> "Real" Analysis is a Degenerate Case of Discrete Analysis
"Real" Analysis is a Degenerate Case of Discrete Analysis

By Doron Zeilberger

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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.

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.

Gene Klotz kindly took pictures of this historic event: Pic 1    Pic 2    Pic 3    Pic 4    Pic 5    Pic 6    Pic 7    Pic 8    Pic 9    Pic 10    Pic 11    Pic 12    Pic 13    Pic 14    Pic 15    Pic 16   

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.

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,

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