The greatest mathematician no one ever knew By Susan Hurley Corbran ‘73 Noted mathematician Herb Wilf gave that title to Sister M. Celine Fasenmyer, the humble woman who spent 73 years of her life as a Sister of Mercy and more than 34 years teaching students at Mercyhurst College. Wilf, who died in 2012, was in a good position to know. The prize-winning WZ theory he helped create grew directly out of Sister Celine’s research. And, 70 years after she wrote her doctoral thesis, other researchers are still building on her ideas.
Born and raised in Pennsylvania’s oil country, Mary Fasenmyer entered the Mercy order during her senior year in high school in 1923. She taught in parochial schools around the diocese for the next 10 years, while taking evening, weekend and summer classes until she earned a
Mother Borgia Egan – a master at grooming talented young sisters for the Mercyhurst faculty – sent Sr. Celine to the University of Pittsburgh to get her master’s and then to the University of Michigan to pursue a Ph.D. (A Mercy hospital within walking distance of the university housed sisters from all over the country while they took classes there.) She spent three years at Michigan, working with mentor Earl Rainville, Ph.D. She became interested in special functions, completed her thesis titled “Some Generalized Hypergeometric Polynomials,” earned her doctorate in 1945, and published two academic papers. Then she returned to Erie to run Mercyhurst’s math department. “My whole aim in getting my doctor’s degree was for our college,” she told Wilf. “I didn’t want to do more research, except what would help me be a better teacher.”
Her work might have languished on a library shelf forever were it not for Rainville. Fifteen years later, in 1960, he credited Sr. Celine’s work in his own book on special functions. But the full impact of Sr. Celine’s work wouldn’t be revealed until a couple more decades had passed. Wilf, of the University of Pennsylvania, and Doron Zeilberger, then at Temple University, discovered the obscure paper and built on it. Together they developed “WZ theory,” which used computers to prove many combinatorial identities. Their landmark 1996 book A=B devoted two chapters to Sr. Celine’s polynomials. WZ Theory earned the prestigious Leroy P. Steele Prize from the American Mathematical Society in 1998.
degree in mathematics at Mercyhurst. Looking back, she traced her love of
mathematics to a single high school math class. The teacher usually told the class to take a theorem and memorize it. But a substitute teacher, unfamiliar with the day’s lesson, instead suggested “Now, let’s think this through.” “From that moment on I never memorized any mathematics,” Sr. Celine told Wilf during a visit in 1993. Once she began teaching, she didn’t expect her students to memorize either. “I try to get them to think. It isn’t memorizing; it’s thinking and using the concepts.”
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