Week 2 | Math & Art

This week, I learned how mathematics serves as a bridge between art and science, shaping how we perceive and represent the world. One key insight came from Linda Henderson’s article, which explored how early 20th-century artists like Marcel Duchamp were inspired by the idea of the fourth dimension and non-Euclidean geometry. It was interesting to see how these concepts helped artists break from traditional, linear perspectives and create abstract, multidimensional works​. Edwin Abbott’s Flatland’s use of a two-dimensional world to explore the limitations of perception helped me grasp how higher dimensions, especially the fourth, can work to challenge our assumptions and expand how we understand our reality. The lecture video also demonstrated how patterns like the golden ratio and fractals appear both in nature and human-made creations. It showed how artists use math to understand beauty, structure, and form.

Under the Wave off Kanagawa, Katsushika Hokusai, underlaid with the golden rule

One piece of artwork I had the pleasure of seeing in person and enjoy is Pablo Picasso’s Guernica. It's a powerful example of how mathematics can be used to express deep emotion and critique through art. The painting depicts the horrors of the bombing of the town Guernica during the Spanish Civil War, using fragmented, angular forms to portray chaos, pain, and destruction. Picasso drew on the geometric principles of Cubism, to break the subjects into abstract shapes and forms, which allowed him to convey multiple perspectives at once.

Guernica, Pablo Picasso

Scale of Guernica

This mathematical approach to visual structure allows Guernica to go beyond realism. The disjointed bodies and overlapping figures, which seem to exist in a warped, multi-perspective space, reflect concepts similar to those discussed in Henderson’s article on the fourth dimension​

. Just as early 20th-century artists used non-Euclidean geometry to challenge traditional perspective, Picasso used fractured space and shifting angles to immerse the viewer in a moment of trauma that feels timeless and inescapable.

Seeing how Picasso integrated geometry into a deeply emotional and political piece helped me better understand the influence of mathematics in both art and science. In this case, math doesn’t just shape the structure of the piece it amplifies its meaning as well.

M.C. Escher's Relativity, mathematics as a creative tool

This week taught me that both artists and scientists rely on mathematics as a creative tool. Artists use geometric forms, symmetry, and ratios to guide composition, while scientists use those same principles to model physical systems. Math is not just about numbers, it’s rather a language that expresses patterns, relationships, and possibilities across disciplines.

We see that mathematics, art, and science may seem separate, but they often overlap in surprising ways. They each seek to uncover truths but when combined, they offer a fuller, more imaginative view of reality. This week showed me that the boundaries between them are more fluid than I thought and that’s where some of the most exciting ideas can emerge.

Refrences:

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

Frantz, Marc. “Lesson 3: Vanishing Points and Looking at Art.” CS@UCF, University of Central Florida, https://www.cs.ucf.edu/courses/cap6938-02/refs/VanishingPoints.pdf. 

Gessler, Nicholas. "Where the Wild Things Are." The Institute For Figuring, https://www.theiff.org/publications/cab21-gessler.html. 

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

Lesser, Casey. “What Makes Guernica Picasso’s Most Influential Painting.” Artsy, 12 June 2017, https://www.artsy.net/article/artsy-editorial-guernica-picassos-influential-painting. 

Math in Art and Science. YouTube, uploaded by UC Online, 5 Dec. 2016,https://www.youtube.com/watch?v=mMmq5B1LKDg  

Image 1: https://www.artandobject.com/slideshows/golden-ratio-revealed-7-masterpieces 

Image 2,3:https://www.artsy.net/article/artsy-editorial-guernica-picassos-influential-painting 

Image 4: https://moa.byu.edu/m-c-eschers-relativity/