Gregory John Chaitin ( ; born 25 June 1947) is an

Argentine Argentines, Argentinians or Argentineans are people from Argentina. This connection may be residential, legal, historical, or cultural. For most Argentines, several (or all) of these connections exist and are collectively the source of their ...

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, p ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

computer scientist A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on ...

. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and

metamathematics Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheory, metatheories, which are Mathematical theory, mathematical theories about other mathematical theories. Emphasis on metamathematics (and ...

, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem. He is considered to be one of the founders of what is today known as algorithmic (Solomonoff–Kolmogorov–Chaitin, Kolmogorov or program-size)

complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...

together with

Andrei Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

and

Ray Solomonoff Ray Solomonoff (July 25, 1926 – December 7, 2009) was an American mathematician who invented algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference),Samuel Rathmanner and Marcus Hutter. ...

. Along with the works of e.g.

Solomonoff Ray Solomonoff (July 25, 1926 – December 7, 2009) was an American mathematician who invented algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference),Samuel Rathmanner and Marcus Hutter. A ...

Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

, Martin-Löf, and

Leonid Levin Leonid Anatolievich Levin ( ; ; ; born November 2, 1948) is a Soviet-American mathematician and computer scientist. He is known for his work in randomness in computing, algorithmic complexity and intractability, average-case complexity, fou ...

, algorithmic information theory became a foundational part of

theoretical computer science Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Associati ...

information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

, and

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

. It is a common subject in several computer science curricula. Besides computer scientists, Chaitin's work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy.

Mathematics and computer science

Gregory Chaitin is

Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...

. He attended the

Bronx High School of Science The Bronx High School of Science is a State school, public Specialized high schools in New York City, specialized high school in the Bronx in New York City. It is operated by the New York City Department of Education. Admission to Bronx Science ...

and the

City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a Public university, public research university within the City University of New York (CUNY) system in New York ...

, where he (still in his teens) developed the theory that led to his independent discovery of

algorithmic complexity Algorithmic may refer to: *Algorithm, step-by-step instructions for a calculation **Algorithmic art, art made by an algorithm **Algorithmic composition, music made by an algorithm **Algorithmic trading, trading decisions made by an algorithm **Algo ...

. Chaitin has defined

Chaitin's constant In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will ...

Ω, a

real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...

whose digits are

equidistributed In mathematics, a sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences ...

and which is sometimes informally described as an expression of the probability that a random program will halt. Ω has the mathematical property that it is definable, with asymptotic approximations from below (but not from above), but not

computable Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is cl ...

. Chaitin is also the originator of using

graph coloring In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a Graph (discrete mathematics), graph. The assignment is subject to certain constraints, such as that no two adjacent elements have th ...

to do

register allocation In compiler optimization, register allocation is the process of assigning local automatic variables and Expression (computer science), expression results to a limited number of processor registers. Register allocation can happen over a basic bloc ...

compiling In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs tha ...

, a process known as

Chaitin's algorithm Chaitin's algorithm is a bottom-up, graph coloring register allocation algorithm that uses cost/degree as its spill metric. It is named after its designer, Gregory Chaitin. Chaitin's algorithm was the first register allocation algorithm that made ...

. He was formerly a researcher at IBM's Thomas J. Watson Research Center in New York. He has written more than 10 books that have been translated to about 15 languages. He is today interested in questions of metabiology and

information-theoretic Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through ...

formalizations of the theory of

evolution Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...

, and is a member of the Institute for Advanced Studies at

Mohammed VI Polytechnic University University Mohammed VI Polytechnic (UM6P; ) is a Moroccan non-profit private research university. Its main campus is located within the Green City of Benguerir. Centered on African development, the university is oriented towards applied resear ...

Other scholarly contributions

Chaitin also writes about

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

, especially

metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...

and

philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...

(particularly about epistemological matters in mathematics). In metaphysics, Chaitin claims that algorithmic information theory is the key to solving problems in the field of

biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...

(obtaining a formal definition of 'life', its origin and

) and

neuroscience Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...

(the problem of

consciousness Consciousness, at its simplest, is awareness of a state or object, either internal to oneself or in one's external environment. However, its nature has led to millennia of analyses, explanations, and debate among philosophers, scientists, an ...

and the study of the mind). In recent writings, he defends a position known as digital philosophy. In the

epistemology Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowle ...

of mathematics, he claims that his findings in

and algorithmic information theory show there are "mathematical facts that are true for no reason, that are true by accident". Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a

quasi-empirical Quasi-empiricism in mathematics is the attempt in the philosophy of mathematics to direct philosophers' attention to mathematical practice, in particular, relations with physics, social sciences, and computational mathematics, rather than solely to ...

methodology.

Honors

In 1995 he was given the degree of doctor of science ''

honoris causa An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hono ...

'' by the

University of Maine The University of Maine (UMaine) is a Public university, public Land-grant university, land-grant research university in Orono, Maine, United States. It was established in 1865 as the land-grant college of Maine and is the Flagship universitie ...

. In 2002 he was given the title of honorary professor by the

University of Buenos Aires The University of Buenos Aires (, UBA) is a public university, public research university in Buenos Aires, Argentina. It is the second-oldest university in the country, and the largest university of the country by enrollment. Established in 1821 ...

in Argentina, where his parents were born and where Chaitin spent part of his youth. In 2007 he was given a

Leibniz Medal The Berlin-Brandenburg Academy of Sciences and Humanities (), abbreviated BBAW, is the official academic society for the natural sciences and humanities for the States of Germany, German states of Berlin and Brandenburg. Housed in three locations ...

Zenil, Hector "Leibniz medallion comes to life after 300 years
''Anima Ex Machina'', The Blog of Hector Zenil
3 November 2007. by

Wolfram Research Wolfram Research, Inc. ( ) is an American Multinational corporation, multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. ...

. In 2009 he was given the degree of doctor of philosophy ''honoris causa'' by the

National University of Córdoba The National University of Córdoba (), is a public university located in the city of Córdoba, Argentina. Founded in 1613, the university is the oldest in Argentina, the third oldest university of the Americas, with the first university being ...

. He was formerly a researcher at

IBM International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...

Thomas J. Watson Research Center The Thomas J. Watson Research Center is the headquarters for IBM Research. Its main laboratory is in Yorktown Heights, New York, 38 miles (61 km) north of New York City. It also operates facilities in Cambridge, Massachusetts and Albany, ...

and a professor at the

Federal University of Rio de Janeiro The Federal University of Rio de Janeiro (, UFRJ) is a public university, public research university in Rio de Janeiro, Brazil. It is the largest federal university in the country and is one of the Brazilian centers of excellence in teaching and r ...

Bibliography

*''Information, Randomness & Incompleteness'' (

World Scientific World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore. The company was founded in 1981. It publishes about 600 books annually, with more than 170 journals in var ...

1987)
online
*''Algorithmic Information Theory'' (

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

1987)
online
*''Information-theoretic Incompleteness'' (

1992)
online
*''The Limits of Mathematics'' (

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

1998)
online
) *''The Unknowable'' (

1999)
online
*''Exploring Randomness'' (

2001)
online
*''Conversations with a Mathematician'' (

2002)
online
*''From Philosophy to Program Size''
Tallinn Cybernetics Institute
2003) *''Meta Math!: The Quest for Omega'' (

Pantheon Books Pantheon Books is an American book publishing imprint. Founded in 1942 as an independent publishing house in New York City by Kurt and Helen Wolff, it specialized in introducing progressive European works to American readers. In 1961, it was ...

2005) (reprinted in UK as ''Meta Maths: The Quest for Omega'',

Atlantic Books Atlantic Books is an independent British publishing house, with its headquarters in Ormond House in Bloomsbury, in the London Borough of Camden. It is perhaps best known for publishing Aravind Adiga's debut novel '' The White Tiger'', which re ...

2006) () *''Teoria algoritmica della complessità''
G. Giappichelli Editore
2006) *''Thinking about Gödel & Turing'' (

2007)
online
) *''Mathematics, Complexity and Philosophy''
Editorial Midas
2011) *''Gödel's Way'' (

CRC Press The CRC Press, LLC is an American publishing group that specializes in producing technical books. Many of their books relate to engineering, science and mathematics. Their scope also includes books on business, forensics and information technol ...

2012) *''Proving Darwin: Making Biology Mathematical'' (

2012)
online
*''Philosophical Mathematics: Infinity, Incompleteness, Irreducibility'' ( Academia.edu 2024)
online

References

External links

G J Chaitin Home Page from academia.eduG J Chaitin Home Page from UMaine.edu in the Internet Archive

List of publications of G J Chaitin
*
Video of lecture on "Leibniz, complexity and incompleteness"
* ttp://www.flownet.com/gat/chaitin.html A short version of Chaitin's proofbr>Gregory Chaitin extended film interview and transcripts for the 'Why Are We Here?' documentary seriesChaitin Lisp on github
{{DEFAULTSORT:Chaitin, Gregory 1947 births Living people The Bronx High School of Science alumni City College of New York alumni Argentine mathematicians Argentine computer scientists 20th-century American mathematicians 21st-century American mathematicians American information theorists IBM employees Philosophers of mathematics Epistemologists Metaphysics writers American logicians 21st-century American philosophers Argentine information theorists Mathematicians from New York (state)