What is Mathematics?

There does not exist a "certified" definition for mathematics. In reality, Mathematics can be defined as any number of things, which are totally dependent upon the resource from which the definition was derived.

In the article "What is Mathematics?: An Elementary Approach to Ideas and Methods" by Richard Courant and Herbert Robbins, Mathematics is defined as "an expression of the human mind reflect(ing) the active will, the contemplative reason, and the desire for aesthetic perfection." This definition, though somewhat abstract, provides a fantastic starting point for my beliefs in mathematics. 

Further defining Mathematics in relation to human beings, Reuben Hursh in his book, "What is Mathematics, Really?" explains that Mathematics "must be understood as a human activity, a social phenomena, part of human culture, historically evolved, and intelligible only in a social context." This statement, being valid in every respect, communicates that Mathematics is simply a product of the human mind, not something that was handed down from above; it is an understanding and knowledge base that is attainable by everyone.

In contrast to those above, Google defines Mathematics as:

math·e·mat·ics

maTH(ə)ˈmatiks/

noun

1. 1.
2. the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics ).

This definition is without a doubt "technical", and far less abstract than those above, but in my opinion is still correct. Google defines Mathematics as what we, as human beings, have constructed Mathematics to be, in addition to how use these constructs. I am especially drawn to this definition for I feel it is simple yet concise.

If we were to merge these definitions, I believe one would have a relatively good understanding of what exactly Mathematics is. Unbeknownst to me, I discovered that the Newfoundland and Labrador curriculum has adopted quite an eclectic view of Mathematics. In the curriculum framework, Mathematics is defined as being " one way of trying to understand, interpret and describe our world." It continues to state that, "there are a number of components that define the nature of mathematics ...[including] change, constancy, number sense, patterns, relationships, spatial sense and uncertainty." Most notably, the document concludes to state that, "students learn by attaching meaning to what they do, and they need to construct their own meaning of mathematics."

So what is Mathematics? As stated in the curriculum guide, Mathematics is defined by an individual as what they should have constructed it to be! I have an eclectic understanding of Mathematics, and believe that Mathematics is comprised of several distinct elements that have been constructed by the human mind. Similar to Hursh, I believe that Mathematics is very much a "social phenomena" that will continue to evolve and change in the future!