### Herb Wilf wins 1998 AMS Steele Prize

Herb receives the prize from AMS President Arthur Jaffe as Doron Zeilberger looks on.

On Thursday, January 8, 1998, the American Mathematical Society announced that Professor Herb Wilf, of Penn's Mathematics Department, was awarded a Leroy P. Steele Prize for Seminal Contribution to Research. He shared the award with Doron Zeilberger of Temple University for their joint work on "Rational functions certify combinatorial identities", a paper that appeared in the Journal of the AMS in 1990.

The work for which the prize was awarded involves a new method of finding computer- assisted proofs of formulas that arise in many areas of mathematics and physics. These formulas are of the form A=B, where B is a very complicated expression involving sums and products of many terms, and A is a relatively simple expression. An unprecedented aspect of this proof technique involves how the computer is used: Up to now, mathematicians have been reluctant to accept computer-assisted results as certain, since there is usually no way to verify that the computer program is error-free and that the computer itself has functioned precisely as programmed. But the Wilf-Zeilberger method has the computer work to provide a "validity certificate" for A=B -- this is an auxiliary formula that can be used by humans to check by hand that the equation A=B is correct without having to verify that the computer performed its thousands of operations correctly. The method can also supply the simplified expression A when it is not known (or conjectured) in advance.

The eminent Stanford mathematician and computer scientist Donald Knuth has said of these results: "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....I fell in love with these procedures as soon as I learned them, because they worked for me immediately....The success rate was astonishing."

Herb Wilf is the Thomas A. Scott Professor of Mathematics. He has been at Penn since 1962. He is the author of several books and more than 100 research and expository papers. He has been editor-in-chief of the American Mathematical Monthly, co-founded (with Knuth) the Journal of Algorithms, and co-founded the Electronic Journal of wCombinatorics in 1994. He is a Lindback Award winner at Penn, and in 1996 he received the Haimo Award of the Mathematical Association of American for Distinguished Teaching of College or University Mathematics. He has supervised more than twenty Ph.D. students.