Rigorous Illustrations - Their creation and evaluation for mathematical research

Liste des Contributions

1. Welcome and Introduction to the Workshop Structure

David Bachman (Pitzer College), Edmund Harriss, Gabriel Dorfsman-Hopkins (St. Lawrence University), Martin Skrodzki

19/01/2026 09:30

2. Why rigorous Illustration?

Edmund Harriss

19/01/2026 10:00

Illustration of mathematics can be thought of as a dual to modelling, instead of trying to create a mathematical model of a physical process we create a physical model of a mathematical idea. In both cases we can never have the certainty that the two systems line up perfectly, but can check some of the basic principals. For example if we assume that a flat piece of paper is a Euclidean plane,...

3. Illuminating Impossible Objects

Robert Ghrist (University of Pennsylvania)

19/01/2026 10:30

In 1992, Roger Penrose published a short, enigmatic paper connecting the famous impossible triangle to cohomology. The paper contains a second, stranger figure -- a septagonal ring of Schroder stairs -- with a cohomological interpretation. He closes with a cryptic hint: ``I believe that considerations such as these may open up intriguing possibilities for further exotic types of impossible...

4. From connecting the dots to conjugacy of dynamical systems

M. Pierre Arnoux (Université d'Aix-Marseille)

19/01/2026 11:30

Around 1986, I was working on an interval map which was self-induced, with the Tribonacci constant (real root of $x^3=x^2+x+1$) as coefficient, and I knew that a particular rotation of the 2-torus had been proved (by Gérard Rauzy) to have the same property; were these 2 systems conjugate? The conjugacy would, in that case, be a surjective map from the interval to the torus; what would it look...

5. Illustrating the development of wavelets and beyond

Ingrid Daubechies (Duke University)

19/01/2026 12:00

7. The Body of Proof: How Inscriptions Shape Mathematical Discovery

Shadab Tabatabaeian (Postdoctoral researcher at Georgetown University)

20/01/2026 10:00

Where do mathematical insights come from? According to classic accounts, creativity is a multi-stage process that involves combining ideas in novel ways. Evidence for these accounts, however, is drawn from artificial lab-based settings or is zoomed out from the messy, moment-to-moment details of discovery. Here, I examine a video corpus of expert mathematicians generating proofs in an...

8. Is math big or small?

Elliot Kienzle (UC Berkeley)

20/01/2026 10:30

When Illustrating a mathematical idea, the first thing you need to decide is the scale. Is this concept something you can hold in your hand, or something to wander around in? I will reflect on the scale of various analogies used by research mathematicians, such as Thurston's train tracks and pictures of symplectic manifolds. Topologists use the metaphors of "geography" and "botany" to...

9. The flat and the relief : geometric material models in 19th century France

Frédéric Brechenmacher

20/01/2026 11:30

This talk investigates several historical collections of geometric material models, drawings, photographs and other types of graphical representations in Paris at École polytechnique, Institut Henri Poincaré and Musée des arts et métiers.

The practice of model drawing played a key role in the development of descriptive geometry and, more generally, of mathematics from the mid 18th century...

10. Embodying Mathematics Without Sight: Investigating Perception– Action Loops in the Instrumented Activity of Visually Impaired Learners

Loris Palaj (PhD student at the University of Bologna)

21/01/2026 09:30

This study investigates how perception–action loops manifest within the instrumented mathematical activity of visually impaired learners assisted by digital technologies. Grounded in the Body–Artifact Functional System (BAFS) and Gibson’s ecological theory of perception, the study adopts an embodied and multisensory perspective to explore alternative ways of comprehending a mathematical...

11. Telling Math Stories With Graphics

Jen Christiansen

21/01/2026 10:00

With the goal of prompting researchers and science communicators to think critically about conveying mathematical concepts to broad audiences, Jen will demonstrate how illustrated explanatory diagrams can support text-driven narratives, or encapsulate full concepts as self-contained image-based modules.

12. What is visualization literacy and how should we measure it

Lily Wanqian Ge (Northwestern University)

21/01/2026 10:30

Researchers have proposed many definitions of visualization literacy, targeting various aspects of the term. But we have yet to fully capture what it really means to be literate in visualizations, which has important downstream implications, such as how to effectively teach visualization skills to younger generations. Despite not having a clear sense of what it is, we must design tests that...

13. The Visual, The Poetic, the Mathematical Connecting at the Foundations: Responsive Practice as Research Methodology

Jean Schmitt (University of Arkansas)

21/01/2026 11:30

What can mathematical illustration learn from studio art research methodologies, and how canvisual principles and poetics be developed together to illustrate abstract concepts? Thispresentation bridges two worlds that share more than is immediately visible: both mathematicalresearch and studio art practice pursue forms that do not yet exist, working iteratively throughobservation,...

14. How Not to Draw a Sphere

Philip Ording (Pratt Institute)

21/01/2026 12:00

This talk will describe some of the challenges of communicating mathematical experiences, including the value of rigor and its opposites.

15. Integrating 3D Technologies and Immersive Media into Mathematics Education

Zsolt Lavicza (Linz School of Education, Johannes Kepler University)

22/01/2026 09:30

This talk will explore the evolving research in mathematics and STEAM education at the Linz School of Education, specifically focusing on the integration of 3D Modelling and Printing (3DMP) and immersive media (AR and VR) to support mathematical learning at all levels of education. By examining the intersection of technology and pedagogy, I will highlight how these tools could foster creative...

16. When is enough enough? Proving in an inversive model of Euclidean space

Stacy Brown (California State Polytechnic University, Pomona)

22/01/2026 10:00

Imagine you are proving a proposition in an inversive model of Euclidean space and you’ve end up with is a chaotic pile of circles and lines. How do you decide what to include? When is the construction sufficient? Appropriately aesthetic? Reasonably communicative? The aim of this talk is to share some of the challenges one encounters when generating mathematical illustrations for the dual...

17. Some reflections about the role of visuals in the teaching and learning of mathematics

Greisy Winicki Landman (Department of Mathematics and Statistics, California State Polytechnic University Pomona)

22/01/2026 10:30

In 1990, Michael DeVilliers presented a seminal paper on the function and role of proofs in mathematics. Following the structure he suggested, I will reflect on the roles and the limitations visuals have in my life as a mathematics teacher educator, as a mathematics teacher, and as a problem solver.

18. Rigorous Sculpture?

Glen Whitney (Studio Infinity)

22/01/2026 11:30

Can a public participatory art installation be relevant to the boundary
of current work on unsolved problems? Moreover, the question is also
pertinent in the other direction: should recent research have any
influence on public art? A case study of a Fall 2025 geometric
construction at the University of Colorado, Pueblo will reveal the
positive interactions that can occur: increased...

19. Rigorous and Flexible Illustrations: Inviting Realms of Possibilities

Hortensia Soto (Colorado State University)

22/01/2026 12:00

Using data from my own research on the teaching and learning of undergraduate mathematics (e.g., abstract algebra, linear algebra, complex analysis), I will share the framework of inclusive materialism (de Freitas & Sinclair, 2014), which embraces intra-actions with others and materials such as images, models, and illustrations via gesture, fictive motion, symbols, and other embodied actions....

6. Critique Session

Everyone