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