Week 7 Readings: Math Sculpture & Photography

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?   

Week 7 Activities + Connections: Interview with Nick Sayers

Before we read, I want to apologize to my valued reading group partners for this massive post in which I found so much meaning and inspiration. I would suggest to "pick 2 stops" to check out because I've collected 9 after paring down.   

Interview Link to Nick Sayers (2026): https://vimeo.com/1166172275/3a7a243bce?share=copy&fl=sv&fe=ci

Summary: Sayers presents his many artistic mathematical creations over time. His explanations are rooted in experiencing everyday life, being inspired by moments with others that lead from the personal-level to creating experiences for an audience. Sayers describes his process of creation (my favourite part as these are the keys to thinking and creating) and shows how the meaning of each piece blooms the more he self-reflects. I think I understand this deep connection that he develops with each of his pieces as each second in development is a new joyous puzzle to solve, choice to make and meaning to build.

This theme repeats itself over and over again as he describes his incredible playful creations that include political statement pieces, photography in its many forms, environmentalism, fitness, Earth Science and Astronomy. The materials he uses are again inspired by everyday life, his personal interests, and availability. It seems he is never out of reach from a functional material with which to create.

I am inspired.

Stop 1: @ timestamp 21:38 Sayers mentions "...the endlessness of waste" - the coffee stirrers, train tickets, and realtor signs are shaped as a sphere - an endless surface. 

The metaphor of shape for concept is very fitting. It really helps generate meaning when we look at a product as a whole. Each of these things are meant to be a one-use disposable item. This cycle won't end because we have nothing else and no systems or behaviours in place to replace it. The coffee stirrers and toothpicks have transcended their one use, now living on in a "12-noded blobby stellated polyhedron" (his words, not mine) installation representing higher ideals. (Note to self: Hyperbolic Coffee Cactus made with 630 coffee stirrers, fastened together with 1260 toothpicks)

   

Stop 2: @ timestamp 24:25 Sayers's five platonic solids are called "10 times 5 times zero" mentions each bag is 10 litres in volume, there are 5 solids, with zero in them. I really love these clever names; Half the fun for me in creating something new is naming it. 

 

Stop 3: @ timestamp 28:50 Nick mentions being superstitious about numbers and he can remember the number of bottles in the Christmas tree in Azerbaijan. 

I feel somewhat similar not in a superstitious sense, but in a symbolic way - I would find/make for myself a meaningful connection by attributing the bottles and numbers with my life. In this case, Sayers did just that: 31st is his birthday (# of bottles on the star), 12th month event (# of Christmas lights inside the star to make it glow). I would've felt the same way as Sayers (he looked slightly disappointed - like a missed opportunity) about the number of bottles of the tree, not exactly matching the year that the event took place.

Stop 4: @ timestamp 32:55 Sayers talks about the troubleshooting of the giant 1:6 pantograph. I love process. I love troubleshooting because solutions can be applied as a transferable skill.

Stop 5: @ timestamp 39:45 Sayers demonstrates the patterns created by his bicycle spirograph, he makes the connection between complexity and the sharing of common prime factors on the gears of the crank and sprocket of the wheel. The higher the lowest common multiple, the more complex the pattern before the pattern repeats itself again. "People think it has to do with speed, but it's actually the prime factorization of the cog teeth."

It's really neat to see this idea carried out as I made this connection in week 5 during Sarah Chase's Dancing patterns. I wish there was a video in which he showed a demonstration of the mechanism at work.

Stop 6: @ 47:00 timestamp, Sayers answered one of my wonders about the fragility of some of his structures. He says that he needs to create his machines so that they are not only public interactive, but public proof. This ensures his creations won't hurt anyone or malfunction, creating a positive interactive experience with his audience. 

This kind of troubleshooting and fool-proofing takes up a lot of time and energy. When I show my children or students something I've created, I need to run through a list of do-not-attempt actions so that the creation will last past their interactions - by that time, the excitement has passed and they move on.

Stop 7: @ 1:11:05 timestamp, Sayers shows a picture of the solargraph pinhole camera. It shows the path of the sun as it moves across the sky each day. These are left up for six months at a time and are constructed from a lager can with photographic paper inside. 

The low arches show the sun's path in the winter time and the high arches show the sun's path in the summer. I am blown away. 

I took a group of 50 students to Japan in 2024, and we visited JAXA. During our stay I visualized how I could demonstrate to my students what the pathway of the sun in the sky would look like across the seasons based on the latitude. These images are how I visualized the pathways! These images above are from Brighton @ parallel 50 N. So, this would serve as an excellent analog for Vancouver @ parallel 49 N. 

A few things I am noticing: 

• The path of of the sun is sweeping up into the top of the arch's, then back down. Is this a function of the lager can's cylindrical shape? (This is my guess)
• The paths of the sun across the sky aren't completely solid, some have blanks and spots missing like morse code. Because this exposure takes a long time to accomplish, it must be weather that has blocked the sun's path over long periods of time. 
• If reading the Left side of the images as sunrise, and Right side as sun sets... looking at the bare spots in the paths (at the top left), I would imagine close to the horizon, there are more clouds at night in the winter, probably from a day of convection, whereas during the summer there's many more clouds mid-day, I suspect for the same reason but takes less time to create the natural convection that causes clouds to form.  

This pin-hole camera idea is a fascinating piece of technology that I'm going to look into doing with my students over time to capture the sun's movement for my Earth Science 11 class. 

Stop 8: @ timestamp 1:40:01, Sayers speaks briefly about his phonotrope (?) delving into optical illusions. I didn't realize that the speed of the rotation, and the frames per second of recording would play a role in creating the patterns. 

According to Healthline.com, humans can see smooth motion at between 15-24 FPS, and standard perception is between 30-60 PFS. Modern cinema is 24 FPS which seems like a good trade off for highest motion smoothness with least production cost for "film".

A few years ago I did a demonstration for my children (and Earth Science class) on this idea of visible light (of the Electromagnetic Spectrum) being wavelengths that could be registered by your eyes from a cycle of black and white pulses exhibiting a frequency. I couldn't get the timing of the Newton's Wheel to spin exactly right for my students to see a stable colour, (and safety was a big concern for me considering this was a cardboard disc revving up to material-cutting speeds) but they did report on being able to see blues, purples and some green (which are on the higher end of the visible light spectrum). I'm guessing the reds and oranges were just flashing black and white lines to them.

Here's a video of the reverse! Adding all the colours together creates White! (Cut out, coloured by my son, 5, and daughter, 3, at that time). 

 Stop 9: @ timestamp 1:50:31 Sayers talks about his fractal castles as a political statement piece for the Aral Sea from 1977.

Here's a few wonders I have:

1. How did Sayers know the proper dimensions of the black bottom panel prior to building his creation such that each castle would have a uniform spacing along its boarders? 
   
   (I imagine with measurement techniques perhaps mapping out just one quadrant. Then, multiplying by four knowing there would be overlap along two edges. But then placing the sandcastles down in exactly the right spot might have been preplanned with perhaps a dot or tracing of where it would need to go to assist placement - this is assuming once placed couldn't be moved again.. which leads to second question)
   
   
2. How did Sayers create these sandcastles such that they would not crumble during transport? 
   
   (I imagine Sayers mixed white glue into the water to hold each castle to allow for an increase in structural integrity. This would allow for adjustment after placement if necessary. But would the white glue not create a sheen that would be visible? Would it be naturally compostable if once the installation was complete to toss these mini castles back outdoors? If they were solid and immalleable, did he sell each one as a fundraiser for the event?)

What does this artist's work offer you in terms of understanding math-art connections, and what does it offer you as a math or science teacher?

I really see the connections and the depth of understanding, the courage in experimentation, working with what you're given and giving what you've worked with. I think looking at the world from this artistic and mathematical lens must be so fulfilling. I can see that creating art for/with a purpose is aided by quantities. The idea of quantities can only be accomplished with mathematical principles. Sometimes manual algorithms aid in creation (for example, the bike gear/sprocket to speed ratio - set it, and repeat. It will always churn out the same thing). In fact, the excitement comes when new algorithms are discovered, and you don't yet know what they will churn out! (Understandably, this is also a problem as we just finished our social justice course on it with companies creating algorithms for hiring based on "past successes" and then being surprised when only the same demographic gets chosen).

What this interview and demonstration gave, was more perspective. I already knew math is my favourite tool in my toolbox, science my favourite process, art my favourite mode of self-expression. BUT, the difference is (like an old swiss army knife with an extra secret set of fold-out tweezers you never noticed before) the fields keep unfolding to reveal more uses, crossovers, interconnectedness to develop innovative and rich ways of experiencing and expressing yourself the world. 

Dr. Gerofsky asks a fantastic question earlier on in the set: "How much has to be perfectly planned, and how much does something surprising and new come up?" 

A similar idea was brought up by my group members during an interview with musical mathematician Hans Peter Nutzinger at MACAS 2025. Nutzinger's reply, to paraphrase, was that the teacher must be highly structured in every lesson... but when, and as soon as, the students display creativity in their learning be ready to abandon the plan and go with the flow. (I made the connections to Blooms Taxonomy because they are displaying one of the highest levels).   

With Sayers, it seems his audiences provide him with this advancement in creativity by understanding his structures and helping to improve it - for example, with "thrust bearings" instead of nylon washers on the Pantograph. This openness and presence to life and experiences has really served Sayers well!

Therefore, my main take-away from these moments is physical and mental openness and presence during the experiences are a key factor in creation. Thinking metaphorically, be a satellite dish receiver even when being a transmitter. 

That's all for now.