Haskell Curry

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Haskell Brooks Curry
Born	September 12, 1900 (1900-09-12) Millis, Massachusetts
Died	September 1, 1982(1982-09-01) (aged 81) State College, Pennsylvania
Citizenship	USA
Fields	Mathematics Logic
Institutions	Penn State Universiteit van Amsterdam
Alma mater	Harvard University
Doctoral advisor	David Hilbert
Doctoral students	Maarten Bunder Edward Cogan Bruce Lercher Hilbert Levitz Kenneth Lowen Luis Sanchis Jonathan Seldin
Known for	Combinatory logic Curry–Howard correspondence Curry's paradox
Influences	Alfred North Whitehead Bertrand Russell Moses Schönfinkel

Haskell Brooks Curry (September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic; while the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel, much of the development was done by Curry. Curry is also known for Curry's paradox and the Curry–Howard correspondence. There are three programming languages named after him, Haskell, Brooks and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.

Life

Curry was born on September 12, 1900, in Millis, Massachusetts, to Samuel Silas Curry and Anna Baright Curry, who ran a school for elocution. He entered Harvard University in 1916 to study medicine but switched to mathematics before graduating in 1920. After two years of graduate work in electrical engineering at MIT, he returned to Harvard to study physics, earning a MA in 1924. Curry's interest in mathematical logic started during this period when he was introduced to the Principia Mathematica, the attempt by Alfred North Whitehead and Bertrand Russell to ground mathematics in symbolic logic. Remaining at Harvard, Curry pursued a Ph.D. in mathematics. While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic. In 1927, while an instructor at Princeton University, he discovered the work of Moses Schönfinkel in combinatory logic. Schönfinkel's work had anticipated much of Curry's own research, and as a consequence, he moved to Göttingen where he could work with Heinrich Behmann and Paul Bernays, who were familiar with Schönfinkel's work. Curry was supervised by David Hilbert and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation on combinatory logic.^[1]

In 1928, before leaving for Göttingen, Curry married Mary Virginia Wheatley. The couple lived in Germany while Curry completed his dissertation, then, in 1929, moved to State College, Pennsylvania where Curry accepted a position at Penn State College. They had two children, Anne Wright Curry (July 27, 1930) and Robert Wheatley Curry (July 6, 1934). Curry remained at Penn State for the next 37 years. He spent one year at University of Chicago in 1931–32 under a National Research Fellowship and one year in 1938–39 at the Institute for Advanced Study in Princeton. In 1942 he took a leave of absence to do applied mathematics for the US government during World War II. Immediately after the war he worked on the ENIAC project, in 1945 and 1946. Under a Fulbright fellowship, he collaborated with Robert Feys in Louvain, Belgium. After retiring from Penn State in 1966, Curry accepted a position at the University of Amsterdam. In 1970, after finishing the second volume of his treatise on the combinatory logic, Curry retired from the University of Amsterdam and returned to State College, Pennsylvania.

Haskell Curry died on September 1, 1982 in State College, Pennsylvania.

Work

The focus of Curry's work were attempts to show that combinatory logic could provide a foundation for mathematics. Towards the end of 1933, he learned of the Kleene–Rosser paradox from correspondence with John Rosser. The paradox, developed by Rosser and Stephen Kleene had proved the inconsistency of a number of related formal systems including one proposed by Church (a system which had the lambda calculus as a consistent subsystem) and Curry's own system.^[1] However, unlike Church, Kleene, and Rosser, Curry did not give up on the foundational approach, saying that he did not want to "run away from paradoxes."^[2]

By working in the area of Combinatory Logic for his entire career, Curry essentially became the founder and biggest name in the field. Combinatory logic is the foundation for one style of functional programming language. The power and scope of combinatory logic is quite similar to that of the lambda calculus of Alonzo Church, and the latter formalism has tended to predominate in recent decades.

He taught at Harvard, Princeton, and from 1929 to 1966, at the Pennsylvania State University. In 1942, he published Curry's paradox. In 1966 he became professor of mathematics at the Universiteit van Amsterdam.

Curry also wrote and taught mathematical logic more generally; his teaching in this area culminated in his 1963 Foundations of Mathematical Logic. His preferred philosophy of mathematics was formalism (cf. his 1951 book), following his mentor Hilbert, but his writings betray substantial philosophical curiosity and a very open mind about intuitionistic logic.

Major publications

Curry, Haskell Brooks (1930). "Grundlagen der Kombinatorischen Logik" [Foundations of combinatorial logic]. American Journal of Mathematics (in German) (The Johns Hopkins University Press) 52 (3): 509–536. Retrieved 23 July 2012.
Curry, Haskell B. (1950, 2nd edn. 1957). A theory of formal deducibility. University of Notre Dame Press. Check date values in: |date= (help)^[3]
Curry, Haskell B. (1951). Outlines of a formalist philosophy of mathematics. Amsterdam: Elsevier Science. ISBN 0444533680. Retrieved 23 July 2012.
Curry, Haskell B. (1952). Leçons de logique algébrique (in French). Paris: Gauthier-Villars. ^[4]
Curry, Haskell; Feys, Robert (1958). Combinatory Logic Volume I. Amsterdam: North-Holland Publishing Company.
Curry, Haskell (1963). Foundations of Mathematical Logic. Mcgraw Hill.
- Curry, Haskell B. (1977). Foundations of mathematical logic (Unabridged and corrected of the first publication by the McGraw-Hill book company, in 1963. ed.). New York: Dover Publications. ISBN 0-486-63462-0. Retrieved 23 July 2012.
Curry, Haskell B. (1972). Combinatory Logic Volume II. Amsterdam: North-Holland Publishing Company. ISBN 0720422086.

References

↑ 1.0 1.1 Seldin, Jonathan. The Logic of Curry and Church.
↑ Barendregt, H.P. The Lambda Calculus: Its Syntax and Semantics. Elsevier. p. 4.
↑ Nelson, D. (1952). "Review: A theory of formal deducibility, by H. B. Curry". Bull. Amer. Math. Soc. 58 (3): 415–417.
↑ Marcus, R. Barcan (1952). "Review: Leçons de logique algébrique, by H. B. Curry". Bull. Amer. Math. Soc. 58 (2): 673–674.

External links

O'Connor, John J.; Robertson, Edmund F., "Haskell Curry", MacTutor History of Mathematics archive, University of St Andrews .
Curry archives provides images of several hundred manuscript pages from 1920 to 1931.
CLg. bibliography 587 pp
Haskell Brooks Curry at the Mathematics Genealogy Project

Logic

Overview

Academic areas	Argumentation theory Axiology Critical thinking Computability theory Formal semantics History of logic Informal logic Logic in computer science Mathematical logic Mathematics Metalogic Metamathematics Model theory Philosophical logic Philosophy Philosophy of logic Philosophy of mathematics Proof theory Set theory

Foundations	Abduction Analytic truth Antinomy A priori Deduction Definition Description Induction Inference Logical form Logical consequence Logical truth Name Necessity Meaning Paradox Possible world Presupposition Probability Reason Reasoning Reference Semantics Statement Strict implication Substitution Syntax Truth Truth value Validity

Philosophical logic

Critical thinking Informal logic	Analysis Ambiguity Argument Belief Bias Credibility Evidence Explanation Explanatory power Fact Fallacy Inquiry Opinion Parsimony Premise Propaganda Prudence Reasoning Relevance Rhetoric Rigor Vagueness

Theories of deduction	Constructivism Dialetheism Fictionalism Finitism Formalism Intuitionism Logical atomism Logicism Nominalism Platonic realism Pragmatism Realism

Metalogic Metamathematics

Cantor's theorem Church's theorem Church's thesis Consistency Effective method Foundations of mathematics Gödel's completeness theorem Gödel's incompleteness theorems Soundness Completeness Decidability Interpretation Löwenheim–Skolem theorem Metatheorem Satisfiability Independence Type–token distinction Use–mention distinction

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General	Formal language Formation rule Formal system Deductive system Formal proof Formal semantics Well-formed formula Set Element Class Classical logic Axiom Natural deduction Rule of inference Relation Theorem Logical consequence Axiomatic system Type theory Symbol Syntax Theory

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Propositional calculus Boolean logic	Boolean functions Propositional calculus Propositional formula Logical connectives Truth tables

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Set theory	Set Empty set Enumeration Extensionality Finite set Function Subset Power set Countable set Recursive set Domain Range Ordered pair Uncountable set

Model theory	Model Interpretation Non-standard model Finite model theory Truth value Validity

Proof theory	Formal proof Deductive system Formal system Theorem Logical consequence Rule of inference Syntax

Computability theory	Recursion Recursive set Recursively enumerable set Decision problem Church–Turing thesis Computable function Primitive recursive function

Non-classical logic

Modal logic	Alethic Axiologic Deontic Doxastic Epistemic Temporal

Intuitionism	Intuitionistic logic Constructive analysis Heyting arithmetic Intuitionistic type theory Constructive set theory

Fuzzy logic	Degree of truth Fuzzy rule Fuzzy set Fuzzy finite element Fuzzy set operations

Substructural logic	Structural rule Relevance logic Linear logic

Paraconsistent logic	Dialetheism

Description logic	Ontology Ontology language

Many-valued logic	Three-valued logic Four-valued logic Łukasiewicz logic

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Authority control	WorldCat VIAF: 34535556 LCCN: n84801349 ISNI: 0000 0001 1024 6379 GND: 12283643X BNF: cb12364677d MGP: 7398

Persondata
Name	Curry, Haskell
Alternative names
Short description	American mathematician
Date of birth	September 12, 1900
Place of birth	Millis, Massachusetts
Date of death	September 1, 1982
Place of death	State College, Pennsylvania

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