Alonzo Church
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Alonzo Church (June 14, 1903 – August 11, 1995) was an American
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 ...
, computer scientist,
logician Logic is the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...
, 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". Professor ...
and editor who made major contributions to
mathematical logic Mathematical logic is the study of 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 formal ...
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, the Church–Turing thesis, 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 â€“ 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical c ...
, 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 practical disciplines (includin ...
.


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 Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...
, where he was an exceptional student. He published his first paper on Lorentz transformations in 1924 and graduated the same year with a degree in mathematics. He stayed at Princeton for graduate work, earning a Ph.D. in mathematics in three years under Oswald Veblen. 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 university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
. He received a two-year National Research Fellowship 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 high ...
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 bein ...
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 university, public Land-grant university, land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a Normal school, teachers colle ...
, 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 research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...
in 1985, and the University at Buffalo, The State University of New York 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 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, pe ...
in 1967, to the National Academy of Sciences 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 a decision procedure 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 ...
, 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 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 ...
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'', editing its reviews section for 43 years from 1936 until 1979. *Author of the standard textbook in the field for many generations
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
Alan Turing Alan Mathison Turing (; 23 June 1912 â€“ 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical c ...
'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 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 algor ...
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 A lisp is a speech impairment in which a person misarticulates sibilants (, , , , , , , ). These misarticulations often result in unclear speech. Types * A frontal lisp occurs when the tongue is placed anterior to the target. Interdental lispi ...
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 that ...
languages in general. The Church encoding 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), and the Kurt Gödel Society (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, or the Gödel Prize.


Philosophical work

Church is also known for 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 ...
, 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 ph ...
.


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 Curtis Anthony Anderson (born May 29, 1940) is a contemporary American philosopher, currently Professor of Philosophy at the University of California at Santa Barbara. He earned his Ph.D. in philosophy from University of California at Los Angeles ...
, Peter B. Andrews, George A. Barnard, David Berlinski, William W. Boone,
Martin Davis Martin Davis may refer to: * Martin Davis (Australian footballer) (born 1936), Australian rules footballer * Martin Davis (Jamaican footballer) (born 1996), Jamaican footballer * Martin Davis (mathematician) Martin David Davis (March 8, 1928 â ...
,
Alfred L. Foster Alfred Leon Foster (1904-1994) was an American mathematician. He was a professor at the University of California, Berkeley from 1934 until 1971. In 1932 he was an Invited Speaker at the ICM in Zürich. In 1934 he accepted a regular position at ...
, Leon Henkin, John G. Kemeny, Stephen C. Kleene, Simon B. Kochen,
Maurice L'Abbé Maurice L'Abbé (1920 – July 21, 2006) was a Canadian academic and mathematician. Born in Ottawa, Ontario, L'Abbé obtained his license in mathematics in 1945 from the Université de Montréal, and a doctorate in mathematics from the Pri ...
, Isaac Malitz,
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 and linguistics, philosophy of science, computational philosophy, the philosophy of ...
, Michael O. Rabin, Nicholas Rescher, Hartley Rogers, Jr., J. Barkley Rosser, Dana Scott, Raymond Smullyan, and
Alan Turing Alan Mathison Turing (; 23 June 1912 â€“ 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical c ...
.


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 * 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 Division
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 ''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 ...
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 publishe ...
*
In memoriam: Alonzo Church (1903–1995)
' by
Irving H. Anellis Irving H. Anellis (1946 to 2013) was a historian of philosophy. Anellis began his study of philosophy in Boston, Massachusetts at Northeastern University, gaining his B.A. in 1969. He continued in Pittsburgh, Pennsylvania at Duquesne University, ...
, ''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 ...
'' 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