Alonzo Church

Please help improve this article by expanding it. Further information might be found on the talk page. (March 2007)

Alonzo Church
Alonzo Church (1903–1995)
Born	June 14, 1903(1903-06-14) Washington, DC, USA
Died	November 8, 1995 (aged 92) Hudson, Ohio, USA
Residence	United States
Nationality	American
Fields	Mathematics, Logic
Institutions	Princeton University 1929–67 University of California, Los Angeles 1967–95
Alma mater	Princeton University
Doctoral advisor	Oswald Veblen
Doctoral students	C. Anthony Anderson Peter Andrews George Alfred Barnard Martin Davis Leon Henkin David Kaplan John George Kemeny Stephen Kleene Michael O. Rabin Hartley Rogers, Jr J. Barkley Rosser Nathan Salmon Dana Scott Raymond Smullyan Alan Turing

Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, Church Frege ontology, and the Church-Rosser theorem.

Life

Alonzo Church was born on June 14, 1903 in Washington, DC where his father, Samuel Robbins Church, was the Justice 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, Alonzo Church was able to attend Ridgefield High School in Connecticut. After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformation, and graduating in 1924 with a degree in mathematics. He stayed on at Princeton, earning a Ph.D. in mathematics in three years under Oswald Veblen.

He married Mary Julia Kuczinski in 1925 and 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 and then received a two-year National Research Fellowship. This allowed him to attend Harvard University in 1927–1928 and then both University of Göttingen and University of Amsterdam the following year. He taught at Princeton, 1929–1967, and at the University of California, Los Angeles, 1967–1990.

He died in 1995 and was buried in Princeton Cemetery.

Mathematical work

Church is best known for the following accomplishments:

• His proof that Peano arithmetic and first-order logic are undecidable. The latter result is known as Church's theorem.
• His articulation of what has come to be known as Church's thesis.
• He was the founding editor of the Journal of Symbolic Logic, editing its reviews section until 1979.
• His creation of the lambda calculus.

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.

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.

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, Gary Mar, Michael O. Rabin, Hartley Rogers, Jr, J. Barkley Rosser, Dana Scott, Raymond Smullyan, and Alan Turing. See [1]. A more complete list is at [2] as part of the Mathematics Genealogy Project.

See also

• Lambda calculus
• Church-Turing thesis
• Church-Turing-Deutsch principle
• Higher-order logic
• Universal set
• Church-Rosser theorem

Books

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

Sources and external links

Logic portal

• O'Connor, John J.; Robertson, Edmund F., "Alonzo Church", MacTutor History of Mathematics archive .
• H B Enderton, In memoriam: Alonzo Church
• Alonzo Church at the Mathematics Genealogy Project
• "Fine Hall in its golden age: Remembrances of Princeton in the early fifties" by Gian-Carlo Rota. Contains a section on Church at Princeton.
• Interview of Church about his time at Princeton
• Archived papers
• A bibliography of Church's reviews for The Journal of Symbolic Logic, with a link to each