So... What is Math?

I asked Google the above question and it said, "the abstract science of number, quantity, and space. Mathematics may be studied in its own right (pure), or as it is applied to other disciplines such as physics and engineering (applied)". Oook. Seems fairly straightforward, and not far from how I would define mathematics myself. The term "abstract" throws me off a bit, so I do some more research.

Now I stumble upon Bertrand Russell's definition of mathematics: "the subject in which we never know what we are talking about, nor whether what we are saying is true". Then this quote from Charles Darwin: "a mathematician is a blind man in a dark room looking for a black cat which isn't there". 

We only discussed this briefly in Tuesday's class, but we touched on the idea that our base ten number system didn't just appear out of thin air. Humans invented the terms and parameters surrounding mathematics, and if these terms and parameters didn't exist, mathematics as we know it would not exist. 

In my opinion, another vital aspect of mathematics doesn't involve numbers or symbols in a necessarily concrete way, and that aspect is problem solving. Problem solving is beyond math, it's an imperative life skill that we tend to teach and learn through mathematics, but genuinely applies to every school subject and beyond that, every experience in life. 

The mathematics that I experienced in school operated on a simpler definition, and none of the above concepts ever came into play. It was just solving problems with numbers. In elementary school there was usually a purpose for the math we were performing (such as counting money), but in high school math was seemingly performed for the sake of being performed. I remember sitting in my level three "advanced" math class and whispering to my friend, "what in the world is sine, or cosine? what does it represent? why do we use it?". These answers were not provided. We were just expected to know how to solve the equations.

Math is more than just numbers and problems, and it sure makes life easier. We have discussed in class that math always has an absolute answer, and there isn't exactly room for debate unlike in almost every other subject. However, variation can exist in the methods used to obtain the answer, and this is key. Solving math problems teaches logic and reasoning, which can be applied outside of mathematics.