The challenge: Define math art for yourself, capture an example of it in a picture (or a series of pictures), and share with #MathPhoto20 and #mathartchallenge.
This week #MathPhoto20 and its organizers, Carl Oliver and Erick Lee, are also going to be engaging with the #mathartchallenge by creating some math art challenges and posting those with the same hashtags. Our hope is to spark a discussion about math art, photography, and where and how we see math in the world.
The context: Math art is a poorly defined term. Definitions can be challenging, but clear, precise definitions help us communicate better. I’ve occasionally found heated disagreements quickly resolve once its noticed folk involved are using different definitions. For example: I usually hold that lines do not need to be straight, but for the sake of proving some geometric properties in Euclidean geometry, I’m happy to situationally accept the requirement of “straight”.
80+ challenges in, I would hope we have some *feel* for what math art is (if you need more inspiration, check out the Bridges galleries), but as yet, we are not working from a common definition. Much as art is likely to have a differing definition among many people, I’m perfectly comfortable with us each arriving at our own definitions for math art. That doesn’t make this exercise fruitless – I think in grappling with what we believe math art to be, we can strengthen our connection to the art and the mathematics.
Personally, I will say that it bothers me when we’ve done a math art activity in class and students gleefully exclaim, “We did art instead of math today!” I know some teachers have used #mathartchallenge-s “instead” of math. While I appreciate the enthusiasm for the tasks, this framing grates on me. If you’re doing math art, you ARE doing math. It is as though an Advanced Algebra class, said “we did geometry today instead of math”! Completely nonsensical to me. That said, I can acknowledge that if a significant chunk of my “students” have the same conception, there’s something in my teaching that’s not getting through.
So, I’ve been digging into the question: “What is math art?” I know it when I see it, but can I wrap a definition around it? There are times when I’ve found a piece of math art, but upon reflection, I discard the label for that work. The reverse has also happened. Something I had dismissed as not math art becomes vastly more interesting when someone draws me in by highlighting the mathematical ideas embedded in the piece.
If we can define it, perhaps we can help our students, colleagues, and friends notice it as well. No worries if they take the definition and bend it to their liking – the discussion is what we’re after in this challenge. I accept that some look at the math art I create and think it fanciful to imagine I’m engaged in mathematical ideas. I have yet to meet and converse with someone that was unwilling to revise that opinion upon discussing the pieces with me, however. Unsurprisingly, I have little tolerance for those who think that being “art” makes it somehow less rigorous, less intellectually challenging, or less mathematically worthwhile, although I concede that some discussion may be necessary to help people see their error.
So go forth, my friends, and grapple with the definition. What makes something math art? What elements are necessary? Compare your definitions and images. How does your definition differ from your friend’s? I’ll post along with you. I have a working definition right now, but it’s open to revision upon meeting a reasonable argument.
UPDATE: Here is my contribution for the week:
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
3.) Construct viable arguments and critique the reasoning of others. What is math art? And how could you convince others that your definition is reasonable?
arbitrarilyclose 
Also the difference between and art and a craft. I ran a series last year called mathcraft, because learners were starting with projects that had some instruction to start(theodorus spiral, fractal trees, etc). When they took it to a new level and brought their uniqueness, I think I was seeing more math art. I think these definitions are tough.
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