This week, we got in touch with Professor Natalie Priebe Frank, who has been teaching at Vassar’s Mathematics and Statistics Department since 2000. Her research focuses on the beauty of hierarchical tilings—mathematical models for quasicrystals, physical solids.
The Miscellany News: What drew you to the subject of math and a career in education?
Natalie Priebe Frank: I was always good at math: My mom saved a note from my first grade teacher that says “Natalie is always asking for harder problems.” For some reason though, I thought I wanted to be a psychiatrist. In college I realized I didn’t like the nebulous nature of the research the psychology faculty were doing at the time, so I switched to math.
One reason I picked math was that it would open up a lot of career opportunities for me that wouldn’t involve graduate school. But when I got involved in undergraduate research, I realized that I might like to do mathematics for a living. So I got a PhD, did some postdocs and then got incredibly lucky by getting my tenure- track position at Vassar.
The Misc: What do you love about Vassar?
Frank: The community, and especially the students. Semester after semester, my classrooms are full of smart, interesting people, and I get to show them lots of cool concepts. Even students who end up in my classes to fulfill a requirement are willing to go deep to appreciate the beauty of the ideas. And although not everyone feels this way, I’ve always felt supported here by my department and by the College.
The Misc: Could you tell us a bit about the courses that you’re offering next semester?
Frank: It looks like I’ll be teaching Real Analysis, which is a required course for the math major and is of interest to our graduate school–bound econ majors. Real Analysis is basically calculus on steroids. It’s a hard class, but I love teaching it.
The Misc: Do you have any research project that you’re working on now?
Frank: I study tilings, which are what you think they are: interesting ways to lay down tiles next to one another. I mostly study quasicrystalline tilings, whose structure is sufficiently orderly that you can study them, but not so orderly as to be boring like a checkerboard.
Tilings are good models for the atomic structure of crystals and quasicrystals, and of course chemists study atomic structure via diffraction. So, my collaborators and I have spent a lot of time figuring out what the diffraction of various tilings would be. This year I’ve finished two papers: one on diffraction, and one that is a graduate- level introduction to the study of tilings as I know it.
The Misc: What do you enjoy doing the most outside of the classroom?
Frank: My life outside of Vassar centers on my husband and two sons, ages 12 and 15. We’re all into sports (mine are volleyball and tennis), and I have a big yard where I grow lots of flowers but no food. When I get inspired I make art. I’m also a big fan of napping.
The Misc: Could you elaborate on some of the instances that you find math particularly interesting/applicable in everyday life?
Frank: Math is literally everywhere around us, and of course it is fundamental to science and technology. I know a little bit about the math behind lots of things, and I think about it as I move through the world. But one thing that is especially apparent and beautiful is symmetry.
You see symmetry in the petals of flowers, the leaves of ferns and in the branches of trees. You see it in the amazing animals populating coral reefs. And you see it in art and design. Tilings are everywhere, forming everything from the patterns on the heating grates in Rocky to the windows in the library to the brake lights on your car. Spectacular tilings and patterns are found in Islamic art, and Escher launched an exhaustive study of the mathematics of tilings in order to construct his famous tilings.
The Misc: Would you like to recommend a math-related book to the students?
Frank: A nice coffee-table book is “The Symmetries of Things,” by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss. If you want to get serious about tilings, try “Tilings and Patterns” by Branko Grunbaum and G. C. Shephard. If you’d like to have some fun with myriad different approaches to the binomial theorem (including limericks and music, in addition to serious math), try “Exercises in (Mathematical) Style” by Vassar’s own John McCleary.
The Misc: Are there other activities that encourage students to engage with math?
Frank: I’ve been thinking recently that I’d like to get students involved in art and mathematics. There’s the kind of art I do that is pictured with me in this article, which is based on my research. But there are also many other ways to do art with math, and I’d be interested in exploring any of it with students. In the fall, look for meetings of Vassar’s chapter of the Association for Women in Math, because they’ll be sponsoring it. We are hoping to run studio-type workshops if there is enough interest.