Steele Prize 1998 for Wilf and Zeilberger

[thk (Tom H. Koornwinder)]

On January 13, 1998 I received a message from Doron Zeilberger
to his E-friends that Herbert Wilf and Doron Zeilberger were awarded
with the 1998 Steele prize. He added the responses of Herbert Wilf
and himself to this prize, see below. I congratulate Herbert and
Doron with this well-deserved award.

		Tom Koornwinder

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Response to the Award of the 1998 Steele Prize 
 
by Doron Zeilberger <zeilberg@euclid.math.temple.edu>
 
[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, 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  standarized [grobnerized] me. Gert Almkvist who integralized 
me, and Pierre Cartier, who Bourbakised me. Let them all be blessed!

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Response of Herbert Wilf <wilf@math.upenn.edu> :
 
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.