What is Mathematics Anyway?

Hi again!

When I first read the topic or guiding question for this week's blog, I was immediately intrigued as I had never before considered the complexity of this question nor had I put much thought into it. Considering the fact that mathematics is a core subject of the K-12 curriculum and the fact that I have been engaged in some form of mathematics on a daily basis since kindergarten, both in and outside of the school setting, I find it surprising to think that I had never before considered this question. So what is mathematics anyway?

Google search engine defines mathematics as "the abstract science of number, quantity, and space." According to Google's definition, 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)." When I asked Siri on my iPhone, "what is mathematics?," I was linked to Wikipedia's definition of mathematics: "mathematics is the abstract study of topics such as quantity, structure, space, and change." With two of these brief and specific definitions in mind, I was not satisfied so decided to continue researching and investigating this question.

What is Math About?

In Masao Morita's "What is Math About?" TEDx video, founded on YouTube, Morita describes math as not about numbers, not about calculations, but about logic. According to Morita, "it's the very act of looking inside your mind and encountering with your own self, encountering with your own rich inner universe, your jojo." So what does it mean to do mathematics? To do mathematics, as discussed in this video, one must encounter his or her own mind. It involves both patience and attention.

Throughout my research, I was faced with many deeper thoughts with regards to the subject of mathematics and its definition. I soon found myself, like many math fanatics, pondering the mind-boggling question: is mathematics invented or discovered? Can mathematics be discovered or is it simply invented by the minds of great mathematicians? Upon further research of this question, I came across several distinct theories, each expanding on the debate of mathematics as a human discovery or as a human invention. According to research, favors of the Platonic theory argue that math is a discoverable system that underlies the structure of the universe. In other words, the universe is made of math and the more we understand this vast interplay of numbers, the more we can understand nature itself. Greek philosopher Plato believed that mathematics exists independent of humans and will continue on long after we are extinct. Several other theories support the opposing argument - that math is a man-made tool and just so happens to correspond with the universe. For instance, the logistic theory holds that mathematics is an extension of human reasoning and logic. Similarly, the formalist theory argues that mathematics boils down to the manipulation of man-made symbols. According to research, mathematics has even been linked to fairy tales as in the fictionalist theory.

I feel that a person's defining or viewing of mathematics highly depends on that person's experiences with mathematics and recognition of its existence. I believe that mathematics is all around us. Its existence is unavoidable. It exists within our daily lives in many forms and ways. Like Morita, I believe that mathematics is much more than just numbers and calculations. Everyday there is a new theory, a new idea, a new concept is being created. A world without math is unimaginable.

Natalie