Reference: Futamuro, F. (2025). Writing a mathematical art manifesto. In Bridges 2025 Archive, Eindhoven, NL, 589-594.
First, I did not know what a manifesto was so I googled it. AI overview says "A manifesto is a public, written declaration of the intentions, motives, or views of an individual, group, or organization, often aimed at promoting a new idea or initiating change."
Abstract: In this workshop, we will lay the groundwork for one or several mathematical art manifestos. We will try to clarify what we mean by mathematical art as an art form of creative human expression rather than a subfield of mathematics, a discipline or a pedagogical tool, and follow the general framework of artist manifestos that proliferated during the 20th and 21st centuries.
My Summary: Futamuro presents a framework at the Bridges Conference to determine - via crowd sourcing - what exactly is mathematical art (and what it isn't!) with the end goal of creating a manifesto in response to George Hart's article What Can We Say About "Math/Art"? in which he argues that we have not yet reached a consensus as to mathematical art core values. I cannot tell if Futamuro presents the instructions to writing a manifesto with sarcasm using Marinetti's Futurism as a template, but the requirements (to me) seem quite humourous which involve: vehement criticism, violence, well-defined insults, wit and bombast. Sadly, there is no conclusion or presentation of the data collected from this workshop.
Stop 1: The entire (brief) section of "A Recent History of Art that Uses Mathematics" (pp 590-591).
Seeing the advancements of thought and medium across time is very interesting. Initially, these mathematical concepts were painted by "-ists" I've never heard of but will be googling shortly. (For example, Dadists, Surrealist, Suprematist, Cubists, Constructivist, Minimalist). Then sculpting and photography became popular followed by computational art. This has inspired me to create a fun activity for my students gathering pieces of mathematical art across time, and having them place them chronologically on a timeline looking at trends in what concepts were popular, how they were represented, and hypothesizing/conjecturing the reasoning.
This would be a fascinating exercise in allowing the students to reflect on their own thinking about what might be considered "advanced" - looking at three factors (time vs. concept vs. technique/medium).
Stop 2: “Mathematics creates art”; “Mathematics is art”; “Mathematics renders artistic images”; “Hidden mathematics can be discovered in art”; “Mathematics analyzes art”; “Mathematical ideas can be taught through art.” (Schattschneider, 2005, as cited in Futamuro, 2025).
Schattschneider accurately sums up my feelings on this subject. Although, it is not the point of this article, I feel like this should be a poster or running banner that I tape up on the walls of my classroom.
Stop 3: Specific Artwork That May Be Considered Mathematical Art, Or Not. pp, 592-593.
The pieces described definitely piqued my interest with their brief one line descriptions. The first image of Kazimir Malevich's Painterly Realism of a Boy with a Knapsack - Color Masses in the Fourth Dimension (1915) was a lovely surprise that left me shaking my head wondering how/when/why/what. It really invoked curiosity to understand the narrative surround the piece.
What was the inspiration? (Guess: Probably self-explanatory from the title)
Why was the fourth dimension represented in this way (a realm of pure feeling transcending space & time)? (Guess: Probably from the year of 1915, this was their best imaginings to date?)
Why that?
How did Malevich know they were done painting?
How can you put a quantifiable dollar amount on this painting? What criteria would you use?
After googling the first few, I decided to make a PPT of the collection described so my google searches could be quickly referenced again and perhaps I could share these with my students (or colleagues from MAE3). I have a feeling that over the years I will be adding to this document chronologically to see the transformation of math/art across the generations. I'm not sure if this link works, but if you're interested in a copy, please e-mail: opodwysocki@sd43.bc.ca
Mathematical Art (or Not).pptx
Stop 4: "It is art that embraces the spirit, language and process of mathematics. Both maths and art are concerned with truth, but they differ in their ways of searching for it. Maths uses analysis and proof; art uses the senses and emotions. But maths can harness the spirit of creativity and art can be analytical. Together they form a great alliance for understanding the world around us." (John Sims, 2010, as cited in Futamuro, 2025).
This quote really resonates with me. Visual/Performance arts merges the two fields together: Math's analysis/proof, with Art's emotions/senses. Addressing the second half of the quote, after our EDCP 551 (MfSJ) course, this concept of emotions in representing data due to its innate subjectivity changed my perspective. We talked about Florence Nightingale's 1858 circular bar graphs (Rose diagram) that were presented to the queen about causes of mortality of soldiers in Crimea.
A good representation of data can be visceralized moving emotions beyond what visuals can do. I am still creating a mental foundation for the ideas that "maths can harness the spirit of creativity and art can be analytical" as the flow of thoughts and examples seem somewhat stunted. This may be because it feels like a chicken & egg issue. For someone to create a visual piece, would they not need to pre-plan and have mathematical concepts engaged for the finished product to contain them for analysis? In other words, it is a data visualization that is more pleasing to an audience (rather than a sterile graph). Again, I feel like I'm juicing a lemon rather than stemming a dam of lemonade.
Wonders: I'm a little disappointed by the fact that this paper had no real conclusion. It was a very general "how-to" set of instructions on developing manifesto(s) with this particular case being Math Arts. Although the examples brought forth were intriguing with breadth of history presented, there were no conclusions/data from the questions that were presented via crowd sourcing!!
I would've loved to know what the audience thought about question (e) What established paradigm or tradition in art might we be rejecting through declaring that mathematical art or math/art is art?
In terms of application to the classroom, while reading this paper I couldn't help thinking about the course outlines we are required to produce for our students explaining - what I like to call, the "Rules of the Game", so that my students can play-to-win! In essence, we are creating Mr. Podwysocki's Math 9 Manifesto of 2026 Semester 1 (without following any of the humorous bombastic insulting guidelines as suggested by Marinetti). Dr. Waddington presented a list of expectations that we could expect from him in our very first course EDCP 562 which was impactful to me.
What would our course outlines look like if we took this vehement revolutionary approach to step boldly into the future and reject past iterations while including teacher expectations along with student academic and behavioural expectations?
A long time ago, when I was doing my practicum in an intermediate classroom, my supervisory teacher co-developed a set of expectations with the class by labelling a t-chart teacher jobs:student jobs. It was brilliant to have students list their jobs and was a great anchor to return to throughout my time there. This is kind of like the commitments that Dr. Waddington shared with us - just that the students helped create them, and also added their own. I like your idea of extending this to things from the past that we also reject. I think this could be a powerful tool for creating a class community that can practice mathematical thinking together (a step towards the liftoff I was referencing in my response to your satellite/transmittor notion.)
ReplyDeleteI was wondering about your stop 2: “Mathematics creates art”; “Mathematics is art”; “Mathematics renders artistic images”; “Hidden mathematics can be discovered in art”; “Mathematics analyzes art”; “Mathematical ideas can be taught through art.” (Schattschneider, 2005, as cited in Futamuro, 2025) Math is everywhere, infused in our daily lives. Can we replace the word art with other words and still have this resonate? For example: “Mathematics creates nature”; “Mathematics is nature”; “Mathematics renders natural objects”; “Hidden mathematics can be discovered in nature”; “Mathematics analyzes nature”; “Mathematical ideas can be taught through nature.” Would other words work?