Number Theory & Modular Arithmetic
More often than not, the first mathematical object we are exposed to is Integers. Integers are whole numbers, things like 1, 2, 3. These are simple, and relatively profound in their ability to represent quantities and otherwise unrelated topics. In fact, we have studied integers, known as Number Theory, for thousands of years with no real discernable purpose — until recently. That is to say, not all science comes with some clear endgoal, but it is the search in of itself that provides us with dividends. Number Theory is one such case — where we have built out a system that allows us to encrypt large amounts of data using nothing more than prime factorization for exceptionally large numbers — something that up until today, was almost entirely pointless. ...