Like a researcher laying out a scientific problem, so begins the process by which Illinois State Art Professor James Mai constructs a set of abstract paintings: Given the eight vertices of a regular octagon, what are all the forms that result from connecting four pairs of points with four lines?

Mai answered his question by creating 17 shapes featuring all the possible permutations of the four lines and points inside the octagons. He inserted them into a table that grew as Mai asked more questions of his octagons involving points, planes, and lines, until 359 octagonal forms were set forth in categorical columns.

The permutations of these shapes formed the basis for a series of abstract works Mai painted to explore the inherent order of geometric shape. His process of creating new work conjures the image of a chemist in a lab. It might not be surprising then that Mai considers the periodic table of elements to be one of the great visual creations in human history, on par with any masterpiece in visual art.

“Of course it is nature’s construction, but it’s man’s recognition and visualization of nature’s order that interests me,” he said. “In many ways, the various forms of periodic tables are somewhat analogous to my construction of tables for my little worlds.”

Mai has been creating his “little worlds” for the last 30 years. Once a figurative painter who worked in oil and acrylic, Mai is now an abstract painter who works mostly in digital prints. His artwork and writings have been presented globally, including cross-disciplinary academic conferences in Europe and Asia, and an exhibition this past spring featuring artists represented by the Los Angeles Center for Digital Art.

Regardless of which materials he uses, Mai’s paintings of galaxy-like sets of colorful polygons have the same objective: The works are an attempt to emulate the order, wholeness, and interrelatedness he sees in nature, the study of which he considers as important to the artist as it is to the scientist.

“I would not be making what I make now had I not been trained as a figurative artist to look carefully at nature’s shapes, proportions, and colors,” Mai said. “I learned that the visual study of nature, with all of its subtlety and complexity, expands the possibilities for an artist’s imaginative work. It is the necessary grounding for creative work.”

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Mai works with systems to generate “minimum complete sets” of geometric forms—minimum in that no two forms are alike and complete in that no forms are missing. These sets of forms are used to populate the compositions of his artworks in such a way that the finished work reveals how all the shapes are related.

His work is influenced by a tradition of abstract artists extending back to the Dutch painter Piet Mondrian, who laid out the language for a fully abstract art based on simple colors and forms in the first half of the 20th century. But Mai considers Mondrian’s approach too subjective.

“There was no objective way an independent viewer looking at a Mondrian painting would know why (a line) is over there and not over here,” Mai said. “What I seek in my work is something that lives its own life without either my subjective whim or my verbal interpretation to explain why it is the way it is. I would like my work to be self-explanatory at least at a certain level.  If you spend enough time with it and you look objectively at its shapes and colors, the painting reveals its web of relationships. My purpose is to offer a direct visual experience of order, aside from verbal or mathematical explanations.”

Mai’s work has drawn the attention of mathematicians, including Bellarmine University’s Daylene Zielinski. They have collaborated on papers about his work. The audience for this research is artists and mathematicians interested in the new mathematical shapes and relationships Mai has created. His creative research overlaps with such mathematical topics as symmetry, number theory, and graph theory, including polyominoes—a set of geometric figures composed of squares placed edge to edge.

Zielinski and others consequently label Mai’s work mathematical art. Though he sits on the editorial board of the Journal of Mathematics and the Arts, Mai dismisses the label, noting dryly that his mathematical skills would not impress mathematicians.

“I don’t describe my work as mathematical art, because it doesn’t emerge from mathematics per se,” he said. “The work is perhaps motivated by the same thing that motivates mathematicians: That is to find the underlying order of various aspects of experience. So I think it is more accurate to say that my work and mathematics share some fundamental values and methods.”

Mai compared the geometric relationships in his work to meter in poetry or rhythm in music: “Every art form has its structural language. For visual art, the structure of the language has to be involved to some degree in geometry because the perceptual mechanisms by which we see include recognition of geometric features such as symmetry, edge alignments, shape closures, similarities of scale, angle, spacing, and the like.”

There is no color out there. It’s a purely subjective experience of light phenomena.

The process of seeing is Mai’s other main area of work, as he examines how we experience color. The work in each sphere is different but not mutually exclusive. Color, Mai said, is not a thing, like a chair, or even a stable attribute, like mass or dimension. It is an experience that resides in human perception.

“There is no color out there,” he said. “It’s a purely subjective experience of light phenomena. What is more important is that color is contextual. Any given color changes its appearance simply by placing another color next to it. The way that we process color is always in ensembles.”

His color-interactive paintings explore the changeable nature of color identity. This color-based work plays with the concepts of color convergence (two different colors appear to be the same) and color divergence (the same color appears to be different). An example of the latter is his 2013 piece titled Mirroring (Yellow-Green): A green line appears to change as it passes through yellow, green, and purple vertical rectangles.

“These paintings reflect back to us something that is easily forgotten but very important about our engagement with the world,” Mai said. “We are not passive bystanders who simply move through the world and witness its appearances, as though we are separate from it. We are instead active participants in making the world that we inhabit, because our perceptual systems automatically structure our sensations of it. Color, in my view, makes this clearer than any other experience we can have.”

These paintings build on the work of another 20th-century artist and art theorist, Josef Albers, whom Mai has studied carefully since the 1970s. He considers Albers the most important colorist in the last 100 years, as he established greater awareness than any other artist of color interaction and the questions raised by color perception. Mai’s approach is similar to Albers’ in emphasizing the primacy of perception in art, but Mai has been working to add to Albers’ work by more precisely defining the structure of color interaction and by developing systematic applications of color in paintings.

“In visual art, clarity comes in part, although not entirely, by precise shape and color relationships,” Mai said. “So my interest in a kind of structured clarity means that I am usually not satisfied with things being sort of this way or that way.

“I want to push a color relationship until it reveals some surprise to me that I did not know before. I suppose it is like any academic research in being committed to a precision that pushes through to new territory. I believe I have arrived at some new understandings about the interactions of colors. This understanding about color is, ultimately, an understanding of our own entanglement in the world. And so my work probes that sometimes blurry territory between subjective and objective worlds.”

Mai is attempting to get the viewer to become more aware of their own seeing. “Color doesn’t reside well in memory,” Mai said. “One must be in the presence of color to experience its varied and fugitive appearances.”

School of Art Professor James MaiHis ultimate desire to find new understanding of the world through a commingling of perception, science, and art stretches back to his youth in Wyoming. He grew up knowing how to draw but intending to be a geologist or a paleontologist.

“As a youth, I didn’t think of drawing and the physical sciences as separate or unrelated activities,” Mai said. “For me, both were powerful and very natural ways to explore the world.”

It’s an exploration that has continued throughout his life.

James Mai at a glance

Position: Illinois State professor of art since 2000

Education: B.F.A. and M.F.A. from the University of Wyoming

Awards: College of Fine Arts nominee for Outstanding University Researcher Award, 2009 and 2014; College of Fine Arts Outstanding College Researcher Award, 2008; College of Fine Arts Outstanding Teaching Award, 2005; School of Art Outstanding Teaching Award, 2004

Exhibition and research record: Mai has exhibited his artwork and published and presented papers on his and others’ work in dozens of national and international forums.

Quote from a colleague: “He is so dedicated to his studio practice, to his theory, to his writing, to his review of even international essays and papers—he reviews books, he’s deeply involved in his scholarship, his research, and creative activities. And I think it is noteworthy to say despite these scholarly and artistic accomplishments, his teaching and service to the University community are also exemplary.

“It’s quite a package. I think Illinois State is very fortunate to have Jim on the faculty. He is one of the finest scholars I’ve ever known.”

—Richard Finch, Illinois State art professor emeritus and printmaker