By Doron Zeilberger
Written: Nov. 26, 2001
Appeared in
"New Progress in Difference Equations", edited by
Bernd Aulbach, Saber Elaydi, and Gerry Ladas,
(Proc. ICDEA 2001), Bernd Aulbach, ed., Taylor and Frances, London.
This is the transcript of a plenary talk that I gave at the ICDEA 7
(2001) meeting that took place at Augsburg this summer.
It has the bare outline of an ultrafinitist philosophy of mathematics
and argues for Discrete supremacy.
The conference itself, orgranized by Bernd Aulbach, was a
huge success, with lots of stimulating talks.
Gene Klotz kindly took pictures of this historic event:
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Added May 2, 2020: Read the very
interesting article by José Antonio Vallejo
Added Feb. 18, 2021: Frank Calegari found a nice
argument
explaining why this particular form of the suggested elementarly proof in pp. 6-7 of the paper
could not work. I still believe that there exists an elementary "one-line" proof of FLT, using
the same general ideas, but the "search space" has to be enlarged.
Added Dec. 31, 2022: read Richard Kaufman's Ode to Finitisn,
.pdf
.ps
.tex
Added Jan. 21, 2002: I just finished reading a very interesting
article by Saber Elaydi (selaydi@trinity.edu),
entitled ``Is the world evolving disretely'' that makes a similar point,
but much more convincingly, about the discreteness of the
physical world.
Added April 24, 2006: I just gave a colloquium talk loosely based on
this article to the brilliant students and faculty of Swarthmore
College's Math Dept. It was such a nice day that I asked to give the
talk outside, and luckily their wall was meant to be written on.
The talk was entitled "A diatribe against the so-called infinity"
and I really felt like an evangelical minister preaching the word.
Added April 29, 2006:
Read
Chris ("CJ") Fearnley's Message
Added March 11, 2007: Read
Herb Wilf's Message
about Chandrasekhar and Discrete Analysis.
Added Aug. 5, 2008: Read Michael Livshits's
innovative approach to calculus
Added May 5, 2019: Noson Yanofsky kindly told me about this
interesting article by Nicolas Gisin.
Doron Zeilberger's List of Papers