SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

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

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
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.

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