Week 2: Math + Art

When most people think of mathematics and art, they may assume that they are at opposite ends of the spectrum when in reality, these two disciplines actually overlap. It has always been a matter of “Math versus Art” rather than “Math and Art”, however, as one explores further, they realize that art is critical to the study of math, and vice versa.

As a math major, I have certainly seen how art is implemented. One of my TAs, Joseph Breen, made highlights in our Math 32B class when he decided to produce music dedicated to calculus. Being a well-renowned TA, he was already a great resource but the songs he created somehow made learning more fun, engaging and it was easier to grasp the concepts.

Figure 1. Joseph Breen, The Vector Line Integral Song, 2020.

In ancient times, the compass and straightedge, augmented by other tools were used to develop exquisite architecture. During the Renaissance, grids became popular to portray scenes on flat surfaces. Then, after Einstein’s theory of relativity was popularized, artists began to break away from the one-point and three-dimensional perspectives, and instead depict objects as they would appear in four dimensions (Henderson). Perhaps the most prominent examples of art illuminating mathematics are the paintings of Crockett Johnson. Between 1965 and 1975, Johnson produced over 100 oil paintings, each capturing mathematical theorems and executing them through abstract art.


Figure 2. Crockett Johnson, Point Collineation in the Triangle, 1966.

Consider the painting above that was inspired by Euler and is no doubt striking as it appears to depict a diamond figure that lies within a circumscribed triangle. The piece refers to projective geometry - a branch of mathematics that deals with mappings between objects and that is heavily implemented in the computational geometry, camera calibration and stereo vision that we see today.


Figure 3. Collineation and Perspective.

Nowadays though, the advent of technology has brought with it more sophisticated tools. As was highlighted in my previous post, computers - a product of mathematics and science - can produce art. I’ve realized science is somewhat of a bridge between mathematics and art. When manufacturing a car, for example, the design is part of an artistic process, the calculations are part of mathematics, and the engineering itself combines these two elements into a finished product. I believe this is where the juxtaposition comes it as none of these disciplines can truly work independently; each of the three subjects require the others in order to be.

Works Cited

Abbott, Edwin Abbott. Flatland: A Romance of Many Dimensions. 1884.

Breen, Joseph. “The Vector Line Integral Song.” Song. Youtube, 17 May 2020, https://www.youtube.com/watch?v=ux1W3NNwJ70. Accessed 5 Apr. 2022.

"Collineation and Perspective". https://people.southwestern.edu/~futamurf/collineations-C.pdf. Accessed 5 Apr. 2022.

Field, Judith Veronica. The Invention of Infinity: Mathematics and Art in the Renaissance. Oxford University Press, 2005.

Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, pp. 205–210., https://doi.org/10.2307/1575193.

Hickman, Hope. An Investigation of the Duality Between Art and Math. 2016. The University of Akron, Honors research project. https://ideaexchange.uakron.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=1274&context=honors_research_projects.

Johnson, Crockett. Point Collineation in the Triangle. 1966, https://www.si.edu/object/painting-point-collineation-triangle-euler%3Anmah_694644. Accessed 5 Apr. 2022.

Kappraff, Jay. Connections: The Geometric Bridge between Art and Science. McGraw-Hill, 1991.

Senechal, Marjorie. “The Algebraic Escher.” https://upcommons.upc.edu/handle/2099/1134.

Vesna, Victoria. “Mathematics-pt1-ZeroPerspectiveGoldenMean.mov.” Lecture. Youtube, 9 Apr. 2012. https://www.youtube.com/watch?v=mMmq5B1LKDg.

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