Topic #4 ------------ OP-SF NET 5.1 ------------ January 15, 1998 ~~~~~~~~~~~~~ From: Tom H. Koornwinder
Subject: Wilf and Zeilberger win Steele prize On January 13, 1998 I received a message from Doron Zeilberger to his E-friends that Herbert Wilf and Doron Zeilberger were awarded the 1998 Steele prize. He added the responses of Herbert Wilf and himself to this prize, see below. I congratulate Herbert and Doron on this well-deserved award. Tom Koornwinder ------------------------------------------------ Response to the Award of the 1998 Steele Prize by Doron Zeilberger [Generic Thanks and Expressions of Astonishment.] On 11:05 PM, Dec. 24 (sic!) 1988, Herb Wilf called me up, and with Wilfian enthusiasm, told me how the beautiful one-line proofs of certain classical identities, generated by my beloved computer, Shalosh B. Ekhad, could be made even prettier, and how to obtain as a bonus, a `dual identity', that is often much more interesting than the one originally proved. Thus was born WZ theory. WZ theory has taught me that computers, by themselves, are not yet capable of creating the most beautiful math. Conversely, humans do much better math in collaboration with computers. More generally, combining different and sometimes opposite approaches and viewpoints will lead to revolutions. So the moral is: Don't look down on any activity as inferior, because two ugly parents can have beautiful children, and a narrow-minded or elitist attitude will lead nowhere. We live in the great age of the democratization of knowledge, and even of that elitist ivory-tower called mathematics. Whoever would have believed, thirty years ago, that a 1988 Steele prize would go to Rota for his work in `combinatorics' (a former slum), and whoever would have believed ten years ago that a 1998 Steele prize would go to W and Z for their work on `binomial coefficients identities' (hitherto a slum squared). The computer-revolution, and especially the World Wide Web, is quickly making mathematics accessible and enjoyable to many more people. Especially commendable are the wonderful website of Eric Weisstein's `Eric Treasure Troves', Steve Finch's pages on mathematical constants, the Sloane-Plouffe On-Line Encyclopedia of Integer Sequences, Simon Plouffe's `Inverse Symbolic Calculator', and St. Andrews University's MacTutor site on the history of mathematics. It is very important to make information, in particular mathematical, freely accessible. The pioneering, and extremely successful, Electronic J. of Combinatorics, created by Herb Wilf in 1994, should be emulated. It is very regrettable that the American Mathematical Society has subscription-only electronic journals, and that the electronic versions of its paper journals are only available to paper-subscribers. It is a disgrace that MathSciNet is only viewable for paying customers, thereby making its contents unsearchable by public search-engines. On the positive side, the AMS has been very efficient in taking advantage of the electronic revolution, and the free ERA-AMS, under the leadership of Svetlana Katok, is a real gem! I am really happy, not only for myself and Herb, but also because of the recognition that the field of hypergeometric series (alias binomial- coefficients identities) is hereby granted. There are so many giants on whose shoulders we are standing. Guru Dick Askey, q-Guru George Andrews, and Guru Don Knuth who preached the gospel from the continuous and discrete sides. Sister Celine Fasenmyer, a non-standard, yet very tall, giant. Hacker Bill Gosper who deserves this prize even more, and many others. I should also mention our collaborators in this area: Gert Almkvist and Marko Petkovsek, and the beautiful work of Tewodros Amdeberhan, Frederic Chyzak, J. Hornegger, Bruno Gauthier, Ira Gessel, Wolfram Koepf, Christian Krattenthaler, John Majewicz, Istvan Nemes, John Noonan, Sheldon Parnes, Peter Paule, Bruno Salvy, Marcus Schorn, Volker Strehl, Nobuki Takayama, P. Verbaeten, Kurt Wegschaider, and Lily Yen. Finally, I must mention my main influencers, in roughly chronological order. My terrific seventh-grade math teacher, Devorah Segev, and my great eighth-grade history teacher (and principal), Matityahu Pines. My cousin Mati Weiss, who showed me Joe Gillis's `Gilyonot leMatematika'. Joe Gillis, who in my early teens, first made me into a mathematician through his `Gilyonot leMatematika'. My advisor, Harry Dym, who initiated me into research. My god-advisor, Dick Duffin, who discretized me. Leon Ehrenpreis, who dualized me. Joe Gillis (again!) who deranged me. Gian-Carlo Rota who umbralized me. Dick Askey, who hypergeometrized me. George Andrews who q-ified me. Herb Wilf (the same Herb!) who combinatorized me. Dominique Foata, who bijectified me. Jet Wimp, who asymptotized me. Xavier Viennot, who Schutzenbergerized me. Marco Schutzenberger, who formalized me. Bruno Buchberger, who basically standardized [grobnerized] me. Gert Almkvist who integralized me, and Pierre Cartier, who Bourbakised me. Let them all be blessed! ------------------------------------------------- Response of Herbert Wilf : I am deeply honored to receive the Leroy P. Steele Prize. I might say that doing this research was its own reward -- but it's very nice to have this one too! My thanks to the Selection Committee and to the AMS. Each semester, after my final grades have been turned in and all is quiet, it is my habit to leave the light off in my office, leave the door closed, and sit by the window catching up on reading the stack of preprints and reprints that have arrived during the semester. That year, one of the preprints was by Zeilberger, and it was a 21st century proof of one of the major hypergeometric identities, found by computer, or more precisely, found by Zeilberger using his computer. I looked at it for a while and it slowly dawned on me that his recurrence relation would assume a self dual form if we renormalize the summation by dividing first by the right hand side. After that normalization, the basic "WZ" equation F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k) appeared in the room, and its self-dual symmetrical form was very compelling. I remember feeling that I was about to connect to a parallel universe that had always existed but which had until then remained well hidden, and I was about to find out what sorts of creatures lived there. I also learned that such results emerge only after the efforts of many people have been exerted, in this case, of Sister Mary Celine Fasenmyer, Bill Gosper, Doron Zeilberger and others. Doing joint work with Doron is like working with a huge fountain of hormones - you might get stimulated to do your best or you might drown. In this case I seem to have lucked out. It was a great adventure.