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Encyclopedia > Alonzo Church
Alonzo Church
Alonzo Church (1903–1995)
Alonzo Church (1903–1995)
Born 6/14/1903
Washington, DC, USA
Died 8/11/1995
Residence USA
Nationality USA
Field Mathematics
Institutions Princeton University 1929-1967 University of California, Los Angeles 1967-1995
Alma mater Princeton University
Academic advisor   Oswald Veblen


Alonzo Church (June 14, 1903August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. Born in Washington, DC, he received a bachelor's degree from Princeton University in 1924, completing his Ph.D. there in 1927, under Oswald Veblen. After a post-doctoral fellowship at Göttingen, he taught at Princeton, 1929–1967, and at the University of California, Los Angeles, 1967–1990. Image File history File links This is a lossless scalable vector image. ... Image File history File links Size of this preview: 450 × 600 pixelsFull resolution (682 × 909 pixel, file size: 226 KB, MIME type: image/jpeg)Alonzo Church Princeton University http://libweb. ... Aerial photo (looking NW) of the Washington Monument and the White House in Washington, DC. Washington, D.C., officially the District of Columbia (also known as D.C.; Washington; the Nations Capital; the District; and, historically, the Federal City) is the capital city and administrative district of the United... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Princeton University is a private coeducational research university located in Princeton, New Jersey, in the United States of America. ... The University of California, Los Angeles, generally known as UCLA, is a public university whose main campus is located in the affluent Westwood neighborhood of Los Angeles, California, United States. ... Princeton University is a private coeducational research university located in Princeton, New Jersey, in the United States of America. ... Oswald Veblen (24 June 1880 - 10 August 1960) was an American mathematician. ... June 14 is the 165th day of the year (166th in leap years) in the Gregorian calendar. ... 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... is the 223rd day of the year (224th in leap years) in the Gregorian calendar. ... Year 1995 (MCMXCV) was a common year starting on Sunday (link will display full 1995 Gregorian calendar). ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... A logician is a person, such as a philosopher or mathematician, whose topic of scholarly study is logic. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Aerial photo (looking NW) of the Washington Monument and the White House in Washington, DC. Washington, D.C., officially the District of Columbia (also known as D.C.; Washington; the Nations Capital; the District; and, historically, the Federal City) is the capital city and administrative district of the United... A bachelors degree is usually an undergraduate academic degree awarded for a course or major that generally lasts for three, four, or in some cases and countries, five or six years. ... Princeton University is a private coeducational research university located in Princeton, New Jersey, in the United States of America. ... Doctor of Philosophy, abbreviated Ph. ... Oswald Veblen (24 June 1880 - 10 August 1960) was an American mathematician. ... A postdoctoral (colloquially, post-doc) appointment is a usually temporary academic job held by a person who has completed his or her doctoral studies. ... The Georg-August University of Göttingen (Georg-August-Universität Göttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ... The University of California, Los Angeles, generally known as UCLA, is a public university whose main campus is located in the affluent Westwood neighborhood of Los Angeles, California, United States. ...

Contents

Mathematical work

Church is best known for the following accomplishments:

The lambda calculus emerged in his famous 1936 paper showing the existence of an "undecidable problem". This result preceded Alan Turing's famous work on the halting problem which also demonstrated the existence of a problem unsolvable by mechanical means. He 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. In mathematics, the Peano axioms (or Peano postulates) are a set of first-order axioms proposed by Giuseppe Peano which determine the theory of Peano arithmetic (also known as first-order arithmetic). ... First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ... Undecidable has more than one meaning: In mathematical logic: A decision problem is undecidable if there is no known algorithm that decides it. ... In mathematics, the Entscheidungsproblem (German for decision problem) is a challenge posed by David Hilbert in 1928. ... In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ... The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic—the largest such organization in the world. ... The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ... The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ... 1936 (MCMXXXVI) was a leap year starting on Wednesday (link will take you to calendar). ... Alan Mathison Turing, OBE (23 June 1912 – 7 June 1954) was an English mathematician, logician, and cryptographer. ... In computability theory the halting problem is a decision problem which can be informally stated as follows: Given a description of a program and a finite input, decide whether the program finishes running or will run forever, given that input. ... An artistic representation of a Turing Machine . ... In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ...


The lambda calculus influenced the design of the LISP programming language and functional programming languages in general. The Church encoding is named in his honor. Lisp is a family of computer programming languages with a long history and a distinctive fully-parenthesized syntax. ... Functional programming is a programming paradigm that conceives computation as the evaluation of mathematical functions and avoids state and mutable data. ... Church encoding is a means of embedding data and operators into the lambda calculus, the most familiar form being the church numerals, a representation of the natural numbers using lambda notation. ...


Students

Church's doctoral students were an extraordinarily accomplished lot, including C. Anthony Anderson, Peter Andrews, Martin Davis, Leon Henkin, John George Kemeny, Stephen Kleene, Michael O. Rabin, Hartley Rogers, Jr, J. Barkley Rosser, Dana Scott, Raymond Smullyan, and Alan Turing. See [1]. Curtis Anthony Anderson is a contemporary philosopher, presently Professor of Philosophy at the University of California at Santa Barbara. ... Peter B. Andrews is an American mathematician and Professor of Mathematics at Carnegie Mellon University in Pittsburgh, Pennsylvania. ... Martin Davis, (born 1926, New York City) is an American mathematician, known for his work on Hilberts tenth problem. ... Leon Henkin (19 April 1921–1 November 2006) was a logician at the University of California, Berkeley. ... John George Kemeny (Kemény János) (May 31, 1926–December 26, 1992), U.S. computer scientist and educator best known for co-developing the BASIC programming language in 1964 with Thomas Eugene Kurtz. ... Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science. ... Michael Oser Rabin (born 1931 in Breslau, Germany, today in Poland) is a noted computer scientist and a recipient of the Turing Award, the most prestigious award in the field. ... Hartley Rogers, Jr is a Professor of Mathematics at the Massachusetts Institute of Technology. ... John Barkley Rosser Sr. ... Dana Stewart Scott (born 1932) 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, California. ... Raymond Merrill Smullyan (born 1919) is a mathematician, logician, philosopher, and magician. ... Alan Mathison Turing, OBE (23 June 1912 – 7 June 1954) was an English mathematician, logician, and cryptographer. ...


Death

He died in 1995 and was buried in Princeton Cemetery. Princeton Cemetery is located in Borough of Princeton, New Jersey. ...

Academic Genealogy
Notable teachers Notable students
Oswald Veblen C. Anthony Anderson
Peter Andrews
George Alfred Barnard
Martin Davis
Leon Henkin
David Kaplan
John George Kemeny
Stephen Kleene
John McCarthy (computer scientist)
Michael O. Rabin
Hartley Rogers, Jr
J. Barkley Rosser
Dana Scott
Raymond Smullyan
Alan Turing

Oswald Veblen (24 June 1880 - 10 August 1960) was an American mathematician. ... Curtis Anthony Anderson is a contemporary philosopher, presently Professor of Philosophy at the University of California at Santa Barbara. ... Peter B. Andrews is an American mathematician and Professor of Mathematics at Carnegie Mellon University in Pittsburgh, Pennsylvania. ... George Alfred Barnard (September 23, 1915 - August 9, 2002) British statistician known particularly for his work on the foundations of statistics and on quality control. ... Martin Davis, (born 1926, New York City) is an American mathematician, known for his work on Hilberts tenth problem. ... Leon Henkin (19 April 1921–1 November 2006) was a logician at the University of California, Berkeley. ... David Benjamin Kaplan (1933) is an American philosopher and logician teaching at UCLA. He is known in particular for his work on demonstratives, on propositions, and on reference in opaque (intensional) contexts. ... John George Kemeny (Kemény János) (May 31, 1926–December 26, 1992), U.S. computer scientist and educator best known for co-developing the BASIC programming language in 1964 with Thomas Eugene Kurtz. ... Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science. ... John McCarthy (born September 4, 1927, in Boston, Massachusetts, sometimes known affectionately as Uncle John McCarthy), is a prominent computer scientist who received the Turing Award in 1971 for his major contributions to the field of Artificial Intelligence. ... Michael Oser Rabin (born 1931 in Breslau, Germany, today in Poland) is a noted computer scientist and a recipient of the Turing Award, the most prestigious award in the field. ... Hartley Rogers, Jr is a Professor of Mathematics at the Massachusetts Institute of Technology. ... John Barkley Rosser Sr. ... Dana Stewart Scott (born 1932) 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, California. ... Raymond Merrill Smullyan (born 1919) is a mathematician, logician, philosopher, and magician. ... Alan Mathison Turing, OBE (23 June 1912 – 7 June 1954) was an English mathematician, logician, and cryptographer. ...

See also

In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ... Alonzo Church, Alan Turing, and David Deutsch contributed to the Church-Turing-Deutsch principle, also known as the CTD principle, of computer science. ... In mathematics, higher-order logic is distinguished from first-order logic in a number of ways. ... In mathematics, and particularly in applications to set theory and the foundations of mathematics, a universe or universal class (or if a set, universal set) is, roughly speaking, a class that is large enough to contain (in some sense) all of the sets that one may wish to use. ...

Books

  • Alonzo Church, Introduction to Mathematical Logic (ISBN 0-691-02906-7)

Sources and external links

Logic Portal

  Results from FactBites:
 
Alonzo Church - Wikipedia, the free encyclopedia (320 words)
Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science.
The Church boolean is named in his honor.
Church's doctoral students were an extraordinarily accomplished lot, including C.
Church–Turing thesis - Wikipedia, the free encyclopedia (1601 words)
In computability theory the Church–Turing thesis, Church's thesis, Church's conjecture or Turing's thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers.
A few months earlier Church had proven a similar result in "A Note on the Entscheidungsproblem" but he used the notions of recursive functions and lambda-definable functions to formally describe effective computability.
Lambda-definable functions were introduced by Alonzo Church and Stephen Kleene (Church 1932, 1936a, 1941, Kleene 1935), and recursive functions were introduced by Kurt Gödel and Jacques Herbrand (Gödel 1934, Herbrand 1932).
  More results at FactBites »

 
 

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