What is mathematics anyway?

When I sit and try to come up with a meaning for mathematics, I find it rather difficult to define in concrete terms. After searching the internet for a definition and asking people around me, apparently they find it a difficult word to define as well. Some of what I found included things like:

 

"The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols." (Free Online Dictionary)

 

"mathematical procedures, operations, or properties." (Dictionary.com)

 

"Mathematics is a human endeavour, a discipline, and an interdisciplinary language and tool." (University of Oregon)

 

While all of these definitions have certain traits in common, they are all different from one another. I first think of it in terms of it's subject matter: addition, subtraction, multiplication, division and so on. This is what is taught to us in the school system which is why I think these are my first thoughts when exploring this topic. I believe it is a combination of all of these things, plus much more we are still unaware of.

 

 

So, what do we do with this information? What does it mean to do mathematics? Just as the definition of math spans wide across many areas, I feel that the concept of doing math does as well. As I remember from my school years in doing mathematics and from what I have seen through my observation days in both the primary and elementary grades, math most commonly done through a process of teaching a concept, doing examples and then working on questions from a text book or a worksheet. Since we cannot define math is concrete terms, why should try to constrict it's practice to something as basic as this? Doing mathematics involves all kinds of mental capacities such as numerical reasoning, spatial reasoning, linguistic reasoning as well as the ability to handle abstractions and when these are paired with a combination of creativity and a desire for success, students will see great personal growth in areas of mathematics. It is a variety of thought processes and actions all leading towards one final goal.

 

As I write this, I realize that I am thinking mathematically. I am wondering and reasoning about all this information I have found in order to come up with a definition, I feel, is sufficient and encompasses what I feel mathematics is. Doing math and thinking about math does not always need to involve numbers, it is about sorting through your thoughts and ideas in order to come up with one of many possible answers for a question, problem or even just an idea.

 

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

 

This quote by Bertrand Russell may say it best, and even though it seems to express a sentiment of uncertainty, when you really sit and think about it, it makes perfect sense.