This note discusses how art can be used to motivate students to study mathematics and how artists can benefit from looking at art in a systematic way. The study of art and science together is a good way to create a thinker who is both analytic and creative.
It is often said that scientists are analytical in their thinking while artists are creative. Of course each must, to some degree, be both but it is a fact that much of science is analytic and much of art is creative.
This separation of skills means that often neither kind of individual understands what the other is doing, or what is their motivation for doing it.
But if we take a student who is not already predisposed to favour art over science or the other way around, and we teach them both subjects together, perhaps we will create a person who thinks in a new way. At the very least we may create a person who has a balanced respect for both art and science.
As an example, let me discuss how a student, already of artistic persuasion, could be convinced that it may be of benefit to study mathematics, in order better to understand their art. And for this example, let me also assume that the art we are interested in is visual art, in particular pictures.
This brings me to geometry, one of the oldest branches of mathematics. Visual artists use geometry all the time, but often only intuitively. They may learn the rules of linear perspective and the means of getting that right by construction with ruler and compass, but they are not fully appreciating the beautiful mathematics that lies beneath these constructions.
However, perspective is only the most obvious use of geometry and certainly not the simplest, so probably not the place to start if what we are trying to do is to persuade our artist to study mathematics.
More exciting, and fortunately involving simpler mathematics, is the notion of patterns that we find, for example, in wallpaper, in textiles and in many aspects of architecture such as tiling. Mathematicians have studied these ideas since ancient times and come up with elegant and surprising discoveries.
Artists, meanwhile, have generated beautiful objects based on patterns they have devised without recourse to the mathematics. These parallel developments may have evolved independently, but they can be studied together with significant benefit.
This is only one example of the potential for taking movements in art and using the corresponding developments in mathematics to understand them from a new point-of-view. If the objective is to create students who are equally at ease with art and science, why not try to get the artist to appreciate the mathematics and the scientist to appreciate how the artist has created beauty.
There is a distinction to be made in the way that creativity is exercised by artists and scientists respectively (although designers and engineers may fall somewhere in between). For an artist, creativity means freedom. Freedom to choose subject, material, style and a whole host of other parameters without constraint. A scientist is creative in another way. They are creative within a tight set of rules. They create a machine that obeys the rules of physics, or a theory that obeys the rules of the domain in which they want their theory to be valid.
These two aspects of creativity create different types of individual. Even musicians, who are artists working within rules designed to make it possible for them to reproduce (i.e. perform repeatedly) their art, have much more freedom than scientists.
Returning to our example of the artistically inclined student being shown the mathematics behind some artistic movement, our hope would be that we would then create a person who was able to be creative in both ways. To be able to apply both the mathematics and the intuition that underlies the type of object that we are analysing.
The example could equally well apply to a scientist being able to learn to appreciate the artist’s intuition and, by learning to love the middle ground, to become much more creative in their preferred domain.
So, why did I mention computers in the title? This is because they are an instrument which is equally important in both art and science. Being able to drive a computer is a significant contemporary skill that all individuals acquire, and need.
Much of what an artist does with a brush, they could do instead with a computer, although they would not be as happy with the outcome I expect. But from the point-of-view of teaching art to scientists and mathematics to artists, I can think of no better instrument.
The computer would allow the student to translate mathematics into pictures on the one hand, and to analyse existing art, capturing its description in an equation that a mathematician (and a computer) would understand. Take, for example, the patterns found in Moorish or Celtic Art.
This happy trio of disciplines Fine Art, Mathematics and Computer Science seem to me to be uniquely placed to create the renaissance person that will see a new type of progress for mankind. A convergence of thinking that will correct the divergences of the past.