What IS Mathematics anyway?

According to Wikipedia, “mathematics is 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 )”. Aristotle believed that mathematics is defined as “the science of quantity”.

Throughout my research for finding a definition that I believe to be true of “mathematics”, I finally found one that was from a woman named Elaine J. Horn on the following site http://www.livescience.com/38936-mathematics.html. She states that “mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports”.

For me, mathematics can be performed in many different ways and at a very early age. Children can be exposed to mathematics before they even reach kindergarten which may be as simple as counting and being familiar or pronouncing their age. As a child enters into primary/elementary school, mathematics becomes more challenging and will introduce the children to many different ways of “doing” that subject area. To be more specific, in kindergarten mathematics may include identifying shapes and patterns, grade one would focus on adding and subtracting, grade two may begin place value, and even/odd numbers, and in grade three children may perform multiplication facts or line graphs. These are just a few examples of how children in primary would “do” mathematics. It is evident, that at every stage of a child’s life there are new and different ways of performing math. On a different note, mathematics can be done other ways that doesn’t always consist in school. Imagine how many times a day we are “thinking mathematically” and don’t even realize it? I personally encounter math at least three or four times a day which may include telling the time on a clock or counting the money I have in my wallet. According to Reuben Hersh who is the author of the book “What is Mathematics, Really?”, there are two different sides to thinking mathematically. He believes that math has a front and back. The front consists of formal, precise, abstract thinking and can be broken down into definitions, theorems and remarks. Each question from the front of mathematics is either answered or labelled an “open question”. At the back, mathematics is informal, tentative, and intuitive which often leads us to trying this or that to solve the problem/answering a question. His view on what “thinking mathematically” is quite interesting!