Is mathematics an art? In this series of posts I will attempt to explore and answer this question. I encourage readers to also contribute their ideas in the comments.
The term art itself has undergone a metamorphoses over the centuries, so we should start by examining what humanity has meant by art and see if mathematics might fall under any of the definitions used over time. But beyond these definitions, we should examine whether we feel that mathematics is an art. Whether it is or not, what definition should art have in order to be consistent with the existence of mathematics? Only be examining these two angles will we gain insight into both art and mathematics, and how we as humans fit into both.
One of the earliest descriptions of art is the Platonic one, which says that art is imitation . This view is echoed by Leon Battista Alberti (1404-1472), who thought that painting should be as faithful a reproduction or imitation of the real scene being constructed. Obviously this is a very limited definition by today's standards, but nonetheless worth looking at, as the germ of creating a reproduction of a scene using any media is still alive today, at least as a motivating factor to create art.
How would the people subscribed to this viewpoint consider mathematics? Is mathematics an imitation? Much of the early mathematics, and even modern mathematics, does contain a form of imitation: that is, the kind that describes the real world. The description is a depiction, just not a visual one. Differential equations, equations describing gravity, and such theories attempt to describe the real world. Unlike many visual depictions, they describe general situations rather than specific instances. However, that is not so much a difference in my mind, either. If one were to draw a scene of a mountain or a bicycle, it might be from a specific instance, yet there is also an element of generalization that takes place in that the depiction contains simplifications that simply cannot be represented exactly on the chosen medium.
Mathematics then has an element of imitation in it. On the other hand, we must be careful to consider where the imitation lies. If the imitation lies in the axioms, then mathematics is just a set of rules to make inferences from those axioms. The axioms themselves are a verbal or written description of rules that attempt to imitate reality. Whether or not those axioms are art, they are themselves not mathematics.
I don't want to dwell too much on the imitative aspects of math because the imitative definition of art seems too restrictive to apply it to our modern understanding of art. However, there is one point to consider. That is, whether or not the axiomatic description of the world is artistic, Plato and many other early humans believed that mathematics was a set of discoveries, and hence the entire process itself of mathematics is less of a creation of art but rather a series of explorations into another realm.
So if we accept the Platonistic view of mathematics, does that not rule it out as an art? Not necessarily. One could apply the same view to painting. There are only so many arrangements of molecules of paint that we can distinguish with our eyes. That number is large but also finite, and painting could also be said to be a discovery of a representation in a space of all possible paintings using the experience we have already gained from the interaction of our senses with the real world, even if the depictions are not true to any particular scene and even deviate significantly from it. So, the philosophical point of what mathematics is, whether it be discovered, a process, or a creation, does not really place evidence for or against math being an art. It may however, influence how individuals think of mathematics with regard to art.
That is enough for now, but in the next part we will continue to explore these ideas and new ones from what we considered as art over the ages.