Penn State

Peter Wilf - Professor of Geosciences, Penn State University Park

Book Title: A=B

Author: Marko Petkovšek, Herbert S. Wilf, Doron Zeilberger

Book Description:

 In A=B, my father and his colleagues presented revolutionary breakthroughs in automating, via computational algorithms, the discovery and proof of a large class of math problems, combinatorial identities. Previously, centuries of labor had gone into proving identities one at a time. The work A=B showed, in very lively and engaging style, that most of the proofs can instead be done by machines, no ingenuity required, and demonstrated that each identity was paired with a counterpart, thus bringing to light large numbers of previously unknown identities. The functions that validate the part and counterpart identities quickly became known as Wilf-Zeilberger (W-Z) pairs.


An article about my father's role in this work was titled How the Grinch Stole Mathematics (B.A. Cipra, Science 245, 595, 1989). Indeed, A=B opens with the following, bold and absolutely correct statement: "One of the major themes of the past century has been the growing replacement of human thought by computer programs. Whole areas of business, scientific, medical, and governmental activities are now computerized, including sectors that we humans had thought belonged exclusively to us."


My father believed that knowledge should be freely available to all, and in 1994 he cofounded, with Neil Calkin, The Electronic Journal of Combinatorics, which was one of the first electronic journals and also the first open-access journal in mathematics. Originally greeted with much skepticism, that journal now enjoys very high prestige. In keeping with this tradition, A=B itself can be downloaded at no cost, currently at


I remember well the moments of brilliant insight when my father first made these discoveries, which have inspired me ever since.


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