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Meta Math!: The Quest for Omega Paperback – November 14, 2006

3.8 out of 5 stars 32 customer reviews

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Editorial Reviews

From Booklist

Note the exclamation point: Chaitin is on fire about math and is unable to restrain his enthusiasm. No mere number cruncher, he is renowned for finding another proof of Kurt Godel's incompleteness theorem and another for Alan Turing's "halting problem" in computation. Chaitin explains these two achievements here, in prose that is difficult for general readers to follow, but the spirit he brings to his subject will be apparent to all. Chaitin radiates his zeal like a preacher seeking converts. His asides often directly speak to students who might want to become professional mathematicians, stoking their fire, for example, with the vulnerability of even ancient theorems to new analysis (he sketches two ways, in addition to Euclid's, to prove the infinity of prime numbers). Chaitin's freewheeling expressions of mathematical creativity will be this work's lasting impression. Gilbert Taylor
Copyright © American Library Association. All rights reserved --This text refers to an out of print or unavailable edition of this title.

Review

“A startling vision of the future of mathematics. . . . The Chaitinesque intellectual future will be eternally youthful and anarchic.”–American Scientist

“Math’s dark secret is out. . . . Chaitin explains why omega, a number he discovered thirty years ago, has him convinced that math is based on randomness.”
Time Magazine

“Captivating. . . . With extraordinary skill and a gentle humor, Chaitin shares his profound insights.”
–Paul Davies, author of How to Build a Time Machine

“A clearly written and witty look at a difficult subject. . . . Chaitin explains with infectious enthusiasm how mathematics doesn't equal certainty.” –Science News
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Product Details

  • Paperback: 240 pages
  • Publisher: Vintage (November 14, 2006)
  • Language: English
  • ISBN-10: 1400077974
  • ISBN-13: 978-1400077977
  • Product Dimensions: 5.2 x 0.6 x 8 inches
  • Shipping Weight: 12.6 ounces (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (32 customer reviews)
  • Amazon Best Sellers Rank: #495,451 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover
Chaitin is a good mathematician, not a great one as he seems to think. His invention of algorithmic complexity (independent of the parallel work of the truly great mathematician Kolmogorov) is a permanent feature of the mathematical landscape, and will ensure the immortality of his name, but his other mathematical work, while sound and original, is of technical interest only.

However, he is a better philosopher than he is usually given credit for. His views on the foundations and meaning of mathematics are very original. By avoiding, on the one hand, the formalistic view that mathematical statements are meaningless, and, on the other hand, the conventional view that the current mathematical foundations (for the specialist, I am referring to the ZFC axioms for set theory augmented by large cardinal axioms) are adequate, he is able to show that mathematics is ultimately an empirical science.

The overwhelming inexhaustibility of mathematics is clearer in Chaitin's formulation than in Godel's -- the sense that everything we know about math is an infinitesimal fraction of what there is to know about it. The other major theme which Chaitin clarifies is that mathematics is not logically prior to physics, which Godel also knew, but which is now much more sharply established. And his approach provides a very intuitive way, for those familiar with computer programming, to understand the work of Godel and Turing that avoids the usual self-referential fussing.

That doesn't mean this is a good book. It is badly written, unnecessarily self-congratulatory, and at an uneven technical level.
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Format: Hardcover
As someone who studied meta-mathematics at Caltech and UCLA, I found this book disappointing-stylistically, mathematically and philosophically. To paraphrase the physicist Pauli, this isn't right; this isn't even wrong. This well-meaning man's editors should do a little bit of legwork before reprinting a man's inflated self-appraisal. I am so disappointed in this book that I am seriously considering returning it for a refund.

I guess I should blame myself. My first response to the editorial comment naming the author as the intellectual heir to Gödel and Turing was, "Gregory who?" Shelah, Solovay, Martin: these are names I know, but who is Gregory Chaitin? I should have gone with my gut. In retrospect, it is telling that all the jacket quotes are from freewheeling authors of popularizations, not from respected philosophers, logicians, or scientists.

The entire book is written in an embarrassingly gushing, adolescent style full of boldface and exclamation points. I know that the author was trying to write an enthusiastic, accessible book of philosophical and methodological advocacy, but this doesn't excuse shoddy editorial craftsmanship.

Don't take my word for it. Let the author speak for himself. From page 7, "Gödel's 1931 work on incompleteness, Turing's 1936 work on uncomputability, and my own work on the role of information, randomness and complexity have shown increasingly emphatically that the role that Hilbert envisioned for formalism in mathematics is best served by computer programming languages[.]"

Imagine if a working composer wrote, "Bach's preludes and fugues, Beethoven's symphonies, and my own string quartets have shown increasingly emphatically...
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Format: Hardcover
Modesty is a most desirable quality in a scientist, even in the most brilliant. I have no doubt that Gregory Chaitin is a fine and respected mathematician. However, his book "Meta Math!: The Quest for Omega" is written in a style that transmits the impression that he lacks the humility that usually characterizes a true great master scientist. I cannot imagine, for instance, Professor Stephen Hawking comparing his own mind to that of Isaac Newton and referring to himself as the successor of Einstein. Even if it were true, and many people think it is, it would certainly be arrogant if stated by Hawking himself. In fact, this is exactly what Chaitin appears to be doing in his book. He is not embarrassed at all when he claims to be at the same intellectual level (even as a teenager) as Leibniz. He describes his proof for diophantine equations as being side by side with those of Euclid and Euler. Moreover, he refers to Kurt G?del as his "predecessor", something that I think is absolutely unfair considering G?del as the original author of the incompleteness theorem. And, amazingly enough, there is a section included in the book that deals with egotism in science and how it should be avoided- very subtly written. In this section, Chaitin claims that no scientific idea should have only one name associated with it and as an example, he describes the chain of thoughts that inspired mathematicians since Zeno up to himself. I am in total agreement with this concept. However, in the next paragraph, Chaitin explains how, "...the best minds in the human race...." join together to create these theories. Hence, he has almost subliminally included himself in this group of distinguished intellectuals.Read more ›
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