Doron Zeilberger 's Response to the Award of the 1998 Steele Prize for Seminal Contributions to Research to Herb Wilf and Doron Zeilberger

by Doron Zeilberger

[Appeared in the Program of the Award Ceremony at the Joint Math Meeting at Baltimore, Jan. 8, 1998, and in the Notices of the AMS, v.45, no. 4, (April 1998), 504-508.].

[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 MacTutur 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, Helmut Prodinger, Craig Orr, Axel Riese, 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, ( her reply ) 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 standarized [grobnerized] me. Gert Almkvist who integralized me, and Pierre Cartier, who Bourbakised me. Let them all be blessed!

Biographical Sketch

Doron Zeilberger was born on July 2, 1950, in Haifa, Israel, to Ruth (Alexander) and Yehudah Zeilberger. He received his Ph.D. in 1976, from the Weizmann Institute of Science (as a student of Harry Dym (a student of Henry McKean (a student of William Feller (a student of Richard Courant (a student of David Hilbert))))).

In 1979 he married Jane D. LeGrange (Ph.D., Physics, Illinois, 1980, currently at Lucent Tech. Bell Labs). Their children are Celia (b. 1983), Tamar (b. 1986), and Hadas (b. 1990).

In Jan. 1996 he delivered the second Gillis memorial lecture at the Weizmann Institute.

Including this Steele prize, his earnings-to-date from mathematical prizes are 2600 US dollars ((1/2)(4000)+ 500 [MAA's 1990 L.R. Ford award] + (1/2)50 [from Dick Askey and George Andrews, for a proof of the q-Dyson conjecture, joint with Dave Bressoud] + (1/2)50 [from Dick Askey for a proof of the G2 case of Macdonald's conjecture, shared with Laurent Habsieger]+ 50 [from Dick Askey, for a proof of the G2-dual case of Macdonald's conj.], 10 bottles of wine [from Xavier Viennot for a certain tree-bijection], and one book [from Mark Pinsky, for a `calculus problem'].

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

Doron Zeilberger's Homepage