Chaitin, Gregory J.
Overview
Works:  63 works in 276 publications in 3 languages and 6,472 library holdings 

Genres:  Interviews Popular works 
Roles:  Author, Author of introduction 
Classifications:  QA267, 511.3 
Publication Timeline
.
Most widely held works about
Gregory J Chaitin
 Conversations with a mathematician : math, art, science, and the limits of reason : a collection of his most wideranging and nontechnical lectures and interviews by Gregory J Chaitin Gregory J Chaitin( Book )
Most widely held works by
Gregory J Chaitin
Randomness and complexity from Leibniz to Chaitin
by
Cristian Calude(
)
9 editions published in 2007 in English and held by 1,147 WorldCat member libraries worldwide
The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. Sample Chapter(s). Chapter 1: On Random and HardtoDescribe Numbers (902 KB). Contents: On Random and HardtoDescribe Numbers (C H Bennett); The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies); What is a Computation? (M Davis); A BerryType Paradox (G Lolli); The Secret Number
9 editions published in 2007 in English and held by 1,147 WorldCat member libraries worldwide
The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. Sample Chapter(s). Chapter 1: On Random and HardtoDescribe Numbers (902 KB). Contents: On Random and HardtoDescribe Numbers (C H Bennett); The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies); What is a Computation? (M Davis); A BerryType Paradox (G Lolli); The Secret Number
Meta math! : the quest for omega
by
Gregory J Chaitin(
Book
)
26 editions published between 2005 and 2013 in English and held by 876 WorldCat member libraries worldwide
Explores the enigmas, paradoxes, and random qualities that exist within the field of mathematics and discusses the author's groundbreaking discovery of the Omega number, a complex representation of unknowability
26 editions published between 2005 and 2013 in English and held by 876 WorldCat member libraries worldwide
Explores the enigmas, paradoxes, and random qualities that exist within the field of mathematics and discusses the author's groundbreaking discovery of the Omega number, a complex representation of unknowability
Algorithmic information theory
by
Gregory J Chaitin(
Book
)
40 editions published between 1977 and 2004 in English and Undetermined and held by 695 WorldCat member libraries worldwide
40 editions published between 1977 and 2004 in English and Undetermined and held by 695 WorldCat member libraries worldwide
Thinking about Gödel and Turing essays on complexity 19702007
by
Gregory J Chaitin(
)
12 editions published between 2007 and 2008 in English and held by 679 WorldCat member libraries worldwide
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing.This book contains 23 nontechnical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of programsize co
12 editions published between 2007 and 2008 in English and held by 679 WorldCat member libraries worldwide
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing.This book contains 23 nontechnical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of programsize co
The limits of mathematics : a course on information theory and limits of formal reasoning
by
Gregory J Chaitin(
Book
)
37 editions published between 1993 and 2014 in English and Undetermined and held by 525 WorldCat member libraries worldwide
"This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Godel is much more widespread and serious than hitherto suspected."Jacket
37 editions published between 1993 and 2014 in English and Undetermined and held by 525 WorldCat member libraries worldwide
"This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Godel is much more widespread and serious than hitherto suspected."Jacket
Proving Darwin : making biology mathematical
by
Gregory J Chaitin(
Book
)
10 editions published between 2012 and 2013 in English and held by 405 WorldCat member libraries worldwide
Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world
10 editions published between 2012 and 2013 in English and held by 405 WorldCat member libraries worldwide
Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world
Information, randomness & incompleteness : papers on algorithmic information theory
by
Gregory J Chaitin(
Book
)
20 editions published between 1987 and 1990 in English and Italian and held by 382 WorldCat member libraries worldwide
The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on "Algorithmic Information Theory" by the author. There the strongest possible version of Gödel's incompleteness theorem, using an informationtheoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictabilit
20 editions published between 1987 and 1990 in English and Italian and held by 382 WorldCat member libraries worldwide
The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on "Algorithmic Information Theory" by the author. There the strongest possible version of Gödel's incompleteness theorem, using an informationtheoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictabilit
The unknowable
by
Gregory J Chaitin(
Book
)
15 editions published between 1999 and 2000 in English and held by 360 WorldCat member libraries worldwide
"This companion volume to Chaitin's "The Limits of Mathematics", also published by Springer, gives a historical survey of the work this century on the foundations of mathematics, in which the author was a major participant. "The Unknowable" is a readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for "The Unknowable" can be downloaded from the author's Web site."BOOK JACKET
15 editions published between 1999 and 2000 in English and held by 360 WorldCat member libraries worldwide
"This companion volume to Chaitin's "The Limits of Mathematics", also published by Springer, gives a historical survey of the work this century on the foundations of mathematics, in which the author was a major participant. "The Unknowable" is a readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for "The Unknowable" can be downloaded from the author's Web site."BOOK JACKET
Gödel's way : exploits into an undecidable world
by
Gregory J Chaitin(
Book
)
9 editions published between 2011 and 2012 in English and held by 343 WorldCat member libraries worldwide
"This accessible book gives a new detailed and elementary proof of the Gödel incompleteness theorems and then presents the Chaitin results and their relation to the da CostaDoria results, which are given in full, but with no technicalities. Besides theory, the lively historical report, the personal stories about the main character, and the writing process of this volume make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences"
9 editions published between 2011 and 2012 in English and held by 343 WorldCat member libraries worldwide
"This accessible book gives a new detailed and elementary proof of the Gödel incompleteness theorems and then presents the Chaitin results and their relation to the da CostaDoria results, which are given in full, but with no technicalities. Besides theory, the lively historical report, the personal stories about the main character, and the writing process of this volume make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences"
Exploring randomness
by
Gregory J Chaitin(
Book
)
12 editions published between 2000 and 2002 in English and held by 304 WorldCat member libraries worldwide
This essential companion volume to CHAITIN's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of programsize complexity, also known as algorithmic information theory. (The two previous volumes are more concerned with applications to metamathematics.) LISP is used to present the key algorithms and to enable computer users to interact with the author's proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait/ "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything he's seen. Don't miss it." John Casti, Santa Fe Institute, Author of "Goedel: A Life of Logic"
12 editions published between 2000 and 2002 in English and held by 304 WorldCat member libraries worldwide
This essential companion volume to CHAITIN's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of programsize complexity, also known as algorithmic information theory. (The two previous volumes are more concerned with applications to metamathematics.) LISP is used to present the key algorithms and to enable computer users to interact with the author's proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait/ "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything he's seen. Don't miss it." John Casti, Santa Fe Institute, Author of "Goedel: A Life of Logic"
Informationtheoretic incompleteness
by
Gregory J Chaitin(
Book
)
9 editions published between 1992 and 1998 in English and Undetermined and held by 153 WorldCat member libraries worldwide
In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance. The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific. The technical survey contains many new results, including a detailed discussion of LISP program size and new versions of Chaitin's most fundamental informationtheoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in Gšdel's classroom at the University o
9 editions published between 1992 and 1998 in English and Undetermined and held by 153 WorldCat member libraries worldwide
In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance. The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific. The technical survey contains many new results, including a detailed discussion of LISP program size and new versions of Chaitin's most fundamental informationtheoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in Gšdel's classroom at the University o
Hasard et complexité en mathématiques
by
Gregory J Chaitin(
Book
)
2 editions published in 2009 in French and held by 72 WorldCat member libraries worldwide
2 editions published in 2009 in French and held by 72 WorldCat member libraries worldwide
Conversations with a mathematician : math, art, science, and the limits of reason : a collection of his most wideranging and nontechnical lectures and interviews
by
Gregory J Chaitin(
Book
)
10 editions published between 2001 and 2003 in English and held by 72 WorldCat member libraries worldwide
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 wideranging and nontechnical 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 ÄrandomnessÜ is a profoundly rich concept." Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER
10 editions published between 2001 and 2003 in English and held by 72 WorldCat member libraries worldwide
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 wideranging and nontechnical 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 ÄrandomnessÜ is a profoundly rich concept." Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER
Logica matematica : strutture rappresentazioni deduzioni
by
Vincenzo Manca(
Book
)
2 editions published in 2001 in Italian and held by 14 WorldCat member libraries worldwide
2 editions published in 2001 in Italian and held by 14 WorldCat member libraries worldwide
Information and randomness : an algorithmic perspective
by
Cristian Calude(
Book
)
6 editions published between 1994 and 2002 in English and held by 10 WorldCat member libraries worldwide
The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge. "Professor Calude has produced a firstrate exposition of uptodate work in information and randomness." D.S. Bridges, Canterbury University, coauthor, with Errett Bishop, of Constructive Analysis; "The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician; "This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics
6 editions published between 1994 and 2002 in English and held by 10 WorldCat member libraries worldwide
The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge. "Professor Calude has produced a firstrate exposition of uptodate work in information and randomness." D.S. Bridges, Canterbury University, coauthor, with Errett Bishop, of Constructive Analysis; "The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician; "This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics
Alla ricerca di omega
by
Gregory J Chaitin(
Book
)
2 editions published in 2007 in Italian and held by 9 WorldCat member libraries worldwide
2 editions published in 2007 in Italian and held by 9 WorldCat member libraries worldwide
Numeri, caso e sequenze
by Roberto MAGARI(
Book
)
1 edition published in 1988 in Italian and held by 7 WorldCat member libraries worldwide
1 edition published in 1988 in Italian and held by 7 WorldCat member libraries worldwide
Logica
(
Book
)
1 edition published in 1991 in Italian and held by 6 WorldCat member libraries worldwide
1 edition published in 1991 in Italian and held by 6 WorldCat member libraries worldwide
Teoria algoritmica della complessità
by
Gregory J Chaitin(
Book
)
1 edition published in 2006 in Italian and held by 4 WorldCat member libraries worldwide
1 edition published in 2006 in Italian and held by 4 WorldCat member libraries worldwide
Speculations on biology, information and complexity
by
Gregory J Chaitin(
)
1 edition published in 2006 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 4 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Calude, Cristian 1952 Author Editor
 Costa, Newton C. A. da
 Doria, Francisco Antônio
 Mansuy, Roger
 Forget, Hugo
 Centre for Discrete Mathematics & Theoretical Computer Science
 Cambridge University Press Publisher
 Manca, Vincenzo Author
 黒川, 利明 1948
 Salomaa, Arto Author of introduction
Useful Links
Associated Subjects
Algorithms BiologyMathematical models BiologyPhilosophy Biomathematics Coding theory Combinatorial analysis Computational complexity Computer algorithms Computer programming Computer programmingPhilosophy Computer science Computer scienceMathematics Computer software Distribution (Probability theory) Electronic data processing Evolution (Biology)Mathematical models Evolution (Biology)Mathematics Evolution (Biology)Philosophy EvolutionMathematical models EvolutionMathematics EvolutionPhilosophy Gödel's theorem Incompleteness theorems Information theory Information theory in mathematics Kolmogorov complexity LISP (Computer program language) Logic, Symbolic and mathematical Machine theory Mathematics MathematicsPhilosophy Metamathematics Reasoning Science Statistics Stochastic processes Turing machines