Article Summary:
Futamura's article Writing a Mathematical Art Manifesto, starts by highlighting the first art manifesto by Filippo Marinetti, the Manifesto of Futurism. Emphasizing the inspiration from Karl Marx and the use of strong imagery and fiery language. Aiming to introduce a new aesthetic, his manifesto was naming and rejecting an old paradigm just as much as it was about defining Futurism. Manifestos became a way for artists to distinguish themselves, during the modernist age. Becoming an art form in itself, manifestos were used to announce radical ideas and new directions to push the status quo.
In preparation for workshop, they discuss the beginnings of the foundations for a mathematical art manifesto, centering the perspective of creative human expression apposed to its usefulness as demonstration, illustration or pedagogy. Following the process of naming and rejecting an old paradigm to establish a new one, they needed to ensure not only an understanding of mathematical art but how it additionally rejects an artistic belief or norm.
The workshop structure:
- Facilitator introduces manifestos and goals
- In small groups discuss: What is mathematical art, or math/art, as a physical manifestation of creative expression?
-Groups share ideas
-Facilitator hands out images of artwork, in small groups discuss: Are the following works considered mathematical art according to your understanding of mathematical art as a physical manifestation of creative expression?
-Groups share ideas
-Facilitator goes more in depth of structure of the manifesto, presenting examples of rejected artistic paradigms.
- In small groups discuss: What established paradigm or tradition in art might we be rejecting through declaring that mathematical art or math/art is art? Specifically, what criticisms do we have about the established paradigm?
-Groups share ideas
- Facilitator leads reflection and creation of an outline for a mathematical manifesto
They acknowledge that some may argue that this contrasts the welcoming nature and inclusive spirit of many mathematical artists as seen at the Bridges Conference. Stating that most if not all artists use mathematics either consciously or unconsciously.
The article covers a recent history of art that uses mathematics, recognizing that mathematical art can be found far back in the history of many cultures before framing the focus of this article on visual artwork produced in the west in the 20th and 21st century. Many mathematical developments inspired artists in the 20th century, in these works the mathematics was not the focus but used as metaphors with transcendent experiences. Mathematical models have captivated and inspired artists who have created guided by intuition and pattern not necessarily a strict following of a mathematical equation. Artists re-discover mathematical ideas like the Mobius Strip and Riemann Surfaces, through artistic experimentation.
The introduction of computers fostered fascination with visualizations and mathematical curiosities, some images were just visualizations, but some mathematicians and computer sciences started to use computers as its own artistic medium. Carlos Sequin presented "Art, Math and Computers: New Ways of Creating Pleasing Shapes" at the first Bridges Conference, explaining his process of using a computer to virtually design complex geometric shapes similar to minimal surfaces that could be sculpted out of wood.
Art with underlying mathematical themes and processes became popular in the mathematical community in the 21st century, with support of established organizations like Bridges. Mathematical Art is still performed among people who primarily identify as artists, but increasingly there have been mathematicians who have found artistic expression through mathematical art.
In discussing what is mathematical art the article shares that mathematical art recently has be characterized as a subfield of mathematics. In Farris' 2021 article Mathematical Art as a Discipline he claims that mathematical art has become a discipline in its own right. George Hart places math/art within mathematics, and a liminal space in between. Mathematics connects to art in a variety of ways. They ask what if the focus on mathematical art as a form of creative expression over its practical purpose?
The article shifts to share the characteristics of a manifesto, sourcing from Hart's 2024 article What Can We Say About Math/Art"? he posed the question of if a mathematical art manifesto should be the goal, sharing that he believes that there is not enough consensus on the core values of mathematical art. Futamura shares that while the first Futurist Manifesto was written in 1909 over 50 more were written over the next decade, concluding that a group with common views can come together and write separate manifestos. While there are many different styles and content that can come together in a manifesto, from poetic forms to short numbered declarations, there is a general three step formula developed by Marinetti that many follow.
Steps:
1. Identify and define an established Paradigm in art.
2. Criticize the paradigm ( with strong passion)
3. Introduce a new paradigm to counter the old (again with strong passion).
Marinetti declares that a good manifesto "must have violence and precision, a specific accusation and a well-defined insult, wit and bombast, and a sense of style that mimics the art itself." (Futamura, 2025, p. 592)
The article shares specific artworks that may or may not be considered mathematical art, these are works that are not by known mathematical artists, followed by quotes from mathematical artists.
One of the works shared in the list was John Sims, Seeing Pi, felt fitting with Pi day coming up and was the only fiber arts based piece on the list.
Math artist John Sims is living a life of pi. QUARTZ. (2022, July 20). https://qz.com/quartzy/1571241/pi-day-math-artist-john-sims-creates-a-life-of-pi
"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, Artist
(Futamura, 2025, p. 593)
Futamura concludes the article sharing examples of rejected paradigms from art manifestos, and that many more can be found in 100 Artists' Manifestos edited by Alex Danchev.
Stop 1: "if an artist decides that their art is mathematical art, then it is." (Futamura, 2025, p. 590)
I wonder if in their intention of this statement they were saying, mathematics just is and the line of weather art is mathematical art is in the artists acknowledgement of such, because it is present, it exists, so is it the naming, acknowledging, and seeing of it by the artist that is the determining factor.
Stop 2: "'Mathematics creates art'; 'Mathematics is art'; 'Mathematics renders artistic images'; 'Hidden mathematics an be discovered in art'; 'Mathematics analyzes art'; 'Mathematical ideas can be taught through art'" (Futamura, 2025, p. 591)
I really enjoyed this quote, the lens for art and math are so rooted in each other and I appreciated the way this quote summarized that.
I was intrigued by the works by Felix Klein and Alfred Clebsch that the article mentioned and looked up some of their works and saw similarities of these curved images and structures to the work Nick Sayers shared in their interview. Multiple points in the article there was mention of violence in writing manifestos, I found this to be a jarring word, after my first read through I wondered if its use was more intended to be provocative and invoke a reaction or feeling, if that's what their intent with the manifesto and with their use of words like violence in their description of it, when I started to reframe it with that as the intent I additionally considered the nude art pieces that Nick mentioned in the interview and how that could also be considered provocative to invoke a reaction or feeling.
Question:
What do you think defines mathematical art for you? Does it just exist? Are there specific defining features that are needed?
Futamura, F. (2025). Writing a Mathematical Art Manifesto. Bridges Conference, 589–594.
Math artist John Sims is living a life of pi. QUARTZ. (2022, July 20). https://qz.com/quartzy/1571241/pi-day-math-artist-john-sims-creates-a-life-of-pi
What is mathematical art? I do like a philosophical question. Mainly because I know so little about the world, about math, about art. The idea of trying to define what mathematical art is feels difficult, because mathematics is a study of the world in a very universal language. No matter what piece of visual art is placed in front of me, there are ways of describing it mathematically--for example, Kandinsky's concentric circles being a fun way of exploring combinatorial thinking.
ReplyDeleteTo me, all art is mathematical not because we apply the concepts and values of mathematics to it. It's mathematical because art exists in this world--the form of the world is inherently mathematical and describable. I fear that many students try to separate the math from the art, but such an action is actually impossible to do. The paper that I read on geometric forms in basket weaving is an example of the math inherent in art. And Melanie's paper on craft and mathematical experiences show that the connections between mathematics and art can be quite valuable in the teaching of "curricular math". It is the emotion that is inherent in art--the boredom of a student doodling on the margins of their paper; the frustrated excitement of a student carefully creating a pointilism piece--that opens up the space for the inherent mathematics to be explored.
Your first stop — “if an artist decides that their art is mathematical art, then it is” — made me pause as well. Although I didn’t read that particular article, the line feels like it is exploring the tension between personal creation and institutional standards. As the creator, there is power in claiming and naming your own work. Yet the deeper tension may not actually be about what counts as mathematical art, but about who gets to define what counts as art in the first place — and that is a far more complex and complicated conversation.
ReplyDeleteWhen I consider what defines mathematical art for me, I find myself returning to George Hart’s argument in this week’s readings (2024). Hart suggests that while a piece of art may contain a mathematical element, such as a single shape or number, that does not necessarily make it mathematical art. Mathematical art must contain what he calls mathematical pleasure. There needs to be a deeper structural or conceptual engagement with mathematics. Something more sophisticated than simply including the shape of a zero or writing a number on a page is required to meet the definition (Hart, 2024, p. 524).
For example, if a student creates a sketch that simply features a number, that alone may not constitute math/art. However, if that same sketch embeds pattern, symmetry, proportion, or hidden relationships within its design, if the mathematics shapes the composition in meaningful ways, then it begins to move into the realm of mathematical art. I don’t know if Hart’s definition is needed, but I appreciate the distinction.
I want to echo Mel here: Is a work of art mathematical simply because the artist says it is? Imagine an installation consisting of a pair of jeans hanging on a clothesline in a dark room, with mathematical operators such as +, −, and × projected alternately onto the left and right legs. The artist declares it mathematical art. But is it really?
ReplyDeleteIt reminds me of Albert Einstein's statement that 'time is what the clock says', by which he is believed to have meant that time is defined as the thing that clocks measure. The point was to bracket metaphysical debates about the nature of time in order to get on with the business of physics; in his case, of special relativity. On this approach, art is what artists do. So, if she says it is mathematical at that, then why argue?
Arthur Danto is my favourite philosopher of art. In his book What is Art? (2013), he takes a more risky stance. He acknowledges that, "art today is pluralistic", since it is, "an open concept". Danto wants to respect these truths of contemporary art, but seeks to point to sometime more. Imitation only has meaning if it, "looks like the real thing but isn't the real thing". Serious people like Plato want the real thing. Artists, Danto notes, "could draw a table, meaning they knew how tables appear. But could they actually make a table? Not likely -- but what good really was the appearance of a table?".
Maybe the appearance of mathematics can matter. Even when a work does not deepen mathematical understanding, it may still place mathematics into richer relation with the societies that produce it, live under its authority, and experience its consequences.