View source for Haskell Curry

{{Short description|American mathematician (1900-1982)}}
{{Infobox scientist
| name              = Haskell Brooks Curry
| image             =
| birth_date        = {{Birth date|1900|09|12|mf=y}}
| birth_place       = [[Millis, Massachusetts]], US
| death_date        = {{Death date and age|1982|09|01|1900|09|12|mf=y}}
| death_place       = [[State College, Pennsylvania]], US
| residence         = 
| field             = [[Mathematics]]<br/>[[Logic]]<br/>[[computer science]]
| workplaces        = [[Pennsylvania State University]]<br/>[[University of Amsterdam]]
| alma_mater        = {{ubl |[[Harvard University]] |[[University of Göttingen]]}}
| doctoral_advisor  = [[David Hilbert]]
| doctoral_students = 
| known_for         = [[Curry's paradox]]<br/>[[Currying]]<br/>[[Curry–Howard correspondence]]<br/>[[Scott–Curry theorem]]<br/>[[B, C, K, W system]]<br/>[[Combinatory logic]]<br/>[[Formalism in the philosophy of mathematics]]
| prizes            = 
| footnotes         = 
| signature         =  
}}
'''Haskell Brooks Curry''' ({{IPAc-en|ˈ|h|æ|s|k|əl}} {{respell|HAS|kəl}}; September 12, 1900 – September 1, 1982) was an American [[mathematician]], [[logic]]ian and [[computer scientist]]. Curry is best known for his work in [[combinatory logic]], whose initial concept is based on a paper by [[Moses Schönfinkel]],{{sfn|Schönfinkel |1924}} for which Curry did much of the development. Curry is also known for [[Curry's paradox]] and the [[Curry–Howard correspondence]]. Named for him are three [[programming language]]s: [[Haskell]], [[BrookGPU|Brook]], and [[Curry (programming language)|Curry]], and the concept of ''[[currying]]'', a method to transform functions, used in [[mathematics]] and [[computer science]].

== Life ==
Curry was born on {{Birth date|1900|09|12}} 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 [[Massachusetts Institute of Technology]] (MIT), he returned to Harvard to study [[physics]], earning a [[Master of Arts]] (M.A.) in 1924. Curry's interest in mathematical logic began 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 [[Doctor of Philosophy]] (Ph.D.) in mathematics. While he was directed by [[George David Birkhoff]] to work on [[differential equation]]s, 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 [[University of 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.{{sfn|Seldin|2008}}

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 [[Pennsylvania State University|Pennsylvania 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 1931–1932 under a [[National Academies of Sciences, Engineering, and Medicine#Program units|National Research Fellowship]] and one year in 1938–1939 at the [[Institute for Advanced Study]] in Princeton. In 1942 he took a leave of absence to do applied mathematics for the United States government during [[World War II]], notably at the [[Frankford Arsenal]]. Immediately after the war he worked on the [[ENIAC]] project, in 1945 and 1946. Under a [[Fulbright Program|Fulbright fellowship]], he collaborated with [[Robert Feys]] in [[Leuven|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 {{Death date and age|1982|09|01|1900|09|12}}, 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 [[J. Barkley Rosser|John Rosser]]. The paradox, developed by Rosser and [[Stephen Cole Kleene|Stephen Kleene]], had proved the inconsistency of a number of related [[formal system]]s, including one proposed by [[Alonzo Church]] (a system which had the [[lambda calculus]] as a consistent subsystem) and Curry's own system.{{sfn|Seldin|2008}} 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."{{sfn|Barendregt|1984|page=4}}

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 are quite similar to that of the [[lambda calculus]] of Church, and the latter formalism has tended to predominate in recent decades.

During World War II, Curry worked at the [[Frankford Arsenal]],
where he developed a ''steepest descent'' algorithm, based on work by [[Augustin-Louis Cauchy|Cauchy]].
<ref>{{cite journal |last1=Curry |first1=Haskell B. |title=The method of steepest descent for non-linear minimization problems |journal=Quarterly of Applied Mathematics |date=1944 |volume=2 |issue=3 |pages=258–261 |doi=10.1090/qam/10667 |url=https://www.ams.org/journals/qam/1944-02-03/S0033-569X-1944-10667-3/ |access-date=7 November 2024 |language=en |issn=0033-569X|url-access=subscription }}</ref>
This became a foundational example of modern [[gradient descent]] methods.

In 1947 Curry also described one of the first high-level programming languages and provided the first description of a procedure to convert a general arithmetic expression into a code for one-address computer.{{sfn|Knuth|Pardo|1976|page=22}}

He taught at Harvard, [[Princeton University|Princeton]], and from 1929 to 1966, at the [[Pennsylvania State University]]. In 1942, he published [[Curry's paradox]]. In 1966 he became professor of logic and its history and philosophy of exact sciences at the [[University of Amsterdam]], the successor of [[Evert Willem Beth]].{{sfn|University of Amsterdam|2023}}

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 (philosophy of mathematics)|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 ==
* {{cite journal |display-authors=0 |last=Curry |first=Haskell Brooks |author-link=Haskell Curry |date=1930 |title=Grundlagen der Kombinatorischen Logik |trans-title=Foundations of combinatorial logic |journal=American Journal of Mathematics |publisher=The Johns Hopkins University Press |language=de |doi=10.2307/2370619 |volume=52 |number=3 |pages=509–536 |jstor=2370619}}
* {{cite book |display-authors=0 |last=Curry |first=Haskell B. |author-link=Haskell Curry |date=1950 |title=A theory of formal deducibility |url=https://archive.org/details/theoryofformalde0000curr |url-access=registration |publisher=University of Notre Dame Press}}{{sfn|Nelson|1952}}
** {{cite book |display-authors=0 |last=Curry |first=Haskell B. |author-link=Haskell Curry |date=1957 |title=A theory of formal deducibility |edition=2nd |publisher=University of Notre Dame Press}}
* {{cite book |display-authors=0 |last=Curry |first=Haskell B. |author-link=Haskell Curry |date=1951 |title=Outlines of a formalist philosophy of mathematics |publisher=Elsevier Science |location=Amsterdam |url=https://books.google.com/books?id=tZHrBQgp1bkC |access-date=23 July 2012}} {{isbn|0444533680 }}.
* {{cite book |display-authors=0 |last=Curry |first=Haskell B. |date=1952 |title=Leçons de logique algébrique |publisher=Gauthier-Villars |location=Paris |language=fr}}{{sfn|Marcus|1952}}
*{{cite book| last1=Curry|first1=Haskell Brooks|author-link1=Haskell Curry|last2=Feys|first2=Robert|author-link2=Robert Feys|title=Combinatory Logic|volume=I|year=1958|publisher=[[Elsevier|North Holland Publishing Company]]|location=Amsterdam}} {{isbn|0-7204-2208-6}}.
* {{cite book |display-authors=0 |last=Curry |first=Haskell |date=1963 |title=Foundations of Mathematical Logic |publisher=Mcgraw Hill}}
** {{cite book |display-authors=0 |last=Curry |first=Haskell B. |date=1977 |title=Foundations of mathematical logic |edition=Unabridged and corrected Dover |publisher=Dover Publications |location=New York |isbn=0-486-63462-0 |url=http://store.doverpublications.com/0486634620.html |access-date=23 July 2012}}
* {{cite book| last1=Curry|first1=Haskell Brooks|author-link1=Haskell Curry|last2=Hindley|first2=J. Roger|author-link2=J. Roger Hindley|last3=Seldin|first3=Jonathan P.|title=Combinatory Logic|volume=II|year=1972| publisher=North Holland |location=Amsterdam | isbn=0-7204-2208-6}}

== Notes ==
{{Reflist|2}}

== Further reading ==
*{{harvtxt|Seldin|Hindley|1980}} {{mdash}} Includes biographical essay.

== References ==
*{{cite book| last=Barendregt|first=Hendrik Pieter|author-link=Henk Barendregt|year=1984|title=The Lambda Calculus, Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics|volume=103| publisher=[[North-Holland Publishing Company|North Holland]] |isbn=0-444-87508-5}}
*{{cite book|last1=
Knuth|first1=Donald Ervin|author1-link=Donald Knuth|last2=Pardo|first2=Luis Trabb |year=1976|title=Early development of programming languages|publisher=Stanford University, Computer Science Department}}
*{{cite journal |last=Marcus |first=R. Barcan |author-link=Ruth Barcan Marcus |date=1952 |title=Review: ''Leçons de logique algébrique'', by H. B. Curry |journal=Bulletin of the American Mathematical Society |doi=10.1090/s0002-9904-1952-09657-9 |volume=58 |issue=2 |pages=673–674 |url=https://www.ams.org/journals/bull/1952-58-06/S0002-9904-1952-09657-9/|doi-access=free}}
*{{cite journal |last=Nelson |first=D. |author-link=Nels David Nelson |date=1952 |title=Review: ''A theory of formal deducibility'', by H. B. Curry |journal=Bulletin of the American Mathematical Society |doi=10.1090/s0002-9904-1952-09596-3 |volume=58 |issue=3 |pages=415–417 |url=https://www.ams.org/journals/bull/1952-58-03/S0002-9904-1952-09596-3/|doi-access=free}}
*{{cite journal |first=Moses |last=Schönfinkel |author-link=Moses Schönfinkel |year=1924 |url=http://www.cip.ifi.lmu.de/~langeh/test/1924%20-%20Schoenfinkel%20-%20Ueber%20die%20Bausteine%20der%20mathematischen%20Logik.pdf |title=Über die Bausteine der mathematischen Logik |journal=Mathematische Annalen |volume=92 |issue=3–4 |pages=305–316 |doi=10.1007/bf01448013|s2cid=118507515|language=de|quote=The article that founded combinatory logic. English translation: {{harvtxt|Schönfinkel|1967}}}}
*{{cite book |first=Moses|last=Schönfinkel|author-link=Moses Schönfinkel|orig-year=1924|translator-first=Stefan|translator-last=Bauer-Mengelberg|title=Über die Bausteine der mathematischen Logik|trans-title=On the building blocks of mathematical logic|editor-first= Jean|editor-last=Van Heijenoort|editor-link=Jean van Heijenoort|year=1967|series=From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931|publisher=[[Harvard University Press]]| location=Cambridge, MA, USA|language=en|pages=355–366|isbn=978-0674324497|oclc=503886453}}
* {{cite book|editor1-last=Seldin|editor1-first=Jonathan P.|editor2-last=Hindley|editor2-first=J.R.|year= 1980|title=To H.B. Curry: Essays on combinatory logic, lambda calculus, and formalism|publisher= Academic Press}}
*{{cite web|last=Seldin|first=Jonathan P.|title=The Logic of Curry and Church|date=3 March 2008|url=http://people.uleth.ca/%7Ejonathan.seldin/CCL.pdf|access-date=23 September 2023}}

== External links ==
* {{Cite IEP |url-id=curry |title=Haskell Brooks Curry (1900-1982) |first=Jonathan P. |last=Seldin}}
* {{MacTutor|id=Curry}}
* [https://web.archive.org/web/20040406093224/http://www.sadl.uleth.ca/gsdl/cgi-bin/library?a=p&p=about&c=curry Curry archives] provides images of several hundred manuscript pages from 1920 to 1931.
* [https://web.archive.org/web/20040328092820/http://adam.science.uva.nl/~inge/Bib/bib.ps CLg. bibliography 587 pp]
*{{cite web|url=https://albumacademicum.uva.nl/id/id001294|title=Album Academicum - Professors and PhD graduates from 1632 to this day|editor=University of Amsterdam|year=2023|access-date=23 September 2023}}

{{Haskell Curry}}
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{{DEFAULTSORT:Curry, Haskell}}
[[Category:1900 births]]
[[Category:1982 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:American logicians]]
[[Category:Harvard University alumni]]
[[Category:American philosophers of mathematics]]
[[Category:Harvard University Department of Philosophy faculty]]
[[Category:Pennsylvania State University faculty]]
[[Category:Princeton University faculty]]
[[Category:Academic staff of the University of Amsterdam]]
[[Category:People from Millis, Massachusetts]]