Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist,

Introduction to Mathematical Logic

*The Church–Rosser theorem The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem. This result preceded

Alonzo Church: Life and Work

Introduction to the ''Collected Works of Alonzo Church'', MIT Press, not yet published. * Enderton, Herbert B.

In memoriam: Alonzo Church

''The Bulletin of Symbolic Logic'', vol. 1, no. 4 (Dec. 1995), pp. 486–488. * Wade, Nicholas

(obituary), ''The New York Times'', September 5, 1995, p. B6. * Hodges, Wilfred

Obituary: Alonzo Church

''The Independent (London)'', September 14, 1995.

interviewed by William Aspray on 17 May 1984. ''The Princeton Mathematics Community in the 1930s: An Oral-History Project'', transcript number 5. * Rota, Gian-Carlo

Fine Hall in its golden age: Remembrances of Princeton in the early fifties

In ''A Century of Mathematics in America, Part II'', edited by Peter Duren, AMS History of Mathematics, vol 2, American Mathematical Society, 1989, pp. 223–226. Also available

* *

The Alonzo Church Papers, 1924–1995: finding aid.

* *'' ttps://www.nytimes.com/1995/09/05/obituaries/alonzo-church-92-theorist-of-the-limits-of-mathematics.html Alonzo Church, 92, Theorist Of the Limits of Mathematics' New York Times obituary *

OBITUARY: Alonzo Church

' from

In memoriam: Alonzo Church (1903–1995)

' by Irving H. Anellis, ''Modern Logic'' Vol. 5, No. 4 (1995). *

In memoriam: Alonzo Church 1903–1995

' by H. B. Enderton, '' The Bulletin of Symbolic Logic'' Vol. 1, No.5 (1995). {{DEFAULTSORT:Church, Alonzo 1903 births 1995 deaths 20th-century American mathematicians American logicians American Presbyterians Computability theorists Princeton University alumni Harvard University alumni Princeton University faculty University of California, Los Angeles faculty Burials at Princeton Cemetery Philosophers from Washington, D.C. Philosophers from California Philosophers from New Jersey Mathematicians from Washington, D.C. 20th-century American philosophers Corresponding Fellows of the British Academy

logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

, philosopher, professor
Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professo ...

and editor who made major contributions to mathematical logic and the foundations of theoretical computer science
computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory.
It is difficult to circumscribe th ...

. He is best known for the lambda calculus, the Church–Turing thesis
In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of com ...

, proving the unsolvability of the Entscheidungsproblem, the Frege–Church ontology The Frege–Church ontology is an ontology, a theory of existence. Everything is considered as being in three categories, object (referent, denotation), name, or concept ( sense). The ontology was developed by Alonzo ChurchChurch, Alonzo. "A Form ...

, and the Church–Rosser theorem. He also worked on philosophy of language (see e.g. Church 1970). Alongside his student Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...

, Church is considered one of the founders of computer science.
Life

Alonzo Church was born on June 14, 1903, in Washington, D.C., where his father, Samuel Robbins Church, was a Justice of the Peace and the judge of the Municipal Court for the District of Columbia. He was the grandson of Alonzo Webster Church (1829-1909), United States Senate Librarian from 1881-1901, and great grandson of Alonzo Church, a Professor of Mathematics and Astronomy and 6th President of the University of Georgia. As a young boy, Church was partially blinded by an air gun accident. The family later moved to Virginia after his father lost his position at the university because of failing eyesight. With help from his uncle, also named Alonzo Church, the son attended the private Ridgefield School for Boys in Ridgefield, Connecticut. After graduating from Ridgefield in 1920, Church attended Princeton University, where he was an exceptional student. He published his first paper onLorentz transformation
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation ...

s in 1924 and graduated the same year with a degree in mathematics. He stayed at Princeton for graduate work, earning a Ph.D.
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in mathematics in three years under Oswald Veblen
Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...

.
He married Mary Julia Kuczinski in 1925. The couple had three children, Alonzo Jr. (1929), Mary Ann (1933) and Mildred (1938).
After receiving his Ph.D., he taught briefly as an instructor at the University of Chicago. He received a two-year National Research Fellowship that enabled him to attend Harvard University in 1927–1928, and the University of Göttingen and University of Amsterdam
The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other bei ...

the following year.
He taught philosophy and mathematics at Princeton for nearly four decades, 1929–1967. He held the Flint Professorship of Philosophy and Mathematics at the University of California, Los Angeles, 1967–1990. He was a Plenary Speaker at the ICM in 1962 in Stockholm.
He received honorary Doctor of Science degrees from Case Western Reserve University
Case Western Reserve University (CWRU) is a private research university in Cleveland, Ohio. Case Western Reserve was established in 1967, when Western Reserve University, founded in 1826 and named for its location in the Connecticut Western R ...

in 1969, Princeton University in 1985, and the University at Buffalo, The State University of New York
The State University of New York at Buffalo, commonly called the University at Buffalo (UB) and sometimes called SUNY Buffalo, is a public university, public research university with campuses in Buffalo, New York, Buffalo and Amherst, New Yor ...

in 1990 in connection with an international symposium in his honor organized by John Corcoran.
He was elected a Corresponding Fellow of the British Academy
The British Academy is the United Kingdom's national academy for the humanities and the social sciences.
It was established in 1902 and received its royal charter in the same year. It is now a fellowship of more than 1,000 leading scholars span ...

(FBA) in 1966, to the American Academy of the Arts and Sciences in 1967, to the National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nat ...

in 1978.
A deeply religious person, Church was a lifelong member of the Presbyterian church. He died on August 11, 1995 at the age of 92. He is buried in Princeton Cemetery.
Mathematical work

Church is known for the following significant accomplishments: *His proof that the Entscheidungsproblem, which asks for adecision procedure
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whet ...

to determine the truth of arbitrary propositions in a first-order mathematical theory, is undecidable. This is known as Church's theorem.
*His invention of the lambda calculus.
*His utilization of the lambda calculus to prove that Peano arithmetic is undecidable.
*His articulation of what has come to be known as the Church–Turing thesis
In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of com ...

.
*Being a founding editor of the ''Journal of Symbolic Logic
The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zent ...

'', editing its reviews section for 43 years from 1936 until 1979.
*Author of the standard textbook in the field for many generationsIntroduction to Mathematical Logic

*The Church–Rosser theorem The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem. This result preceded

Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...

's work on the halting problem, which also demonstrated the existence of a problem unsolvable by mechanical means. Upon hearing of Church's work, Turing enrolled at Princeton later that year under Church for a Ph.D. Church and Turing then showed that the lambda calculus and the Turing machine used in Turing's halting problem were equivalent in capabilities, and subsequently demonstrated a variety of alternative "mechanical processes for computation". This resulted in the Church–Turing thesis.
The efforts for automatically generating a controller implementation from specifications originates from his ideas.
The lambda calculus influenced the design of Lisp and functional programming
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions tha ...

languages in general. The Church encoding
In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded ...

is named in his honor.
In his honor the Alonzo Church Award for Outstanding Contributions to Logic and Computation was established in 2015 by the Association for Computing Machinery Special Interest Group for Logic and Computation (ACM SIGLOG
ACM SIGLOG or SIGLOG is the Association for Computing Machinery Special Interest Group on Logic and Computation. It publishes a news magazine (''SIGLOG News''), and has the annual ACM-IEEE Symposium on Logic in Computer Science (LICS) as its flag ...

), the European Association for Theoretical Computer Science (EATCS), the European Association for Computer Science Logic (EACSL
The European Association for Computer Science Logic (EACSL), founded 14 July 1992,

. Description of goals from EACSL official web ...

), and the . Description of goals from EACSL official web ...

Kurt Gödel Society The Kurt Gödel Society was founded in Vienna, Austria in 1987. It is an international organization aimed at promoting research primarily on logic, philosophy and the history of mathematics, with special attention to connections with Kurt Gödel, ...

(KGS). The award
is for an outstanding contribution to the field published within the past 25 years and must not yet have received recognition via another major award, such as the Turing Award, the Paris Kanellakis Award The Paris Kanellakis Theory and Practice Award is granted yearly by the Association for Computing Machinery (ACM) to honor "specific theoretical accomplishments that have had a significant and demonstrable effect on the practice of computing". It wa ...

, or the Gödel Prize.
Philosophical work

Church is also known for theFrege–Church ontology The Frege–Church ontology is an ontology, a theory of existence. Everything is considered as being in three categories, object (referent, denotation), name, or concept ( sense). The ontology was developed by Alonzo ChurchChurch, Alonzo. "A Form ...

, which he created based on the philosophical ideas of Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic phi ...

.
Students

Over the course of his academic career, Church oversaw 31 doctoral students. Many of them have led distinguished careers in mathematics, computer science, and other academic subjects, including C. Anthony Anderson, Peter B. Andrews, George A. Barnard, David Berlinski, William W. Boone, Martin Davis, Alfred L. Foster,Leon Henkin
Leon Albert Henkin (April 19, 1921, Brooklyn, New York - November 1, 2006, Oakland, California) was an American logician, whose works played a strong role in the development of logic, particularly in the theory of types. He was an active schola ...

, John G. Kemeny
John George Kemeny (born Kemény János György; May 31, 1926 – December 26, 1992) was a Hungarian-born American mathematician, computer scientist, and educator best known for co-developing the BASIC programming language in 1964 with Thomas E ...

, Stephen C. Kleene
Stephen Cole Kleene ( ; January 5, 1909 – January 25, 1994) was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of ...

, Simon B. Kochen, Maurice L'Abbé, Isaac Malitz
Isaac Richard Jay Malitz (born 1947, in Cleveland, Ohio) is a logician who introduced the subject of positive set theory in his 1976 Ph.D. Thesis at UCLA
The University of California, Los Angeles (UCLA) is a public university, public Lan ...

, Gary R. Mar, Michael O. Rabin
Michael Oser Rabin ( he, מִיכָאֵל עוזר רַבִּין; born September 1, 1931) is an Israeli mathematician and computer scientist and a recipient of the Turing Award.
Biography Early life and education
Rabin was born in 1931 in ...

, Nicholas Rescher
Nicholas Rescher (; ; born 15 July 1928) is a German-American philosopher, polymath, and author, who has been a professor of philosophy at the University of Pittsburgh since 1961. He is chairman of the Center for Philosophy of Science and was ...

, Hartley Rogers, Jr. Hartley Rogers Jr. (July 6, 1926 – July 17, 2015) was a mathematician who worked in computability theory, and was a professor in the Mathematics Department of the Massachusetts Institute of Technology.
Biography
Born in 1926 in Buffalo, New Yor ...

, J. Barkley Rosser, Dana Scott
Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, Ca ...

, Raymond Smullyan, and Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...

.
Books

* Alonzo Church, ''Introduction to Mathematical Logic'' (1944) () * Alonzo Church, ''The Calculi of Lambda-Conversion'' (1941) () * Alonzo Church, ''A Bibliography of Symbolic Logic, 1666–1935'' () * C. Anthony Anderson and Michael Zelëny, (eds.), ''Logic, Meaning and Computation: Essays in Memory of Alonzo Church'' () * Tyler Burge and Herbert Enderton (eds.), ''The Collected Works of Alonzo Church'' (2019) (ISBN 978-0-262-02564-5)See also

* Church–Turing–Deutsch principle *Higher-order logic
mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expr ...

* List of pioneers in computer science
* Platonism#Modern Platonism
* Universal set
Notes

References

* Enderton, Herbert B.Alonzo Church: Life and Work

Introduction to the ''Collected Works of Alonzo Church'', MIT Press, not yet published. * Enderton, Herbert B.

In memoriam: Alonzo Church

''The Bulletin of Symbolic Logic'', vol. 1, no. 4 (Dec. 1995), pp. 486–488. * Wade, Nicholas

(obituary), ''The New York Times'', September 5, 1995, p. B6. * Hodges, Wilfred

Obituary: Alonzo Church

''The Independent (London)'', September 14, 1995.

interviewed by William Aspray on 17 May 1984. ''The Princeton Mathematics Community in the 1930s: An Oral-History Project'', transcript number 5. * Rota, Gian-Carlo

Fine Hall in its golden age: Remembrances of Princeton in the early fifties

In ''A Century of Mathematics in America, Part II'', edited by Peter Duren, AMS History of Mathematics, vol 2, American Mathematical Society, 1989, pp. 223–226. Also available

* *

External links

* * Princeton University Library, Manuscripts DivisionThe Alonzo Church Papers, 1924–1995: finding aid.

* *'' ttps://www.nytimes.com/1995/09/05/obituaries/alonzo-church-92-theorist-of-the-limits-of-mathematics.html Alonzo Church, 92, Theorist Of the Limits of Mathematics' New York Times obituary *

OBITUARY: Alonzo Church

' from

The Independent
''The Independent'' is a British online newspaper. It was established in 1986 as a national morning printed paper. Nicknamed the ''Indy'', it began as a broadsheet and changed to Tabloid (newspaper format), tabloid format in 2003. The last p ...

*In memoriam: Alonzo Church (1903–1995)

' by Irving H. Anellis, ''Modern Logic'' Vol. 5, No. 4 (1995). *

In memoriam: Alonzo Church 1903–1995

' by H. B. Enderton, '' The Bulletin of Symbolic Logic'' Vol. 1, No.5 (1995). {{DEFAULTSORT:Church, Alonzo 1903 births 1995 deaths 20th-century American mathematicians American logicians American Presbyterians Computability theorists Princeton University alumni Harvard University alumni Princeton University faculty University of California, Los Angeles faculty Burials at Princeton Cemetery Philosophers from Washington, D.C. Philosophers from California Philosophers from New Jersey Mathematicians from Washington, D.C. 20th-century American philosophers Corresponding Fellows of the British Academy