I previously talked about one of my favorite authors being Lewis Carroll, who wrote about concepts like imaginary numbers and induction in his Alice in Wonderland books. I was much delighted to read FlatLand by Edwin Abbott. Like Carroll, Abbott used mathematical concepts (in Abbott’s case, multi-dimensional geometry) to make a commentary on social classes in the Victorian era. To me, this is one of the most important uses of any artistic tool.
As Henderson explains in her essay “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion,” the development of higher-dimensional geometry inspired many artists in abstract fields. One such artist is Theo van Doesburg who portrayed the fourth dimension in many of his paintings through the limited capabilities of a two-dimensional canvas. It is inspiring that artists like him are not limited by their own imagination and can interpret high-level mathematical thinking and rework it into their own set of skills and social concepts.
“Card Players,” oil painting by Theo van Doesburg, 1917
Besides art being a reflection of some mathematical concepts, art can also use math to reflect other messages. Robert Lang is a 3D origami artist who uses geometry to create animals out of paper. His detailed portrayal of natural and wildlife is a beautiful use of traditional origami.
"Vertical Pond II", 60 uncut squares of custom-made Origamido paper, 2014, by Robert Lang
It seems that mathematics is a huge part of developing realistic and complex art. Historically, they have had a complimentary relationship. So why are the arts and mathematics juxtaposed so often?
A traditional African blanket with fractal patterns
Perhaps it comes from our current education system, which pits these two disciplines against each other and. Nonetheless, art would not be where it is today without mathematical innovation, and perhaps math would not be where it is today without the innovative minds of a stereotypical “artist.” It was, after all, the dual-ly talented minds of such artists/mathematicians as Leonardo da Vinci that made huge leaps in both fields.
Abbott, Edwin. “Flatland: A Romance of Many Dimensions.” N.p., n.d. Web. 12 Oct. 2012. <https://cole.uconline.edu/content>.
"African Fractals." African Fractals. N.p., n.d. Web. 26 June 2016. <http://www.ccd.rpi.edu/Eglash/csdt/african/African_Fractals/homepage.html>
The Editors of Encyclopædia Britannica. "Theo Van Doesburg." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 26 June 2016. <http://www.britannica.com/biography/Theo-van-Doesburg>
Henderson, Linda. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” MIT Press. 17.3 (1984): 205-10. Print.
Lang, Robert J. "Artwork: Vertical Pond II." Robert J. Lang Oragami. N.p., 2014. Web. 26 June 2016. <http://www.langorigami.com/artwork/vertical-pond-ii>