Chaitin, Gregory J.
Overview
Works:  70 works in 346 publications in 4 languages and 7,513 library holdings 

Genres:  Interviews Popular works Filmed interviews Educational films 
Roles:  Author, Author of introduction 
Publication Timeline
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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( Book )
Most widely held works by
Gregory J Chaitin
Meta math! : the quest for omega by
Gregory J Chaitin(
Book
)
31 editions published between 2005 and 2008 in English and Undetermined and held by 810 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
31 editions published between 2005 and 2008 in English and Undetermined and held by 810 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
)
50 editions published between 1977 and 2004 in English and Undetermined and held by 701 WorldCat member libraries worldwide
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a socalled exponential diophantine equation
50 editions published between 1977 and 2004 in English and Undetermined and held by 701 WorldCat member libraries worldwide
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a socalled exponential diophantine equation
The limits of mathematics : a course on information theory and limits of formal reasoning by
Gregory J Chaitin(
Book
)
35 editions published between 1997 and 2014 in English and held by 532 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
35 editions published between 1997 and 2014 in English and held by 532 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
)
6 editions published between 2012 and 2013 in English and held by 399 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
6 editions published between 2012 and 2013 in English and held by 399 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
)
24 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
24 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
)
23 editions published between 1999 and 2001 in English and Japanese and held by 380 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."Jacket
23 editions published between 1999 and 2001 in English and Japanese and held by 380 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."Jacket
Exploring randomness by
Gregory J Chaitin(
Book
)
16 editions published between 2000 and 2002 in English and held by 305 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."
16 editions published between 2000 and 2002 in English and held by 305 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."
Gödel's way : exploits into an undecidable world by
Gregory J Chaitin(
Book
)
9 editions published between 2011 and 2012 in English and Undetermined and held by 236 WorldCat member libraries worldwide
"Kurt Gödel (19061978) was an AustrianAmerican mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he proved that Einstein's theory admits time machines. The Gödel incompleteness phenomenon  one cannot prove nor disprove all true mathematical sentences in the usual formal mathematical sentences  is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin's groundbreaking work and on the da CostaDoria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da CostaDoria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book's writing process, 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 Undetermined and held by 236 WorldCat member libraries worldwide
"Kurt Gödel (19061978) was an AustrianAmerican mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he proved that Einstein's theory admits time machines. The Gödel incompleteness phenomenon  one cannot prove nor disprove all true mathematical sentences in the usual formal mathematical sentences  is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin's groundbreaking work and on the da CostaDoria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da CostaDoria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book's writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences."
Thinking about Gödel and Turing : essays on complexity, 19702007 by
Gregory J Chaitin(
Book
)
20 editions published between 2007 and 2008 in English and held by 197 WorldCat member libraries worldwide
On the difficulty of computations  Informationtheoretic computational complexity  Randomness and mathematical proof  Gd̈el's theorem and information  Randomness in arithmetic  Randomness in arithmetic and the decline & fall of reductionism in pure mathematics  A century of controversy over the foundations of mathematics  A century of controversy over the foundations of mathematics  Metamathematics and the foundations of mathematics  Paradoxes of randomness  Two philosophical applications of algorithmic information theory  On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility  Leibniz, information, math & physics  Leibniz, randomness & the halting probability  Complexity & Leibniz  The limits of reason  How real are real numbers?  Epistemology as information theory: From Leibniz to [symbol]  Is incompleteness a serious problem?  Speculations on biology, information & complexity  How much information can there be in a real number?  The halting probability [symbol]: irreducible complexity in pure mathematics  The halting probability [symbol]: concentrated creativity
20 editions published between 2007 and 2008 in English and held by 197 WorldCat member libraries worldwide
On the difficulty of computations  Informationtheoretic computational complexity  Randomness and mathematical proof  Gd̈el's theorem and information  Randomness in arithmetic  Randomness in arithmetic and the decline & fall of reductionism in pure mathematics  A century of controversy over the foundations of mathematics  A century of controversy over the foundations of mathematics  Metamathematics and the foundations of mathematics  Paradoxes of randomness  Two philosophical applications of algorithmic information theory  On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility  Leibniz, information, math & physics  Leibniz, randomness & the halting probability  Complexity & Leibniz  The limits of reason  How real are real numbers?  Epistemology as information theory: From Leibniz to [symbol]  Is incompleteness a serious problem?  Speculations on biology, information & complexity  How much information can there be in a real number?  The halting probability [symbol]: irreducible complexity in pure mathematics  The halting probability [symbol]: concentrated creativity
Informationtheoretic incompleteness by
Gregory J Chaitin(
Book
)
11 editions published between 1992 and 1998 in English and Undetermined and held by 144 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 of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer
11 editions published between 1992 and 1998 in English and Undetermined and held by 144 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 of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer
Randomness and complexity : from Leibniz to Chaitin by
Cristian Calude(
Book
)
10 editions published in 2007 in English and held by 107 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
10 editions published in 2007 in English and held by 107 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
Hasard et complexité en mathématiques by
Gregory J Chaitin(
Book
)
2 editions published in 2009 in French and held by 78 WorldCat member libraries worldwide
2 editions published in 2009 in French and held by 78 WorldCat member libraries worldwide
Pioneers. against method(
Visual
)
1 edition published in 2016 in English and held by 72 WorldCat member libraries worldwide
Gregory Chaitin (b. 1947) is a mathematician, an expert in complexity. Already as a young prodigy he contributed greatly to the philosophy of mathematics and computer science. Chaitin states that although there are truths in science that cannot be proven, there is reason for huge optimism. He sketches a theory of the source of beauty and creativity in nature. We'll be meeting Chaitin at the tiny Brazilian island of Paqueta, his philosophical retreat. About the Series: Pioneers is one and only film project devoted to the most unorthodox contemporary thinkers who have had the courage to challenge current paradigms. The emotions of discovering and stresstesting new theories; the passion which prompts one to go against the expectations of others, against the "publish or die" model; the joys and sorrows of exploring frontiers of the known and the unknown  this is what Pioneers is about
1 edition published in 2016 in English and held by 72 WorldCat member libraries worldwide
Gregory Chaitin (b. 1947) is a mathematician, an expert in complexity. Already as a young prodigy he contributed greatly to the philosophy of mathematics and computer science. Chaitin states that although there are truths in science that cannot be proven, there is reason for huge optimism. He sketches a theory of the source of beauty and creativity in nature. We'll be meeting Chaitin at the tiny Brazilian island of Paqueta, his philosophical retreat. About the Series: Pioneers is one and only film project devoted to the most unorthodox contemporary thinkers who have had the courage to challenge current paradigms. The emotions of discovering and stresstesting new theories; the passion which prompts one to go against the expectations of others, against the "publish or die" model; the joys and sorrows of exploring frontiers of the known and the unknown  this is what Pioneers is about
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
)
14 editions published between 2001 and 2003 in English and held by 64 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
14 editions published between 2001 and 2003 in English and held by 64 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 18 WorldCat member libraries worldwide
2 editions published in 2001 in Italian and held by 18 WorldCat member libraries worldwide
The limits of mathematics by
Gregory J Chaitin(
Book
)
8 editions published between 1994 and 2001 in English and Japanese and held by 17 WorldCat member libraries worldwide
Abstract: "This condensed version of RC 20190 will be the main handout for a course on algorithmic information theory to be given 2229 May 1996 at the Rovaniemi Institute of Technology, Rovaniemi, Finland (see announcement at http://www.rotol.fi)."
8 editions published between 1994 and 2001 in English and Japanese and held by 17 WorldCat member libraries worldwide
Abstract: "This condensed version of RC 20190 will be the main handout for a course on algorithmic information theory to be given 2229 May 1996 at the Rovaniemi Institute of Technology, Rovaniemi, Finland (see announcement at http://www.rotol.fi)."
Information and randomness : an algorithmic perspective by
Cristian Calude(
Book
)
6 editions published between 1994 and 2002 in English and held by 12 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 12 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 12 WorldCat member libraries worldwide
2 editions published in 2007 in Italian and held by 12 WorldCat member libraries worldwide
Teoria algoritmica della complessità by
Gregory J Chaitin(
Book
)
1 edition published in 2006 in Italian and held by 9 WorldCat member libraries worldwide
1 edition published in 2006 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 8 WorldCat member libraries worldwide
1 edition published in 1988 in Italian and held by 8 WorldCat member libraries worldwide
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Algorithms Biology BiologyMathematical models BiologyPhilosophy Biomathematics Chaitin, Gregory J 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, Kurt Gödel's theorem Incompleteness theorems Information theory Information theory in mathematics Kolmogorov complexity LISP (Computer program language) Logic, Symbolic and mathematical Machine theory Mathematicians Mathematics MathematicsPhilosophy Metamathematics Philosophy Reasoning Statistics Stochastic processes Turing, Alan Mathison, Turing machines
Alternative Names
Chaitin, G. J.
Chaitin, G. J. 1947
Chaitin, G. J. (Gregory J.)
Chaitin , Gregory
Chaitin, Gregory 1947
Chaitin, Gregory J.
Chaitin, Gregory John
Chaitin, Gregory John 1947
Gregori Dzon Cejtin
Gregory Chaitin Amerikaans wiskundige
Gregory Chaitin amerikansk datavetare och matematiker
Gregory Chaitin amerikansk informatikar og matematikar
Gregory Chaitin amerikansk informatiker og matematiker
Gregory Chaitin matematico e informatico argentino naturalizzato statunitense
Gregory Chaitin mathématicien américain
Gregory Chaitin USamerikanischer Mathematiker
Хайтин, Грегори
غريغوري تشايتين
グレゴリー・チャイティン
チャイティン, G. J
チャイティン, グレゴリー
チャイティン, グレゴリー・J
格里戈里·蔡廷 美国数学家
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