A Century of Controversy over the Foundations of Mathematics

author: Gregory Chaitin, University of Auckland
published: Oct. 17, 2008,   recorded: September 2008,   views: 15003

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I'll tell the dramatic story of the recent disputes over the foundations of mathematics. I'll start with the problems in Cantor's theory of infinite sets and then discuss the work of Bertrand Russell, David Hilbert, Kurt Godel and Alan Turing, and finally my own work using complexity. This complexity-based analysis of the foundations of mathematics suggests to me that perhaps mathematics is more similar to physics and to biology than is commonly believed, and should sometimes be carried out quasi-empirically, that is, more in the spirit of an experimental science.

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Reviews and comments:

Comment1 Aubrey Wanliss-Orlebar, March 3, 2009 at 12:36 a.m.:

Chaitin's lecture on A Century of Controversy concerning the Foundations of Mathematics suffers from a drastic sound and image cut arond the 18 min. 15-sec. mark which anyone competent can notice. He has after this glitch clearly already introduced Godel's work and his own. This part must be found in entia and put where it belongs. From that point in the lecture (which should regain its normal length when you find the missing massive middle) has sound that is intermittenlty present and cut off (save for the noises of frcition of the microphone or its machinery). These problems must be solve please. Thankyou.

Comment2 Gregory Chaitin, March 10, 2009 at 5:13 a.m.:

Sorry this video is in such poor condition.
You can find the foils I used for this lecture at


Comment3 Rama Naidu Ravipalli, July 31, 2009 at 10:07 p.m.:

This is interesting.

Comment4 Gregory Chaitin, October 10, 2009 at 10:27 p.m.:

You can find a complete (one hour plus)
video of another version of this talk at


Comment5 Gregory Chaitin, October 18, 2009 at 11:05 p.m.:

I've written up my Jerusalem/Waterloo talk on
The Search for the Perfect Language.
You can find it here:

Comment6 Elias Lanides, September 18, 2010 at 10:25 p.m.:

I love this sort of stuff!

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