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Diana J. Davis

Instructor in Mathematics
Diana Davis

"I only have this one life."


B.A. Williams College

M.S. Brown University

Ph.D. Brown University


Diana Davis grew up in seacoast New Hampshire. She was a four-year student at Exeter, a three-season captain and a Cox medalist. After completing a mathematics major at Williams College, she returned to Exeter for a year as an intern in the Math Department, during which she lived in Dunbar and coached running and crew. 

She earned a Ph.D. in mathematics from Brown University in 2013, on the geometry of surfaces. While a graduate student, she won an international award for the video she created to explain her Ph.D. thesis result using colors and dance, which "went viral" in the mathematics community. She then did a postdoc at Northwestern University, followed by visiting professorships at Williams College and Swarthmore College. She taught algebra at Exeter Summer for five years between 2008 and 2014.

Dr. Davis is passionate about transforming math courses, at every level of education, to active learning. To teach her own college courses, she built on Exeter's materials, modifying them and also writing her own problem books from scratch. Since 2012, she has taught courses for high school math teachers at Exeter's Anja S. Greer Conference on Mathematics and Technology, on how to write and teach problem-based curricula. In 2016, she did a study comparing the pedagogical effectiveness of discussion-based and lecture-based math courses. She showed that while students in the two types of courses learned a similar amount of material, students in discussion-based courses learned more communication skills, and chose to take significantly more math classes in subsequent semesters than those in lecture-based courses. 

In an effort to bring the beauty of mathematics to a wider audience, and to show the many ways in which we can illustrate a mathematical idea, Dr. Davis recently published a book on mathematical illustration. She has also published over a dozen research papers, mostly on aspects of mathematical billiards and dynamical systems, and has given over 100 talks in 22 states and nine countries. Dr. Davis has spent six summers leading groups of high school and college students in original research. Most recently, she has been leading a research team of several dozen students working on the problem of detecting and combating political gerrymandering, and applying the same techniques to detecting and combating segregation in school districting. 

Outside of teaching and creating mathematics, she enjoys long-distance running, recreational sailing, traveling, and thinking about how to build community and create a sustainable world.



Illustrating Mathematics, American Mathematical Society (2020).

Dynamics Done with your Bare Hands, European Mathematical Society (2017). With Bryce Weaver, Roland Roeder and Pablo Lessa.


Inquiry-based learning in a first-year honors course, PRIMUS, 28(5), 387-408 (2018).

The shape of Thurston's master teapot, Advances in Mathematics (2020). With Harrison Bray, Kathryn Lindsey and Chenxi Wu.

How to hear the shape of a billiard table, Annales de l'Institut Fourier (2020). With Aaron Calderon, Solly Coles, Justin Lanier and Andre Oliveira. 

Periodic paths on the pentagon, double pentagon and golden L (2019). With Samuel Lelièvre.

The typical measure preserving transformation is not an interval exchange transformation (2018). With Jon Chaika.

Tiling billiards on triangle tilings, and interval exchange transformations, Bulletin of the London Mathematical Society (2019). With Paul Baird-Smith, Elijah Fromm and Sumun Iyer. 

Periodicity and ergodicity in the trihexagonal tiling, Commentarii Mathematici Helvetici (2019). With W. Patrick Hooper.

Cutting sequences on Bouw-Möller surfaces: an S-adic characterization, Annales scientifiques de l’Ecole normale superieure (2019). With Irene Pasquinelli and Corinna Ulcigrai.

Negative refraction and tiling billiards, Advances in Geometry, 18(2), 133-159 (2018). With Kelsey DiPietro, J.T. Rustad and Alexander St Laurent.

Average pace and horizontal chords, The Mathematical Intelligencer, 39(4), 41-45 (2017). With Keith Burns and Orit Davidovich. 

Geodesic trajectories on regular polyhedra, Discrete Mathematics, 340(1), 3183-3196 (2017). With Victor Dods, Cynthia Traub and Jed Yang.

Billiards and Flat Surfaces, A Snapshot of Modern Mathematics for Oberwolfach, (2014). Also available in German.

Cutting sequences on translation surfaces, New York Journal of Mathematics, Volume 20, 399-429 (2014).

Cutting sequences, regular polygons, and the Veech group, Geometriae Dedicata, 162(1), 231-261 (2013).

Periodic trajectories in the regular pentagon, Moscow Mathematical Journal, vol. 3 (2011). With Dmitry Fuchs and Sergei Tabachnikov.

Double Bubbles in Gauss Space and Spheres, Houston Journal of Mathematics, 34(1) (2008). With Joseph Corneli, Ivan Corwin, Stephanie Hurder, Vojislav Sesum, Ya Xu, Elizabeth Adams, Michelle Lee, Regina Visocchi and Neil Hoffman.

Isoperimetric Regions in Gauss Sectors, Rose-Hulman Undergraduate Mathematics Journal, 8(1) (2007). With Elizabeth Adams, Ivan Corwin, Michelle Lee and Regina Visocchi.