But Why?

One of the most common questions in introductory mathematics courses "why?":  Many things are taught with seemingly little motivation for their definitions, and this leads to some of the most common misconceptions about the field.  From the outside, mathematics often appears to be a collection of abstract symbols, manipulated without regard to anything except a precise and abstract logical framework.  It is often not until one has learned "enough" mathematics that one begins to glimpse the beauty behind the symbols, the abstract world which we have created out of pure thought and brought to life out of our inalienable curiosity.

Mathematics is not a collection of symbols any more than poetry a collection of letters; the mathematics lies in the meaning of the symbols, in their interpretation. I am not going to try here to argue for the beauty of mathematics, but rather I will simply try to present a few useful things I have come to notice along my journey, with the hope that it will help all the symbols not appear so arcane.  I hope that through being able to put a mental picture to the symbols; you will be able to find a bit of the beauty yourself.  I will try and not assume too much knowledge of mathematics as to increase the usefulness of these posts, but some topics by nature may require more knowledge than others.