If science is defined by the English language as “a discipline devoted to the description of nature and its laws”, then mathematics does not fit into this definition. It is more accurately described as a study of patterns and relationships. It is a way of thinking. It is an art. It is characterized by universal consistency and employs the use of concise symbols and terms; therefore it can be used as a language. When its logical components are utilized, it is also an extremely powerful tool that can help to draw assumptions from a set of data. For all of these reasons, mathematics is in an area of its own.
If “science begins with the world we live in, accepting its data and trying to explain its laws”, then mathematics can be one of the conclusions that you arrive at. When science attempts to “[construct] a model of a possible way or interpreting experience”, it is delving into the areas of mathematics, literature, and music. Northrop Frye labels these as “languages of the imagination” for many reasons. Mathematics can be used to explain science. It can create models for the patterns that we observe in experiments, and therefore, can be seen as being in a class of its own.
On the other hand however, one can also see mathematics as a science. If applied mathematics, or arithmetic, is used to model and solve real world problems, then theoretical or pure mathematics can be used to model and solve problems in imaginary worlds. It is a study of what might or could occur. In this way, mathematics can also be seen not only as a hypothetical science, but a fundamental one as well. What makes one discipline more fundamental than another? Paul Dirac, a renowned physicist stated that physics is more fundamental than chemistry and therefore can be used to explain it. He also said that if the laws of one science are based on the laws of a second science, than the second science can be seen as more fundamental. As well, if the laws of a science are more general than the laws of another, than it is also seen as more fundamental.
Using these rules, mathematics can be defined as being the most fundamental science of all. All other sciences use it and build upon it, and it has to the ability to be both very general and very specific. The science of mathematics can be used as a language to describe and explain other sciences. On the other hand, it is impossible to explain or describe mathematics using other sciences.
In this way, literature and music are also languages of the imagination. They all have an element of the imagination in them, something that is the creation of the mind. Just as music can conjure up feelings and emotions, literature and mathematics can as well. In his book A Mathematician’s Apology, G.H Hardy says “Beauty is the first test: there is no place in this world for ugly mathematics”, just as ugly music or literature is useless as well. All three of these disciplines are fundamental and essential in order to describe and explain all other disciplines. For example, try explaining quantum-mechanics without the use of literature or language. Or try watching the world’s best ballet dancers perform “Swan Lake”…without Tchaikovsky’s music score. Or try explaining chemical equilibrium without math. It is impossible.
All in all, regardless of whether we decide if pure mathematics is a science or not, or if it is more fundamental than others, it is ultimately irrelevant to the real world. Its language is comprehended by the few who dwell in the imaginary world of pure math, and its beauty admired by those who can actually see it. For the common layperson, the area of pure mathematics can never be fully understood. In fact, most people do not even know it exists. Most of us, including myself, are happy with the arithmetic that we learn in school and are content to leave the world of mathematics to the mathematicians out there.
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Northrop Frye; The Educated Imagination
