Mathematics, with Imagination – a course proposal

Since this summer I have been secretly working on pitching a course, in fact, something that has been growing in my mind throughout my time in mathematics. This is a course that presents mathematics, especially geometry and topology, as artistic inspiration rather than a practical tool. I finally decided to write about it in this post. I would be more than happy to hear your response and suggestions on both the course itself and its topic selections!

The current state of this is that I have finally found the perfect home for the course: The Art Center in Pasadena. After a few month of poking around I made it into the administration and attracted quite some interest from various people. Two days ago I was asked to speak about curvature for half an hour in the faculty meeting. So I might start teaching there this spring and will find out soon~ Wish me luck!


`The best mathematics uses the whole mind, embraces human sensibility, and is not at all limited to the small portion of our brains that calculates and manipulates symbols. Through pursuing beauty we find truth, and where we find truth we discover incredible beauty.’ — William Thurston

Much like art, mathematics is all about idealizing and simplifying the real world. I have always believed that, when exposed to the right set of topics, artists in all disciplines can get inspiration from mathematics. The objective of this course is to present a set of visually interesting topics from a wide range of advanced mathematics in a fashion that would be appealing to artistically creative minds.


The first half of the semester will consist of lectures on one topic per week, the topics are typically at advanced undergraduate to graduate level, but presented in a way that’s tailored especially for artists (i.e. lots of imagination required, absolutely no numbers and formulas). Some rigorous proofs will be presented followed by discussions. Every week there will be some interesting homework problems related to the topic in order to solidify student’s understanding, as well as some more creative homework that helps generating ideas for art inspired by the topic. Starting from week 7 we will develop a final project in which students can pick one of the thumbnail ideas from the pervious weeks and develop it into a project. I will present some inspirational projects (such as hyperbolic geometry inspired fashion design, 3D printings, fine art sculptures, digital fractal art, screen prints and film/animation projects).

In the eighth week we will talk about individual projects, make sure they are scientifically sound and meaningful as well as resolving practical difficulties. The remaining part of the semester will consist of lecture and discussion sessions on some more abstract topics which would serve as exposition rather than demanding precise understanding, no problem sets will be given on those. We will touch base on the progress of projects at the end of each class. Many potential in-class activities could be included, for example one could spend a class having students collaborate on building a human sized four-dimensional polytope out of the geometric construction tool `Zome’, or play teamwork games on knots and links. The last class will be a presentation and review of projects.

Weekly plan

Week 1: Surfaces from an ant’s perspective

Week 2: From peeling orange to metric structures

Week 3: Knots and links

Week 4: Fractals, natural and man-made

Week 5: Geometry of paper folding

Week 6: Pathological spaces

Week 7: Inspirations for final project

Week 8: Project planning

Week 9: Cubes and polytopes, in all dimensions

Week 10: Collaborative Zome tool construction

Week 11: Shapes of Universes

Week 12: Real estate in hyperbolic space

Week 13: Infinity and beyond

Week 14: Project presentation and discussion


This course will develop student’s skills in imagining abstract spaces and visual problem-solving as well as giving them a brief tour into the fascinating world of contemporary mathematics. The final project would ideally serve as a demonstration of student’s ability to integrate sophisticated scientific ideas into a piece of beautiful artwork which we will submit to the annual Joint Mathematics Meeting art exhibit, and the International Bridges Conference which links mathematics with Music, Art, Architecture and Culture. A successful project would make an excellent portfolio piece.

5 thoughts on “Mathematics, with Imagination – a course proposal

  1. Definitely you should do it! But instead of in a university where only the special people can see it, you should do some very short Youtube videos or interactive toys.

    BTW, I believe Thurston did do such a course in Minneapolis (and posted it online).

    As far as critical feedback:
    – I think the “ant” metaphor is worn out
    – There are too many topics
    – More applications to real life make it more interesting for students.

    Also the more they can draw (crayons for example — )

    or draw on a computer (

    In general think mathematicians remove themselves from the story, whereas an English teacher will be more personal. We know which subject is more popular; I think a personal touch of why it moves you, why you find it interesting, and even more reaching out to whoever is participating and how they came to like it.


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