Editing Haskell Curry (section)

== 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}}</ref>
This became a foundational example of modern [[Gradient descent|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]].