Mathematics

Why do I care

To me, mathematics is interesting for two primary reasons. Firstly, it is necessarily true. 2+2 could never equal 5. Different axioms can be chosen, but there is always an underlying and true-in-all-worlds system. Secondly, is is emergent. From simple axioms, extremely complex truths derive, and, for the most part (see Gödel's incompleteness theorems for more information), these truths can be proven from these axioms. My favorite example of this is the Classification of Simple Finite Groups Theorem. From these axioms which describe a group, as well as definitions describing the structures that arise from these axioms, it can be proven (in a 1500 page long proof!) that all finite simple groups are either a cyclic group of prime order, an alternating group of degree less than 5, a Lie group, or on of 27 "sporadic groups" (including the infamous monster group). Like a particularly hazardous swimming pool, it gets very deep very fast.