META MATH! (All Editions) with Reviews & Errata

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The Sunday Business Post (Eire), 12 August 2007

Mathematician Gregory Chaitin has written books on the randomness of his seemingly methodical subject before, but now presents his ideas in a single book that charts the history of maths up to and beyond his own discovery of "omega" more than 30 years ago.

Also a philosopher, Chaitin draws certain larger themes from his discoveries about randomness in maths, and has specific ideas about the future study of mathematics --- ideas with which not all in his field agree.

Financial Times Magazine, August 25/26 2007

Meta Maths is truly idiosyncratic. Informal, chatty and cerebral, it's almost a personal statement: it mixes mathematics with Chaitin's outlook on life and philosophy. For example, computer programming language shares a chapter with Kurt Gödel, friend of Einstein and developer of an immensely important theory of the limitations of mathematical methods. DNA and biological systems turn up intermittently. Where Chaitin wants to emphasize a word, a sentence or a paragraph, he prints it in bold. It's a bit like shouting in the reading room of the British Library.

This tendency to jump between subjects is perhaps not surprising. Chaitin's reputation is based on his work on randomness in mathematics. Meta Maths explains how he arrived at an infinitely long and completely incalculable number he calls "omega" --- which has to do with the probability that a computer program will eventually halt (another question that mathematicians love). Chaitin's book is great fun even if his style can be irritating.

full review

Buzz, October 2007

By no means a light read for anyone coming down off a Harry Potter high, Gregory Chaitin's Meta Maths is a fulfilling read if you have a head for numbers and a heart for maths. Charting the history of "omega", a number so dense in its complexity that were our mere minds capable of comprehending such a number, we would implode under the weight of such a revelation (I reckon), Chaitin's loving retelling of the history and study of the number makes for a rewarding read.

Sciences & avenir, mars 2009
Les nombres existent-ils vraiment ?

Les maths réservent toujours des surprises. Un spécialiste en la matière expose ici ses connaissances sur de bien curieux objets. Des nombres réels qui n'existent pas. D'autres qui existent mais qu'on ne peut calculer, ou dont on se demande s'ils sont aléatoires... Prenant prétexte de vulgariser l'une de ses principales découvertes, celle d'oméga, un nombre justement incalculable, aléatoire mais bien défini, le mathématicien nous invite à partager sa passion des nombres et de l'informatique. L'originalité de son livre tient justement dans l'exposé du rôle, parfois méconnu, de l'informatique en maths. Gregory Chaitin montre ainsi qu'il est possible de démontrer des théorèmes très connus en faisant appel au raisonnement informatique plutôt qu'à l'algèbre ou à l'analyse. Petit à petit, le lecteur se retrouvera également plongé dans des interrogations philosophiques. L'Univers laisse-t-il la place au hasard ? L'espace-temps est-il continu ou discontinu ?

French edition of Meta Math! (January 2009)

Reviews in French in Quadrature in La Recherche

Italian edition of Meta Math! (October 2007)

Review in La Stampa

Un celebre matematico ci guida in un viaggio di esplorazione
e di scoperta nella remota regione di confine dove si incontrano
la matematica, la filosofia e la moderna teoria dell'informazione.

Japanese edition of Meta Math! (September 2007)

Message to Japanese Readers----Thoughts on Seeing Five Films by Yasujiro Ozu

The past three nights at my home I have had the privilege of seeing five films by Ozu not previously available on DVD in the United States. Five late films, perhaps not at the level of his greatest work such as Tokyo Monogatari, but nevertheless films by Ozu.

I have admired Ozu for many years. I first saw Ozu's films at the Museum of Modern Art in New York, many years ago. Tokyo Monogatari and Late Spring were unforgettable, and I was struck by the beauty of the minimalist interiors and the minimalist dialogue.

When some of these films became available on DVD, I savored them again. The serenity and wisdom of these films beckons to us. For me, they are a refuge from the ``sound and fury, signifying nothing'' (Shakespeare) of our postmodern world, much as mathematics is.

It seems to me that we in the West have much to learn from the Eastern attitude quietly expressed in Ozu's films. Perhaps our Western obsession with loud Absolute Truth, so brutal, so brittle, so unyielding, can be tempered by an Eastern appreciation of the limited nature and the ephemerality of all knowledge, all achievement, all understanding? A view, let me add, that I hope this book helps to advance.

And what would Ozu think of this book? Dare I imagine his reaction might be in the form of a film, with Chishu Ryu and Setsuko Hara reflecting on randomness, on incompleteness, and on life?

Somehow all great art is connected---film, math, Eastern, Western----it enables us to feel we understand. But by its very nature, this can only be a fleeting sensation.

Gregory Chaitin, June 2007

Errata:

  1. On page 60, about one-third of the way down the page, "C. MacDonald Ross" should read "G. MacDonald Ross".

  2. On page 95, in the displayed formula for π/4 just below the middle of the page, the fourth minus sign should be a plus sign. (Minus and plus signs should alternate.)

Errata:

  1. On page 60, about one-third of the way down the page, "C. MacDonald Ross" should read "G. MacDonald Ross".

Errata:

  1. On page 58, about three-eighths of the way down the page, "C. MacDonald Ross" should read "G. MacDonald Ross".

  2. On page 60, about one-third of the way down the page, "C. MacDonald Ross" should read "G. MacDonald Ross".

  3. On page 95, in the displayed formula for π/4 just below the middle of the page, the last (rightmost) plus sign should be a minus sign. (Minus and plus signs should alternate.)

  4. On page 158, "books on the Reimann hypothesis" should read "books on the Riemann hypothesis".

  5. On page 221, "2002) 90164-171" should read "2002) 90, 164-171".

  6. On page 221, "Richard Feyman. Reprinted by The MIT Press" should read "Richard Feynman. Reprinted by permission of The MIT Press".