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

ISBN-13: 9781852335496 / Angielski / Twarda / 2001 / 158 str.

Gregory J. Chaitin

Opis

G. J. Chaitin is at the IBM Thomas J. Watson Research Center in New York. He 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 has put a scratch on the rock of eternity."
Jacob T. Schwartz, Courant Institute, New York University, USA
"(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 ArandomnessU is a profoundly rich concept."
Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER"

Recenzje

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)

Spis treści

A century of controversy over the foundations of mathematics (Lecture).- How to be a mathematician (TV interview).- The creative life: science vs. art (Interview).- Algorithmic information theory & the foundations of mathematics (Lecture).- Randomness in arithmetic (TV interview).- The reason for my life (Interview).- Undecidability & randomness in pure mathematics (Lecture).- Math, science & fantasy (Interview).- Sensual mathematics (TV interview).- Final thoughts.- Recommended further reading.