There are quite a few branches of mathematics. One that has caught my interest on more than one occasion is game theory. Game theory tries to understand how and why people react in certain circumstances. It's about strategic thinking. It's about games we play every day.
Why do we decide to do what we do? How do we judge what is the best course of action? It sounds a bit vague and hard to capture in equations but it is a branch of mathematics.
A Chronology Game Theory has been put together by Paul Walker. It starts with game theory in the Talmud and moves on from there. Mainly it's a collected bibliography but it gives a quick overview of the subjects covered by game theory.
A more detailed work is Roger McCain's Strategy and Conflict: An Introductory Sketch of Game Theory. This started as a work from which to teach an undergraduate course in game theory and eventually ended up rewritten as a complete book. Even before the rewrite it stands as a good guide to the ideas and principles of game theory.
Pretty soon you'll be up to speed on the Prisoner's Dilemma and Tit-for-Tat. At which point you'll either be a better strategist in the areas where game theory is helpful or you'll be even more confused than before. I'm not responsible for what happens.