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Organizing Committee
Pitzer College
Fashion institute of technology
Elon University
University of Warwick
TU Delft
James Madison University
Abstract
Illustration reveals the hidden structures of mathematics, broadening access to its inherent beauty and pushing the boundaries of research. Here two disciplines are interwoven: on the one hand, the art and craft of presenting ideas and on the other hand, the creativity and scholarship of creating mathematics. This program facilitates research and collaboration on these topics, both between and within these groups, and to promote professional support and recognition both for illustration and for building the infrastructure needed for its creation.
We invite both returning and new members to the Illustrating Mathematics community to this workshop, which will bring together mathematicians, and practitioners from the arts. We seek to expand our community to include a more diverse group of faculty, including those from non-R1 institutions and who identify as members of underrepresented and minoritized groups.
We invite both returning and new members to the Illustrating Mathematics community to this workshop, which will bring together mathematicians, and practitioners from the arts. We seek to expand our community to include a more diverse group of faculty, including those from non-R1 institutions and who identify as members of underrepresented and minoritized groups.
Close-up of a CNC routed Cannon-Thurston map for the SnapPy s227 by Saul Schleimer, Henry Segerman and Will Segerman
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Workshop Schedule
Monday, August 11, 2025
9:20 - 9:30 AM EDT
Welcome
11th Floor Lecture Hall
Nathaniel Whitaker, ICERM/ University of Massachusetts Amherst
9:30 - 9:55 AM EDT
Variants of the 15-puzzle and the effects of holonomy
11th Floor Lecture Hall
Speaker
Henry Segerman, Oklahoma State University
Session Chair
Laura Taalman, James Madison University
Abstract
I'll discuss some variants of the classic sliding tile "15 puzzle" that involve holonomy - the phenomenon of traveling around a loop in a curved surface and coming back rotated. I'll demonstrate physical puzzle designs with positive and with negative curvature, and discuss design considerations and consequences.
10:05 - 10:30 AM EDT
Enumerating Truchet tiles on the faces of polyhedra
11th Floor Lecture Hall
Speaker
Peter Kagey, Cal Poly Pomona
Session Chair
Laura Taalman, James Madison University
Abstract
In joint work with Bill Keehn of the Prison Mathematics Project, we generalize a tiling problem in enumerative combinatorics that was perhaps first considered by M.C. Escher. While Escher enumerated tilings on the 2×2 torus grid, we count tilings on the faces of Platonic, Archimedean, and Catalan solids.
10:40 - 11:00 AM EDT
Coffee Break
11th Floor Collaborative Space
11:00 - 11:25 AM EDT
Perspectives on Algebraic Starscapes: How Aesthetic Choices Lead to Mathematical Insight.
11th Floor Lecture Hall
Speaker
Gabriel Dorfsman-Hopkins, St. Lawrence University
Session Chair
Nancy Scherich, Elon University
Abstract
An algebraic starscape is a plot of algebraic numbers–complex numbers which arise as solutions to polynomial equations with rational coefficients. There are many mathematical or artistic choices one can make when creating an algebraic starscape, from choosing polynomials to sample from, to deciding how to color and size the algebraic integers you obtain. In this talk, we will explore some of these different perspectives, observing that the visual outputs can vary widely, and illustrating how one can use this viewpoint to extract new arithmetic results.
11:35 AM - 12:00 PM EDT
Illustrating Mathematics in The Mathematical Intelligencer
11th Floor Lecture Hall
Speaker
Karen Parshall, University of Virginia
Session Chair
Nancy Scherich, Elon University
Abstract
The Mathematical Intelligencer, published by Springer Nature, is something of a rarity among mathematics journals. It aims not only to inform but also to entertain a broad mathematically literate audience. It considers all aspects of “mathematics” from the technical to the social to the historical to the poetic to the artistic. It is also printed in color and specifically focuses on illustrating mathematics in engaging ways. Using examples from the journal, this talk will explore how the Intelligencer seeks to draw its audience into its pages.
12:10 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:25 PM EDT
Embodying Mathematics - Virtual
Virtual
Virtual Speaker
Margaret Wertheim, Institute For Figuring
Session Chair
Saul Schleimer, University of Warwick
Abstract
Mathematics is usually thought of as a symbolic subject that we represent and learn in terms of equations and deductive reasoning. But across the globe, many cultures have developed practices in which sophisticated mathematical concepts are embodied in material forms. Examples include Islamic tiling patterns, African fractal designs, Polynesian sand diagrams, Celtic+Aztec knots. All these beautiful handicraft traditions contain knowledge about deep mathematical principles that long predates the formalistic discovery of such knowledge by Western mathematicians. In Margaret Wertheim's work has been exploring representations of hyperbolic geometry through the art of crochet, which enables crafters to explore the topic of non-Euclidean mathematics in their hands. In this talk, science writer and artist Margaret Wertheim will look at how math is embodied in material practices, and how it can be regarded as a form of artisanal play.
2:35 - 3:00 PM EDT
Turning Math into Dance
11th Floor Lecture Hall
Speaker
Nancy Scherich, Elon University
Session Chair
Saul Schleimer, University of Warwick
Abstract
I will share my creative process to take a mathematical theorem and create a publicly accessible dance video explaining the theorem.
3:10 - 3:30 PM EDT
Coffee Break
11th Floor Collaborative Space
3:30 - 3:55 PM EDT
Show and Ask
Other - 11th Floor Lecture Hall
4:00 - 4:45 PM EDT
Effective Online Publishing of Mathematical Illustrations
11th Floor Lecture Hall
Speaker
Scott Vorthmann, self-employed
Session Chair
Audrey Nasar, Fashion institute of technology
Abstract
A mathematical illustration, like any other information, has more impact when more people see it, and there is no better vehicle for exposure than a web page, particularly when optimized for social media sharing. I'll describe some simple techniques for creating and sharing such web pages. I'll further focus specifically on sharing interactive 3D models on the web, without writing any Javascript code. Finally, I'll introduce my own free geometry application, vZome, and how it can simplify web publishing of certain kinds of 3D models even further.
Request Reimbursement
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
- ORCID iD
- As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
- Acceptable Costs
- 1 roundtrip between your home institute and ICERM
- Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
- Ground Transportation to and from airports and ICERM.
- Unacceptable Costs
- Flights on non-U.S. or non-E.U. airlines
- Flights on U.K. airlines
- Seats in economy plus, business class, or first class
- Change ticket fees of any kind
- Multi-use bus passes
- Meals or incidentals
- Advance Approval Required
- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Flights on a Swiss, Japanese, or Australian airline
- Arriving or departing from airport other than PVD/BOS or home institution’s local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Travel Maximum Contributions
- New England: $350
- Other contiguous US: $850
- Asia & Oceania: $2,000
- All other locations: $1,500
- Note these rates were updated in Spring 2023 and supersede any prior invitation rates.
- Reimbursement Requests
Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via Google Maps PDF
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6–8 weeks after all documentation is sent to ICERM. All reimbursements are reviewed by multiple Brown University offices.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. No submissions are accepted after six months.