Knot theory is a relatively “new” field of mathematics; new in that it has only begun to be explored in the past one hundred or so years.  We will examine knots from a more mathematical angle, including an accepted mathematical procedure of “untangling” a knot, if it can be so done, and determining whether two different-looking knots are actually the same.  We will then consider a way to “add two knots together,” and compare this algebraic operation to addition and multiplication of non-negative integers.  The only knowledge that is required is to know what a knot is and how to add and multiply!