Chapter 1  The Language of Mathematics
Table of Contents Section 1.1  Definitions Section 1.2  Axioms, Theorems, and Proofs Section 1.3  Inverses Section 1.4  Simplifying Section 1.5  Theory versus Application 

The historical development of mathematics is a subject that one could spend years investigating. Contrary to what the general public may believe, the subject was not formed in the order with which we learn it in the classroom. In fact, the chronological progression of our understanding of mathematics is full of awkward leaps in knowledge. Some extremely advanced mathematical concepts came about long before some very simple ones. The reason for this erratic progress is that mathematics has historically been driven by application and necessity rather than philosophy. It is this ebb and flow of mathematical concepts throughout time that makes learning mathematics in "chronological order" (based upon when a concept was discovered) unwieldy.

Historical Note 
The conceptual development of mathematics is how we are going to approach learning mathematics. We will develop the subject at a pace and in such a way that concepts will naturally lead to the next set of consequences. Upon this framework we will place the usefulness of our concepts. That is, we will apply our knowledge to realworld problems.
We will not focus on memorizing large numbers of theorems and definitions\(^1\) nor will we allow ourselves to become intimidated by what many believe to be a cold and lifeless subject. Instead, we will concentrate on understanding why mathematics works the way it does and how we can use this knowledge to open ourselves to a better, more robust understanding of the world we live in. It is my hope that MathemAddicts.com enhances your world view and enables you to apply critical thinking and analysis to a plethora of facets in your life.
With all that said, let us put on our thinking caps and prepare to become philosophers. We are going to figure out what makes mathematics so beautiful and true. This exercise will require brain power and creativity.
We will not focus on memorizing large numbers of theorems and definitions\(^1\) nor will we allow ourselves to become intimidated by what many believe to be a cold and lifeless subject. Instead, we will concentrate on understanding why mathematics works the way it does and how we can use this knowledge to open ourselves to a better, more robust understanding of the world we live in. It is my hope that MathemAddicts.com enhances your world view and enables you to apply critical thinking and analysis to a plethora of facets in your life.
With all that said, let us put on our thinking caps and prepare to become philosophers. We are going to figure out what makes mathematics so beautiful and true. This exercise will require brain power and creativity.
\(^1\) We will talk about what theorems and definitions are momentarily.

