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

Introduction to Mathematical Logic

*The

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'

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, ''

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, structure, space, models, and change.
History
On ...

, computer scientist
A computer scientist is a person who is trained in the academic study of computer science.
Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

, 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
A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

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

and editor who made major contributions to mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

and the foundations of theoretical computer science
Theoretical 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 circumsc ...

. He is best known for the lambda calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...

, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem
In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the state ...

, the Frege–Church ontology, and the Church–Rosser theorem
In lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does not make a difference to the eventual result.
More precisely, if there are two distinct red ...

. 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
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

.
Life

Alonzo Church was born on June 14, 1903, inWashington, D.C.
)
, image_skyline =
, image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...

, where his father, Samuel Robbins Church, was a Justice of the Peace
A justice of the peace (JP) is a judicial officer of a lower or ''puisne'' court, elected or appointed by means of a commission ( letters patent) to keep the peace. In past centuries the term commissioner of the peace was often used with the sa ...

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
The United States Senate Librarian is the chief librarian of the United States Senate Library. The Senate Librarian reports to the Secretary of the United States Senate.
*George S. Wagner, 1871—1875
*George F. Dawson, 1875—1879
*P. J. Pier ...

from 1881-1901, and great grandson of Alonzo Church
Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scien ...

, 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
Ridgefield is a town in Fairfield County, Connecticut, United States. Situated in the foothills of the Berkshire Mountains, the 300-year-old community had a population of 25,033 at the 2020 census. The town center, which was formerly a borough ...

. After graduating from Ridgefield in 1920, Church attended Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

, where he was an exceptional student. He published his first paper on Lorentz transformation
In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant velo ...

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
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

. He received a two-year National Research Fellowship
National may refer to:
Common uses
* Nation or country
** Nationality – a ''national'' is a person who is subject to a nation, regardless of whether the person has full rights as a citizen
Places in the United States
* National, Maryland, ce ...

that enabled him to attend Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

in 1927–1928, and the University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

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 being ...

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
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

, 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 in 1969, Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

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 research university with campuses in Buffalo and Amherst, New York. The university was founded in 1846 ...

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 Nati ...

in 1978.
A deeply religious person, Church was a lifelong member of the Presbyterian
Presbyterianism is a part of the Reformed tradition within Protestantism that broke from the Roman Catholic Church in Scotland by John Knox, who was a priest at St. Giles Cathedral (Church of Scotland). Presbyterian churches derive their nam ...

church. He died on August 11, 1995 at the age of 92. He is buried in Princeton Cemetery
Princeton Cemetery is located in Princeton, New Jersey, United States. It is owned by the Nassau Presbyterian Church. John F. Hageman in his 1878 history of Princeton, New Jersey refers to the cemetery as "The Westminster Abbey of the United Stat ...

.
Mathematical work

Church is known for the following significant accomplishments: *His proof that theEntscheidungsproblem
In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the state ...

, which asks for a decision 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 wheth ...

to determine the truth of arbitrary propositions in a first-order mathematical theory
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...

, is undecidable. This is known as Church's theorem.
*His invention of the lambda calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...

.
*His utilization of the lambda calculus to prove that Peano arithmetic
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly u ...

is undecidable.
*His articulation of what has come to be known as the Church–Turing thesis.
*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'', Zentra ...

'', 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
In lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does not make a difference to the eventual result.
More precisely, if there are two distinct red ...

The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem
In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the state ...

. 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
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a g ...

, 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
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...

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 Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declar ...

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 da ...

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), 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 ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...

, 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
The Gödel Prize is an annual prize for outstanding papers in the area of theoretical computer science, given jointly by the European Association for Theoretical Computer Science (EATCS) and the Association for Computing Machinery Special Interes ...

.
Philosophical work

Church is also known for the Frege–Church ontology, which he created based on the philosophical ideas ofGottlob 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 phil ...

.
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
Peter Bruce Andrews (born 1937) is an American mathematician and Professor of Mathematics, Emeritus at Carnegie Mellon University in Pittsburgh, Pennsylvania, and the creator of the mathematical logic Q0. He received his Ph.D. from Princeton Uni ...

, George A. Barnard
George Alfred Barnard (23 September 1915 – 9 August 2002) was a British statistician known particularly for his work on the foundations of statistics and on quality control.
Biography
George Barnard was born in Walthamstow, Lon ...

, David Berlinski
David Berlinski (born 1942) is an American author who has written books about mathematics and the history of science as well as fiction. An opponent of evolution, he is a senior fellow of the Discovery Institute's Center for Science and Culture ...

, 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 scholar ...

, John G. Kemeny, 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
Simon Bernhard Kochen (; born 14 August 1934, Antwerp) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics.
Biography
Kochen received his Ph.D. (''Ultrafiltered Products and Arithmetical Extens ...

, 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 land-grant research un ...

, Gary R. Mar
Gary R. Mar is an American philosopher specializing in logic, the philosophy of logic, the philosophy of mathematics, analytic philosophy, philosophy of language, philosophy of language and linguistics, philosophy of science, computational philosop ...

, 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 fo ...

, 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 York ...

, J. Barkley Rosser
John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church–Rosser theorem, in lambda calculus. He also developed what is now called the "Rosser siev ...

, 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
Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher.
Born in Far Rockaway, New York, his first career was stage magic. He earned a BSc from th ...

, 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
In computer science and quantum physics, the Church–Turing–Deutsch principle (CTD principle) is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985. The principle states that a universal computing d ...

* 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 express ...

* List of pioneers in computer science
This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do.
Pioneers
: ''To arrange the list by date or person (ascending or descending), click that column's small "up-do ...

* Platonism#Modern Platonism
* Universal set
In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory inc ...

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
''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid d ...

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 format in 2003. The last printed edition was publis ...

*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
The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL is ...

'' 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