The Erwin Schrödinger Institute for Mathematical Physics (ESI) in Vienna, Austria was certainly not on the radar screen of Bill Cable, ’10, or Dan Rudary, ’10, when they enrolled at the University of Richmond in the fall of 2006.

Cable, an English major, and Rudary, a history major, embraced Richmond’s liberal arts curriculum from day one and made the most of an undergraduate research opportunity in the mathematics department. Still, neither student expected that their mathematical research would take them to the ESI, where they would become the first undergraduates ever to give a talk at the distinguished research institution.  

Cable and Rudary are both members of the political science department’s mock trial team and share the goal of attending law school after graduation; they both took a detour, however, when they decided to participate in the LURE program.

LURE, which stands for Long Term Undergraduate Research Experience, offers students the opportunity to participate in mathematical research over the course of two summers. Cable and Rudary were recruited by mathematics professor Della Fenster, whose research focuses on the history of American mathematics in the late 19th and early 20th centuries and who is currently writing a biography of the mathematician Leonard Dickson.

Fenster asked Cable and Rudary to help her on research projects related to the biography. Specifically, Cable would work with her in an investigation of the broader intellectual milieu as a frame of reference for the development of turn-of-the-century American mathematics, while Rudary would explore the mathematical community through reviewing the correspondence of two noted mathematicians, Leonard Dickson and Oswald Veblen.

During their first summer of research, Fenster, Cable, and Rudary took a fully funded trip to the American Mathematical Society Archives in Providence, R.I.

“The time in the archives, with the three of us huddled over one original document after another, provided an especially meaningful teaching opportunity,” said Fenster. “As I introduced Bill and Dan to various people, places and events in the early American mathematical community through these primary sources, they got a very personal look at the key players in this development. The opportunity to travel together created extended time for conversation and discussion in and outside of the archives.”

The conversation continued back in Richmond as they read seminal texts, articles and, especially, primary source materials for these projects.  

“Beginning historical research with an out-of-town trip to an archive lays an impossibly perfect foundation for meaningful research,” said Fenster.

Early on, Cable came up with the idea of using Frederick Jackson Turner’s Frontier Thesis as a lens to study the rise of the American mathematical community. While Turner’s thesis has been applied to many historical studies of America, no one had yet thought to explore the development of mathematics within Turner’s framework.

“Bill is neither a mathematics major nor a history major; he is an English major with an enviable amount of intellectual curiosity and skill,” said Fenster. “His fresh perspective opened up an entirely new way of thinking about Dickson, this mathematician I have studied for more than a decade, and his influential colleagues in the burgeoning American mathematical community.”

Cable’s work investigated how three fundamental figures in this community, E.H. Moore, Leonard Dickson and Oswald Veblen, embodied the characteristics outlined by Turner. Research on the broader intellectual community in the development of turn-of-the-century American mathematics provided a natural jumping off point to study the contributions of Veblen and Dickson.

Using previously undocumented correspondence, Rudary explored their contributions to the American mathematical community through the critical topics Veblen and Dickson took up in their correspondence, including publication issues, World War I and mathematics institutes.

“Through this approach, Dan’s research also advanced our understanding of the very private Dickson through the very public Veblen,” said Fenster. “His research fit beautifully within the broader context provided by Bill’s work.”

Together, Cable and Rudary composed a 30-minute talk for the LURE Undergraduate Research Conference at Central Michigan University in August of 2008, which began with a discussion of the American mathematical community as a whole and then focused on the Dickson-Veblen correspondence. Thanks to their mock trial experience, they gave a presentation as compelling as their research.

Following their talk, the ESI invited Cable and Rudary to join Fenster in offering a joint workshop presentation on mathematics at the turn of the 20th century. In January 2009, the trio travelled together again, this time to Vienna, to present their work. The results of their research and subsequent presentations have also led to manuscripts that will be submitted for publication.
“When I was in Vienna and at the ESI, I couldn’t get over the fact that we were undergraduates participating in a European conference attended by distinguished and experienced scholars,” said Rudary. “This was all possible because of Dr. Fenster’s proactive and engaging attitude, which gave us so many opportunities and set no limits. One of the highlights of coming to Richmond, for me, has been the opportunity to take on a summer research experience like ours and turn it into an adventure, which led me halfway across the world. It really says something about how seriously this university takes undergraduate research and how Richmond students have to opportunity to do what most students can't do until they begin their graduate or Ph.D. work.”