Book review: The Limits of Mathematics by Gregory Chaitin

Chaitin’s website about the book, which seems to include the full contents (in HMTL format): http://www.cs.auckland.ac.nz/~chaitin/lm.html

A PDF draft from 1994 at Arxiv: http://arxiv.org/abs/chao-dyn/9407009

Some other links about the book (putting these here to save people scrolling through many pages of search results & running into journal paywalls):

The only review at Amazon (2 stars): http://www.amazon.com/review/R1ZJVJX57T6YVA/

http://www.scientificexploration.org/journal/reviews/reviews...

http://www.cs.auckland.ac.nz/CDMTCS/chaitin/siam.html

A couple reviews whose "official" URLs are journal-paywalled: http://www.cs.umd.edu/~gasarch/bookrev/30-1.pdf http://tph.tuwien.ac.at/~svozil/publ/greg.htm

Math Trek: http://www.maa.org/mathland/mathtrek_03_06_06.html

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Everything2 page about Chaitin: http://everything2.com/title/Gregory+Chaitin

Several interesting looking papers in this book: http://www.scribd.com/doc/20445762/Randomness-and-Complexity...

Slashdot review/discussion of another Chaitin book, Metamath! The Quest for Omega: http://science.slashdot.org/article.pl?sid=04/06/10/1947247

The page about that book (full text also available, apparently): http://www.cs.auckland.ac.nz/CDMTCS/chaitin/omega.html and Arxiv: http://arxiv.org/abs/math.HO/0404335

http://www.americanscientist.org/bookshelf/pub/two-philosoph...

The Limits of Mathematics---Tutorial Version

http://arxiv.org/abs/chao-dyn/9509010v1

Previously in this LISP code only one-character identifiers were allowed, and arithmetic had to be programmed out. Now identifiers can be many characters long, and arithmetic with arbitrarily large unsigned decimal integers is built in. This and many other changes in the software have made this material much easier to understand and to use.

When i hear something along the lines of "limits of mathematics", a picture of Leibnitz tiresomely counting tortoise and Achilles steps comes to mind. Fortunately, instead of dwelling on, Leibnitz and the other bright minds were able to transcend the limits of the mathematics of the time.

Chaitin is a great mathematician, and there is no doubts about the limits he and others great ones have unquestionably proved. These works are great masterpieces. What looks strange is that it seems that modern human civilization has passively accepted the limits as the ultimate truth instead of trying to transcend them.

I wrote a review of Chaitin's Algorithmic Information Theory a couple of years ago. I talk briefly about his approach in using Lisp. http://blog.fogus.me/2008/12/19/bookpr0n-0-gregory-chaitins-...

I always found Chaitin's books very enjoyable. The guy does not exactly curb his enthusiasm for algorithmic information theory, often with erotic allusions - it's porn for discrete mathematicians :)