Sarah J. Greenwald: The Mathematician on the Blackboard
Somewhere in an episode of *Futurama*, on a blackboard in the background, there is a piece of mathematics labelled the "Greenwaldian theorem." It is there because the show's executive producer, David X. Cohen, put it there, as an acknowledgement to the mathematician who had spent years documenting the jokes his writers were burying in their own scripts. Sarah J. Greenwald is a Riemannian geometer who works on orbifolds. She is also the person who established that a Sunday-night cartoon is one of the most effective mathematics classrooms in America.
Charlotte, Union, Penn
Greenwald was born in Charlotte, North Carolina, in 1969. She began in engineering and switched to mathematics on an advisor's recommendation — she wanted, by her own account, to understand the principles underlying the equations rather than merely apply them. She took a BS in mathematics from Union College in 1991, graduating summa cum laude, and a PhD from the University of Pennsylvania in 1998 under Wolfgang Ziller.
Her dissertation was titled *Diameters of Spherical Alexandrov Spaces and Constant Curvature One Orbifolds*. Orbifolds are the natural objects when a space has symmetry with fixed points — a cone rather than a smooth sheet, a space that looks locally like ordinary geometry divided by a finite group. They are unavoidable in modern geometry and in the physics of spacetime, and they behave in ways that Riemannian intuition does not predict. Greenwald's work concerned how large such a space can be, measured by diameter, given curvature constraints. Her broader research interest is stated plainly on her faculty profile: the geometry of the universe.
Appalachian State
She is professor of mathematics at Appalachian State University and a faculty affiliate in gender, women's and sexuality studies — a joint appointment that is not decorative. Her published research interests cover the connections between mathematics and society, women and minorities in mathematics, the scholarship of teaching and learning, and popular culture. She is associate editor of the Association for Women in Mathematics newsletter, and served as an elected Member at Large of the American Mathematical Society Council from 2021 to 2024.
Her stated conviction about the subject is broad rather than narrow: "Mathematics is pervasive in modern society," she has written; "it is almost impossible to find an academic field of study that does not use mathematics."
The Simpsons Problem
*The Simpsons* has, across decades of episodes, kept smuggling mathematics into its scripts — equations on chalkboards, allusions dropped into dialogue, formulae flashed on screen for a second and a half and never explained. Greenwald, with Andrew Nestler, built simpsonsmath.com to catalogue and explain these references, and turned them into teaching material.
The insight underneath is pedagogically serious. Students arrive in a mathematics classroom with defences up: the subject is difficult, alien, and something other people are good at. A joke in a show they already watch dismantles that in a way no lecture can, because it establishes that mathematics is part of the culture they already inhabit rather than a foreign country. The work led directly to a parallel project on *Futurama*, which proved if anything more mathematically ambitious, and to Greenwald's appearance in the documentary *'Futurama': Bite My Shiny Metal X*, plus consulting on *Flatland: The Movie*.
Access
The third strand of her career is structural. With colleagues Amber Mellon and Jill Thomley she created a Girl Scout mathematics merit badge, and produced a video interview series featuring women in STEM careers who had been Girl Scouts — a design that closes the loop, showing the girls earning the badge what the people who earned it before them went on to do.
She has also worked as an editor of reference material at scale, co-editing with Thomley the three-volume *Encyclopedia of Mathematics and Society*, named Best Reference of 2011 by *Library Journal*, along with a six-volume Singles edition; and co-editing the 2018 Springer volume *Women in Mathematics: Celebrating the Centennial of the Mathematical Association of America*.
The recognitions map onto exactly this profile. She received the Mathematical Association of America's Henry L. Alder Award, which honours distinguished teaching by a beginning college faculty member, in 2005; the Association for Women in Mathematics Service Award in 2018; election as an AWM Fellow in 2020; and appointment as an MAA Pólya Lecturer for 2021–22.
Why Sarah Is Called a Genius
The sources do not use the word and it would be inaccurate to press it. What the record shows is a working geometer of solid specialist standing who has done something genuinely original in an adjacent domain — and the honest account is that the second thing, not the first, is why anyone outside Riemannian geometry has heard of her.
The specific quality is a kind of translational imagination. Recognising that television cartoons contain a usable curriculum, and then doing the unglamorous work of cataloguing, verifying and building teaching material from it, requires seeing pedagogical value where the profession saw noise. It is a modest-seeming insight with large consequences: it changed how a subset of mathematicians think about outreach, and it is why a fictional theorem carries her name on a *Futurama* blackboard. The Girl Scout badge and the interview series show the same instinct — locate the point where a person's existing life already touches mathematics, and build the bridge there rather than expecting them to cross unaided.
The counter-case is straightforward. Her geometric research is specialist and well regarded rather than field-defining; no theorem of hers has redirected Riemannian geometry, and the Greenwaldian theorem is a television joke, not a result. Her awards are for teaching, service and advocacy — the Alder, the AWM Service Award, the AWM Fellowship — which is an accurate reflection of where her distinction lies and not a lesser category, but it is a different category from research eminence. The truthful description is sustained excellence in mathematics education and public engagement, resting on a genuine research foundation, rather than acclaimed mathematical genius.
Legacy
The simpsonsmath.com material is used in classrooms well beyond Appalachian State, and the approach it demonstrated — mining popular culture for legitimate mathematical content — has been widely imitated. The *Encyclopedia of Mathematics and Society* remains a standard reference. The Girl Scout badge is still earned. And there is a durable, slightly absurd monument: for as long as anyone rewatches *Futurama*, a theorem with her name on it will keep flashing past in the background of somebody else's joke.
Achievements
- Held posts at Appalachian State University
- Fields: mathematics, Riemannian geometry and gender
