Alonzo Church
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Alonzo Church (June 14, 1903 – August 11, 1995) was an
American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the United States The United States of America (USA), commonly known as the United States (U.S. or US), or America, is ...

American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces ...

mathematician
and
logician Logic is an interdisciplinary field which studies truth Truth is the property of being in accord with fact A fact is something that is true True most commonly refers to truth Truth is the property of being in accord with fac ...
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 sys ...
and the foundations of
theoretical computer science Theoretical computer science (TCS) is a subset of general computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for the ...

theoretical computer science
. He is best known for the
lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system A formal system is an used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, ar ...
,
Church–Turing thesis In Computability theory (computation), 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) i ...
, proving the unsolvability of the
Entscheidungsproblem In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

Entscheidungsproblem
, Frege–Church ontology, and the
Church–Rosser theorem In lambda calculus, the Church–Rosser theorem states that, when applying Lambda calculus#Reduction, reduction rules to term (logic), terms, the ordering in which the reductions are chosen does not make a difference to the eventual result. More ...
. He also worked on philosophy of language (see e.g. Church 1970).


Life

Alonzo Church was born on June 14, 1903, in
Washington, D.C. ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument The Washington Monument is an obelisk within the National Mall The National Mall is a Landscape architecture, landscape ...
, where his father, Samuel Robbins Church, was the judge of the Municipal Court for the District of Columbia. The family later moved to Virginia after his father lost this position 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 A town is a human settlement. Towns are generally larger than villages and smaller than city, cities, though the criteria to distinguish between them vary considerably in different parts of the world. Origin and use ...

Ridgefield, Connecticut
. After graduating from Ridgefield in 1920, Church attended
Princeton University Princeton University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly tw ...

Princeton University
, 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 coordinate frame in spacetime to another frame that moves at a constant velocity relative to the ...

Lorentz transformation
s and graduated in 1924 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; or ''doctor philosophiae'') is the most common at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Be ...
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 long ...
. He married Mary Julia Kuczinski in 1925. The couple had three children, Alonzo Church, 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) is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an abse ...
. He received a two-year National Research Fellowship that enabled him to attend
Harvard University Harvard University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly t ...

Harvard University
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 i ...
and
University of Amsterdam The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public university, public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the c ...
the following year. He taught philosophy and mathematics at Princeton for nearly four decades, 1929–1967. He taught 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 1882 as a teachers college then known ...
, 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 Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an abse ...
in 1969,
Princeton University Princeton University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly tw ...

Princeton University
in 1985, and the
University at Buffalo, The State University of New York The State University of New York at Buffalo, commonly referred to as the University at Buffalo (UB), is a public In public relations Public relations (PR) is the practice of managing and disseminating information from an individual ...
in 1990 in connection with an international symposium in his honor organized by John Corcoran. A deeply religious person, Church was a lifelong member of the
Presbyterian Presbyterianism is a part of the Reformed tradition Calvinism (also called the Reformed tradition, Reformed Christianity, Reformed Protestantism, or the Reformed faith) is a major branch of Protestantism Protestantism is a form of ...
church. He died in 1995 and was buried in
Princeton Cemetery Princeton Cemetery is located in Princeton, New Jersey Princeton is a municipality with a borough A borough is an administrative division in various English language, English-speaking countries. In principle, the term ''borough'' designate ...

Princeton Cemetery
.


Mathematical work

Church is known for the following significant accomplishments: *His proof that the
Entscheidungsproblem In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

Entscheidungsproblem
, which asks for a
decision procedure In computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set t ...
to determine the truth of arbitrary propositions in a first-order mathematical
theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, G ...
, is undecidable. This is known as
Church's theorem In mathematics and computer science, the ' (, German language, German for "decision problem") 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 ...
. *His proof that Peano arithmetic is undecidable. *His articulation of what has come to be known as the
Church–Turing thesis In Computability theory (computation), 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) i ...
. *He was the founding editor of the '' Journal of Symbolic Logic'', editing its reviews section until 1979. *His invention of the
lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system A formal system is an used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, ar ...
. The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem. This result preceded
Alan Turing
Alan Turing
's work on the halting problem, which also demonstrated the existence of a problem unsolvable by mechanical means. Church and Turing then showed that the lambda calculus and the
Turing machine
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 the LISP programming language and functional programming 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 ACM SIGLOG or SIGLOG is the Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society A learned society (; also known as a learned academy, scholarly society, or academic a ...
), the
European Association for Theoretical Computer Science The European Association for Theoretical Computer Science (EATCS) is an international organization with a European focus, founded in 1972. Its aim is to facilitate the exchange of ideas and results among theoretical computer scientists as well as ...
(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 ...
), 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 ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international for . It was founded in 1947 and is the world's largest scientific and e ...
, the
Paris Kanellakis Award The Paris Kanellakis Theory and Practice Award is granted yearly by the Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society A learned society (; also known as a learn ...
, or the Gödel Prize.


Philosophical work


Students

Many of Church's doctoral students have led distinguished careers, including C. Anthony Anderson, Peter B. Andrews, George A. Barnard,
David Berlinski David Berlinski (born 1942) is an American author who has written books about mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), s ...
, 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 (born March 8, 1 ...
, Alfred L. Foster,
Leon Henkin Leon Albert Henkin (April 19, 1921, Brooklyn, New York - November 1, 2006, Oakland, California) was one of the most important logicians and mathematicians of the 20th century. His works played a strong role in the development of logic, particular ...
,
John G. Kemeny John George Kemeny (born Kemény János György; May 31, 1926 – December 26, 1992) was a HungarianHungarian may refer to: * Hungary, a country in Central Europe * Kingdom of Hungary, state of Hungary, existing between 1000 and 1946 * Hungarians ...
, Stephen C. Kleene, Simon B. Kochen,
Maurice L'Abbé
Maurice L'Abbé
,
Isaac Malitz Isaac Richard Jay Malitz (born 1947, in Cleveland, Ohio, Cleveland, Ohio) is a logician who introduced the subject of positive set theory in his 1976 Doctor of Philosophy, Ph.D. Thesis at University of California, Los Angeles, UCLA. References I ...
, Gary R. Mar,
Michael O. Rabin Michael Oser Rabin ( he, מִיכָאֵל עוזר רַבִּין; born September 1, 1931) is an Israeli mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the st ...
,
Nicholas Rescher Nicholas Rescher (; ; born 15 July 1928) is a United States, German-American philosophy, 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 Philosop ...

Nicholas Rescher
, Hartley Rogers, Jr., 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 Computer science deals with the theoretical foundations of information, algorithms and the architecture ...
,
Raymond Smullyan Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician Logic is an interdisciplinary field which studies truth Truth is the property of being in accord with fa ...
, and
Alan Turing
Alan Turing
. A more complete list of Church's students is available vi
Mathematics Genealogy Project


Books

* Alonzo Church, ''Introduction to Mathematical Logic'' () * Alonzo Church, ''The Calculi of Lambda-Conversion'' () * 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'' ()


See also

* Church–Turing–Deutsch principle *
Higher-order logic In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gener ...
*
List of pioneers in computer science This article presents a list of individuals who made transformative breakthroughs in the creation, development and imagining of what computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of ari ...
*
Modern Platonism Platonism is the philosophy of Plato and school of thought, philosophical systems closely derived from it, though contemporary platonists do not necessarily accept all of the doctrines of Plato. Platonism had a profound effect on Western though ...
*
Universal set In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a universal set leads to Russell's paradox and is consequently not allowed. However, some non-standard var ...


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' The New York Times, New York Times obituary *
OBITUARY: Alonzo Church
' from The Independent *
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