There are some people out there who are just fantastic at writing about mathematics. Mark Chu-Caroll of Good Math Bad Math is one of those people. While I imagine most people who will read this already regularly read his blog, if you do not, or if you just happened to miss this post, you have to read Chu-Caroll’s post about “What is Math“:
To me, math is the study of how to create, manipulate, and understand abstract structures. I’ll pick that apart a bit more to make it more comprehensible, but to me, abstract structures are the heart of it. Math can work with numbers: the various different sets of numbers are examples of one of the kinds of abstract structures that we can work with. But math is so much more than just numbers. It’s numbers, and sets, and categories, and topologies, and graphs, and much, much more.
What math does is give us a set of tools for describing virtually anything with structure to it. It does it through a process of abstraction. Abstraction is a way of taking something complicated, focusing in on one or two aspects of it, and eliminating everything else, so that we can really understand what those one or two things really mean.
Math is unavoidable. It’s a deeply fundamental thing. Without math, there would be no science, no music, no art. Math is part of all of those things. If it’s got structure, then there’s an aspect of it that’s mathematical.(Read the rest)