Most of the world is uncertain — and probability and statistics is the mathematics that reasons carefully about that uncertainty anyway. Probability runs the machine forwards ("given the rules, what is likely to happen?"); statistics runs it backwards ("given what happened, what were the rules?"). Between them they underpin science, medicine, finance, and every algorithm that learns from data.

The area to explore

Dive into statistics — from describing data and the laws of probability through distributions, the central limit theorem, estimation, hypothesis testing and regression, all the way to the rigorous mathematical statistics of a full degree. (The measure-theoretic foundations of probability live next door in measure theory.)