By Christoph Koutschan, Manuel Kauers, and Doron Zeilberger
First Written: Feb. 23, 2010.
About a year-and-a-half ago, Manuel Kauers, Christoph Koutschan, and I gave a beautiful
semi-rigorous
proof of the famous q-TSPP conjecture that failed to impress anyone. We realized that
mathematicians do not care about "truth", they only care about that artificial art-form
called "rigorous proof". In order to humor them, we (or rather Christoph Koutschan)
worked very hard to turn this semi-rigorous proof into a fully rigorous proof.
This was a true computational tour-de-force on his part, requiring brilliant
human insight, and lots of sneaky tricks, to tame the computer to reduce a computation,
that on the face of it, looked like it would take fifty years on a future computer,
to a computation that only took a couple of weeks on a medium-size contemporary computer.
It is a real breakthrough, if we say so ourselves, not only in combinatorics, but
also in symbolic computation, and a great victory of my beloved
holonomic ansatz.
Added Jan. 25, 2011:
This was
written
up
in the Austrian
media.
ajouté Fév. 4, 2011:
en francais (par Maurice Mashaal, rédacteur en chef de Pour la Science).
Added March 2, 2011:
We are also famous in Switzerland!
Read
George Szpiro's wonderful article
(that its global and universal truths make-up for some local inaccuracies, see
my
Email message to Christoph Koutschan and Manuel Kauers).
Added March 8, 2011: Read
Tony Philips's take on math-in-the-media
and
Allyn Jackson's summary .
Added Nov. 2015: This article was the David P. Robbins
prize of the American Mathematical Society
.pdf
LaTeX source
Appeared in the
Proceedings of the National Academy of Science, v. 108, no. 6 (Feb. 8, 2011), 2196-2199.
Very Important
This article is accompanied by
supporting software and data.
Doron Zeilberger's List of Papers