Conversations with a Mathematician: Math, Art, Science and the Limits of Reason [Hardcover]

Gregory J. Chaitin (Author)

Book Description

ISBN-10: 1852335491 | ISBN-13: 978-1852335496 | Publication Date: November 14, 2002

The author, G. J. Chaitin, shows that God plays dice not only in quantum mechanics but also in the foundations of mathematics. According to Chaitin there exist mathematical facts that are true for no reason. This fascinating and provocative text contains a collection of his most wide-ranging and non-technical lectures and interviews. It will be of interest to anyone concerned with the philosophy of mathematics, the similarities and differences between physics and mathematics, and mathematics as art.

Editorial Reviews

Review

From the reviews of the first edition:

MATHEMATICAL REVIEWS

"This is not a standard, pedagogical book of mathematical popularization, but a provocative, intelligent, engaging and fun to read piece of work. The author’s love of mathematics is almost ‘infectious’. The text written in Chaitin’s unmistakable writing style, is full if ideas, ‘bubbly like champagne’, but not light."

MAA ONLINE

"…a collection of three lectures and six interviews originally given between 1989 and 2001. What emerges from this somewhat disparate set of transcripts is a surprising coherent picture of Chaitin and his work. While there is the inevitable repetition of ideas, stories, examples, in the end that very repetition helps to leave the reader with the impression of having become acquainted with Chaitin himself. One way we know our friends is by knowing their important stories…[The book] fills the gap left by Chaitin’s other works by providing a highly engaging and readable account of his explorations into randomness in the foundations of mathematics."

AMERICAN MATHEMATICAL MONTHLY

"The book is a collection of non-technical lectures by, and interviews of, the mathematician Gregory J. Chaitin. His style in both of these settings is extremely clear and personable. What also emerges clearly is the joy he finds in his work, along with positive attitudes towards findings that have been interpreted by some as negative, even disturbing…Throughout the book he paraphrases his ideas in many well-written and beautiful passages…I learned a lot of mathematics from reading this book. I gained some insights about Godel’s work and some much-needed feeling for computer science…This book is wonderful in both senses of the word: superlatively good and full of wonder. Nonmathematicians could read it, too, but as I read it, I felt glad (and proud) to be a mathematician!"

CONVERSATIONS WITH A MATHEMATICIAN fills the gap left by Chaitin's other works by providing a highly engaging and readable account of his explorations into randomness in the foundations of mathematics. Those who want details are given enough pointers to find them.
–MAA ONLINE

The author has shown that God plays dice not only in quantum mechanics, but even in the foundations of mathematics, where Chaitin discovered mathematical facts that are true for no reason, that are true by accident. This book collects his most wide-ranging and non-technical lectures and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art.

"(Chaitin is) one of the great ideas men of mathematics and computer science." - Marcus Chown, author of The Magic Furnace, in NEW SCIENTIST

"Finding the right formalization is a large component of the art of doing great mathematics." - John Casti, author of Mathematical Mountaintops, on Godel, Turing and Chaitin in NATURE

"What mathematicians over the centuries - from the ancients, through Pascal, Fermat, Bernoulli, and de Moivre, to Kolmogorov and Chaitin - have discovered, is that it - randomness - is a profoundly rich concept." - Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER

"Conversations with a Mathematician brings together three of Chaitin’s public lectures and a number of TV and newspaper interviews … . It is a perfect place to start for anyone unfamiliar with the kinds of problems Chaitin addresses. The lecture is at once both fascinating and breezy, both informative and fun. … mathematicians, logicians, and information theorists, can find something worthwhile in this collection. It’s fun for everybody … ." (George Englebretsen, The Review of Modern Logic, Vol. 9 (3-4), 2004)

Product Details

• Hardcover: 168 pages
• Publisher: Springer (November 14, 2002)
• Language: English
• ISBN-10: 1852335491
• ISBN-13: 978-1852335496
• Product Dimensions: 9.3 x 6.1 x 0.6 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #2,436,294 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

21 of 24 people found the following review helpful:

5.0 out of 5 stars Maths limitations, undecidability and randomness: a story, March 30, 2002

By 

Steve Uhlig (Berlin, Germany) - See all my reviews
(REAL NAME)   

This review is from: Conversations with a Mathematician: Math, Art, Science and the Limits of Reason (Hardcover)

These interviews of G. Chaitin provide a good picture of what science is about: just another human activity. It shows how subjectivity is a part of what people call science...The book provides a historical perspective of the work by Hilbert, Godel, Turing,...on maths and its limitations. Mostly computer scientists and mathematicians will be interested in reading this book since it goes all about Godel and Turing's achievements on the limits of formalisms, undecidability and the limits of mathematics in general...without forgetting the work of G. Chaitin in algorithmic information theory and randomness in mathematics that continues the work of these great men.

7 of 13 people found the following review helpful:

5.0 out of 5 stars I love this book, December 6, 2003

By A Customer

This review is from: Conversations with a Mathematician: Math, Art, Science and the Limits of Reason (Hardcover)

I know very little about math, and I say that only to make it clear that I don't have the tools that some people have to explain why I loved reading this book, and why I will read it again, or give it as a gift. But I am a reader, and I couldn't put this book down, and I usually feel that way only about novels. So as a reader I will say that this is a beautiful book. It's almost perfect, in a way. (In the same way that I would say Laurie Colwin's book, Happy All The Time, is the perfect modern American novel.) And that's because it's so hard to put down.

2 of 57 people found the following review helpful:

1.0 out of 5 stars The book is rubbish, October 12, 2003

By A Customer

This review is from: Conversations with a Mathematician: Math, Art, Science and the Limits of Reason (Hardcover)

Do not buy it. You are wasting you time and money.