It might shock you but art and mathematics go back a long way! They have had a lengthy yet underrated historical relationship since the 5th century BC, when the Greek sculptor Polykleitos wrote his Canon, establishing proportions based on the ratio 1:√2 for the ideal male nude. In addition, Luca Pacioli wrote the influential discourse De Divina Proportione on the use of the golden ratio in art. In modern times, the graphic artist M. C. Escher has also made comprehensive use of tessellation and geometry. So, it is not surprising when many artists claim that mathematics is an art just motivated by beauty and logic. In fact, artists have been manipulating art for many millennia to use it as their base work and thus one can assume that mathematics not only inspires art but also helps artists to be accurate, precise and logical.
As established earlier, mathematics produces art. On the practical level, mathematical apparatuses, such as compasses, set squares, protractors etc., have always been used to set the base work in the creation of art. This was taken a step further by Albrecht Durer, who used these tools and simple grids to meticulously depict scenes on flat, two-dimensional surfaces, in line with the laws of linear perspective.
The synergy of art and mathematics during these times as linear perspective and projective geometry were evolving is one of the most outstanding examples of art and mathematics progressing in new directions. One can conclude that without the accuracy of mathematical ratios and relationships, compasses, rulers, and grids would be useless and artworks would lose their precision and accuracy. As a result, a lesser impact would be made on the viewer. So, essentially, art needs mathematics as much as mathematics needs art.
Mathematics generates art as well. This is reflected in one of the most rudimentary concepts of art – patterns. By simply coloring an algorithm, one can produce intricate designs that may be pleasing as handmade drawings. The Mandelbrot set to act as beautiful paragons of this: each pattern is produced by the equation, Zn = (Zn -1)^2 + C. The images produced are not only symmetrical but intrinsic. Moreover, the interminable longevity of the designs makes them and aesthetically gratifying. Correspondingly, this process helps algorithms to take on a visual identity and makes it easier to distinguish them. As a result, these artistic representations help to illuminate mathematical concepts which would have otherwise been hidden in forlorn math textbooks. Thus, one can conclude that as mathematics generates art, art also helps to illuminate and demystify mathematics.
It is often said that while mathematics is logical and precise, art is spontaneous and more liberal. This may be true for some topics of art, but for the most part, art also has to follow certain ratios, theorems, and principles. If artists wager to ignore these mathematical theorems, they will only realize that it is, indeed, impossible. There are many theorems governing proportions. These include Euler’s theorem and Descartes’ theorem state the geometry of polyhedra. Other theorems control certain aspects of symmetry and facts of ratio, proportion, similarity, and so on. I feel mathematics does not confine art or require art to follow these narrow set of rules. Instead, artists can understand essential mathematical principles which will not only allow them to use their innate knowledge and creativity but even to test and push the limits of these so-called restrictions. It is not necessary for constraints to be a burden. In fact, these constraints often depict the limitless possibilities.
I had the opportunity of experimenting with art and mathematics in my Art and Design class. I did follow simple rules of symmetry, balance, and patterns in almost all of the works. While studying forms, structures and different points of perspective, I noticed that sometimes mathematically-produced art could be too accurate or too monotonous to hold the viewer’s attention. So I often used it as my base work; it acted as a template to which I brought my imagination and personal vision. This allowed me to transform my work so that it was mathematically logical but also creative and artistically inclined.