece of text using frequency analysis. Now suppose that I encrypt my text such that each subsequent letter is encrypted using a different permutation, out a list of 10^16 unique permutations. Further suppose that you do not have a computer!
In this talk, we'll speedrun through the math of 20th century cryptography, starting with how Marian Rejewski broke the German enigma in 1933 using simple combinatorics, until 50 years later when Shor came up with his algorithm for breaking the internet.