C u r r e n t p r o j e c t s

mathematical art manifesto

I am currently organizing a group to write a mathematical art manifesto. It grew out of the workshop, Writing a Mathematical Art Manifesto, at Bridges Eindhoven, Netherlands in 2025. An eclectic group interested in math, art, dance, poetry, theatre, music, education and philosophy from the U.S. and Europe gather once a month to discuss issues surrounding mathematical art as contemporary art. If you’re interested in joining us, please send me an email.

P A S T p r o j e c t s

2025 Brown Symposium, Visualizing the Abstract

The Brown Symposium is a biennial event funded through an endowment established by The Brown Foundation, Inc., of Houston, Texas, for professorships at the University. In 2025, together with religion and environmental studies professor Dr. Laura Hobgood, we developed and organized the symposium relating our research areas with the theme, Visualizing the Abstract. As part of the Symposium, we commissioned the sculptor George Hart to create artwork to hang from the ceiling of the Fondren-Jones Science Center. The five sculptures were put together under his direction by students, faculty and staff. Margaret Wertheim also organized a workshop on creating hyperbolic planes using paper. The symposium included a joint exhibit of mathematical artwork by Daina Taimina and Star Varner, along with work by Jennifer Spiller and Mic Dooley. Talks were given by George Hart, Margaret Wertheim, TED-Ed editor Alex Rosenthal and animator Jeremiah Dickey, environmental-justice scholar/activist Dr. Jola Ajibade, and global food expert Dr. Raj Patel.

Brown Symposium Returns with 2025 Theme of “Visualizing the Abstract”, 2025

textbook

This textbook was a dream come true—the culmination of nearly a decade of research into the connections between perspective drawing and projective geometry. Co-authored with Annalisa Crannell and Marc Frantz, the project grew from a curiosity that began years earlier, when I happened to take an upper-level course in projective geometry alongside an art course on perspective drawing. I sensed that there might be deeper links between the two but didn’t explore them seriously until later, as a professor. Collaborating with my co-authors, we connected Desargues’ theorem to shadows and cross ratios to sidewalk tiles, sharing our discoveries through papers, classroom experiments, and museum visits with students. An NSF-DUE grant eventually supported the writing of the book, and, for the icing on the cake, Princeton University Press let me illustrate the cover. This is a IBL workbook-style textbook with perforated pages that can be ripped out and laid flat to make drawing with a ruler easier. An instructor’s manual is available upon request.

Buy the book: Perspective and Projective Geometry, 2019

Southwestern University Math Professor Receives $69,432 NSF Grant, 2011

Perspective and Projective geometry workshops

From 2013 until 2023, Annalisa Crannell, Marc Frantz and I taught minicourses and workshops on perspective and projective geometry at MAA MathFest and the Joint Mathematics Meetings. These were always well attended and full of fun perspective drawing exercises from what eventually became material for our textbook. The participants tried to figure out how to draw the letter A on a pane of glass in perspective and how that related to the proof of Desargues’ theorem, how to draw a 3D block letter T to learn about pencils of lines and ideal points, drew sidewalk tiles to learn about the cross ratio, and found reflections, dilations and rotations of triangular tiles in perspective and how that related to perspective collineations.

EQUIP program

In 2016, I along with Larkin Tom, Dr. Alison Marr and Dr. Emily Niemeyer developed a brand new summer program for incoming freshmen who expressed interest in STEM. The program called EQUIP (Embracing Quantitative Understanding and the Inquiry Process) was designed to introduce students to Southwestern and college life, familiarize students with the rigorous, inquiry-based learning methods taught in most SU science and math classes and create a supportive community among incoming science/math students. I have since taught in the program for many years and gotten to know many cohorts of amazing students.

Explorations in Mathematics: library exhibit

When the conditions are right, the students in my “math for artists” class, Explorations in Mathematics, put on an exhibit in the library. They show the mathematical art they produced throughout the semester. In the slideshow are pictures from the very first exhibit in 2013, right before I gave birth.

Judy Chicago and Donald Woodman’s A multimedia project of Discovery

While I was a 4th year math graduate student, I applied for (with my advisor’s blessing) and was one of 25 artists selected to participate in Judy Chicago and Donald Woodman’s A Multimedia Project of Discovery during their residency at Vanderbilt University. In between writing my dissertation, I took a class in contemporary art theory with Dr. Vivien Green Fryd and developed the concept for eight 3 ft x 6 ft paintings of myself as other people’s preconceptions through Judy Chicago’s feminist participatory art pedagogy. It culminated in the exhibit, Evoke/Invoke/Provoke. The experience deeply affected my understanding of art and art making, and renewed my commitment to art even as I finished my Ph.D. in math and went on to become a math professor.

Chicago in Nashville: Feminist artist Judy Chicago’s latest collaborative work takes shape at Vanderbilt, 2006

Judy Chicago, Institutional Time: A Critique of Studio Art Education, Monacelli Press, 2014, p. 206-210.

Florida without Borders: Women at the Intersections of the Local and Global, edited by Judy A. Hayden, Sharon Kay Masters, Kim Vaz. Chapter 14: Evoke/Invoke/Provoke A Case Study of Judy Chicago’s Feminist Pedagogy, Vanderbilt University, Spring Semester 2006 by Viki D. Thompson Wylder and Keri Fredericks, p. 149-159.

Research and writing

Some award-winning articles:

1. A new perspective on finding the viewpoint co-authored with student Robert Lehr won the 2018 MAA Carl B. Allendoerfer Award (SU news article here) for expository excellence of papers published in Mathematics Magazine in 2017. It describes a new method for finding the viewpoint for a two-point perspective drawing using the cross ratio.

2. Dürer: Disguise, Distance, Disagreements, and Diagonals! (preprint here) co-authored with Annalisa Crannell and Marc Frantz for Math Horizons was reprinted in: The Best Writing on Mathematics 2015, Princeton University Press. It vindicates the artist Albrecht Dürer, whose engraving St Jerome in His Study was eviscerated by the former director of prints at the Met William Mills Ivins Jr., on the 500th anniversary of the engraving.

Other articles without awards that you might still find interesting:

1. F. Futamura, O. Johnson, Jan van Eyck and the Painted Chandelier, preprint.

   • Co-authored with a student, we dig deeper into the geometric evidence to support the Hockney-Falco thesis applied to Jan van Eyck’s The Arnolfini Portrait, that he might have used an optical device of some kind to sketch the scene and more complicated objects within it, like the photorealistic chandelier.

2. F. Futamura, Circles and Perspective in Ancient Roman Wall Paintings, preprint.

   • I propose a new theory for how ancient Romans may have laid out the vanishing points and architectural and decorative elements in scaenographia, or scene paintings.

3. S. Friday, F. Futamura, J. Smith, A. Waclawczyk, Powers of defective matrices from diagonalizable dilations, Linear Algebra Appl., 661 (2023) 202-221.

   • Co-authored with three students, this paper looks at the idea of adding columns and rows to dilate a non-diagonalizable matrix to a diagonalizable one, but in such a way that the original eigenvalues are retained, the eigenvectors are predictable, and powers of the original matrix can be extracted from the powers of its dilation.

4. A. Crannell, M . Frantz, F. Futamura, An (isometric) perspective on homographies, J Geometry and Graphics, 23 no. 1 (2019) 65-83.

5. A. Crannell, M. Frantz, F. Futamura, Factoring a homography to analyze projective distortion, J Math Imaging Vis, 61 no. 7 (2019) 967-989.

   • These two papers discuss the decomposition of homographies into a perspective collineation and a similarity, or in other words, showing how a particular transformation of an image called a homography can be understood to be a rotation, reflection, and/or dilation combined with a projection from a point of a flat surface to its image (like taking a photo of a picture).

6. F. Futamura, A. Marr, Taking Mathematics Abroad: A How-To Guide, PRIMUS, 28 no. 9 (2018) pp. 875-889.

   • My colleague and I give some advice on how to teach mathematics abroad. We both taught in the SU London semester program, and taught classes like Applied Statistics, Cryptography Through the Ages, Mathematical Influences in Art and Victorian Mathematics and Society in Wonderland and Flatland.

   • Math in Wonderland: Southwestern professor who sees math in art brings a new dimension to the Semester in London program, 2011

7. A. Crannell, M. Frantz, F. Futamura, The Image of a Square, Amer. Math. Monthly, 124 no. 2, (2017) pp. 99-115.

   • What can be the image of a square? More than you think.

8. A. Crannell, M. Frantz, F. Futamura, The Cross ratio as a parameter for Dürer's solid (Party game for a 500th anniversary) J. Math. Arts, 8 no. 3-4, (2014),  111--119.

   • The shape of the mysterious polyhedron called Dürer’s solid in Albrecht Dürer’s engraving Melencolia I has been debated in dozens of papers for over a hundred years. We’ll never know his true intentions, but we give what we think is the best theory to date. On the shortlist of four papers considered for the 2016 JMA Outstanding Paper Award.

9. R. Denman, F. Futamura, K.C. Richards, On sharp frame diagonalization, Linear Algebra Appl., 438 no. 5, (2013) 2210-2224.

10. F. Futamura, Frame diagonalization of matrices, Linear Algebra Appl., 436 no. 9, (2012) 3201-3214.

    • These two papers introduce and explore the idea of frame diagonalization, using frames (spanning sets) rather than a basis of eigenvectors to diagonalize otherwise nondiagonalizable nxn matrices. We use a really cool theorem called Lidskii’s Theorem to make eigenvalues explode.

professional experience and outreach

I have taught many classes, at Vanderbilt University and at Southwestern University. For more information, click here.

I have been the chair of many things.

• 2022-present: Currently holder of the John H. Duncan Chair endowed by the Brown Foundation

• 2019-2022: Lord Chair of Mathematics and Computer Science

• 2026-present: Chair of the MAA Christine T. Stevenson Award Committee

• 2022-23: Chair of the SU Diversity, Inclusion, Belonging and Equity (DIBE) Task Force

• 2018-2020: Chair of the SU Department of Mathematics and Computer Science

• 2017-2018: Chair of the SU Curriculum Committee

• 2015-2016: Chair of the SU Enrollment and Retention Committee

I have been on the board or have been an advisor for other things.

• 2021-present: Executive board member, Japan-America Society of Greater Austin (JASGA). I helped revive the organization as Interim co-President in 2022

• 2015-2016: Science Advisor, NPR's Studio 360, Science and Creativity series

• 2013-2016: Advisory board member, Art.Science.Gallery in Austin, TX

I have taught workshops and minicourses in a variety of settings on a variety of math/art-related topics beyond the classroom.

• 2025: Bridges Conference, Writing a Mathematical Art Manifesto, Eindhoven, Netherlands

• 2025: Blanton All Day Programming: Origami Workshop (modular origami), Blanton Museum of Art

• 2013-2023: 7 minicourses on Visualizing Projective Geometry Through Photographs and Drawings, MAA MathFest and Joint Math Meetings (JMM)

• 2023: Math Teacher’s Circle, Mathematical Problem Solving and Discovery Through Perspective Drawing! Santa Cruz, CA

• 2022: Math Teacher’s Circle, How to mathematically immerse yourself in a perspective drawing, Austin, TX

• 2018: Learning station on hyperbolic crochet coral reefs, Hot Science, Cool Talks, Environmental Science Institute, UT Austin

• 2014: Community workshop, Hyperbolic crochet, Art.Science.Gallery, Austin, TX

• 2014, 2013: Community workshop, Mathematical origami ornaments, Art.Science.Gallery, Austin, TX

I have given various accessible talks at universities and to the general public.

• 2025: Video Game Perspectives, IU Indianapolis High School Math Contest Award Ceremony

• 2025: Shedding Light on Art Mysteries with Perspective and Projective Geometry, Public Colloquium, IU Indianapolis

• 2022: Curious invariants in projective geometry, and where to find them in art and music, Rice Undergraduate Colloquium, Rice University, Houston, TX

• 2018: Perspectives of a mathematician artist, Honors Summer Math Camp Colloquium for high school students, Texas State University

• 2018: How to mathematically immerse yourself in art, University Lecture Series, Texas State University

• 2018: When artists become mathematicians, public lecture, Phi Beta Kappa (En)Lightning Talks Houston

• 2017: Fractals in Japanese woodblock prints, Academic Lecture Series, Japan America Society of Greater Austin

If you would like me to speak or organize a workshop on math and art, please feel free to email me: futamurf at southwestern dot edu

media

A Close Knit Community, 2021

From Calculation to Expression: A Professor’s Take on Interdisciplinary Study, 2020

What a Mathematician Says About “Lens Compression” in Photography, 2018