In Memoriam: Sister Celine Fasenmeyer (1906-1996)

Sister Celine’s supervisor Earl Rainville published a book Special Functions two chapters (Chapters 14 and 18) of which presented the results from Sister Celine’s thesis. Although Rainville believed: … that there was some very pretty mathematics going on. … the significance of the results was still not properly recognised.

It was only in 1978 that Doron Zeilberger realised the significance and used Sister Celine’s methods to prove combinatorial identities. Another mathematician Herbert Wilf, Professor of Mathematics at the University of Pennsylvania, read Zeilberger’s paper: “I remember feeling that I was about to connect to a parallel universe that had always existed but which until then had remained very well hidden, and I was about to find out what sort of creatures lived there.”

Wilf and Zeilberger then worked to push Sister Celine’s methods even further to produce what today is called "WZ theory". It allows an extremely elegant proof of certain classes of combinatorial identities and also provides an algorithm to generate new identities from old ones.