’ Illustration from Sr. Celine s 1945 doctoral dissertation, “Some Generalized Hypergeometric Polynomials ”
- Before Sister Celine, there was no pattern or algorithm to tackle such proofs. “She was the frst person to devise an algorithm or a list of steps that would work for all similar proofs,”Yen said. At that time, the proof wasn’t difcult, but it still required very time consuming calculations. “We didn’t realize the power of her method until the ‘80s when Wilf and Zeilberger found her paper and started testing it with a computer,”Yen said. “When you put my research on ‘Generalized Hypergeometric Polynomials’ in a computer, marvelous things come out,” Sr. Celine refected later. Ironically, she didn’t much like computers. “I stay away from computers,” she told oral historian Larie Pintea. “Mechanical things don’t interest me.” The Celine Solution Dr. Lily Yen was a graduate student when she accompanied Wilf to Erie to meet Sr. Celine. Now a faculty member at Canada’s Capilano University and a researcher at Simon Frazier University, she says she and other researchers are still exploring and developing Sr. Celine’s ideas. She tried to put “The Celine Solution” into laymen’s terms. Mathematicians, she explains, have always had to prove very difcult identities – that the left side of an equation equals the right side, or, as Wilf and Zeilberger titled their book, A=B .
- Long-overdue recognition When Wilf visited the Mercy Motherhouse in 1993, he invited the 87-year old Sr. Celine to be his guest at the 25th anniversary meeting of the International Conference of Mathematics Researchers the next year. Wilf’s topic was “Computers Prove Identities: A 50-Year Study,” and he introduced the woman who started it all to 500 researchers from 15 countries. He described the moment later: “She said, casting a level gaze at the assemblage of distinguished mathematicians, ‘I want you all to know – I really did that work.’There wasn’t a dry eye in the house.” After her death in 1996, Zeilberger also paid tribute to the woman he calls one of his great heroes. “Sister Celine Fasenmyer was an obscure college professor, who did not publish anything beyond her thesis work, and of course never had any Ph.D. students.” Zeilberger called her “grossly under-rated” and added “Sister Celine’s greatness only started to emerge with the WZ theory … I am sure that the future will prove her even greater.” In his foreword to A=B (published in 1996), Donald Knuth wrote, “Science is what we understand well enough to explain to a computer. Art is everything else we do. During the past several years an important part of mathematics has been transformed from an Art to a Science: No longer do we need to get a brilliant insight in order to evaluate sums of binomial coefcients, and many similar formulas that arise frequently in practice; we can now follow a mechanical procedure and discover the answers quite systematically.” And that procedure owes its origins to Sr. Celine Fasenmyer.
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