Moses Schönfinkel
Encyclopedia
Moses Ilyich Schönfinkel, also known as Moisei Isai'evich Sheinfinkel' (Шейнфинкель) (September 4, 1889 Ekaterinoslav
(now Dnipropetrovsk
, Ukraine
) – 1942, Moscow
), was a Russian
logician and mathematician
, known for the invention of combinatory logic
.
, studying mathematics under Samuil Osipovich Shatunovskii (1859–1929), who worked in geometry
and the foundations of mathematics
. From 1914 to 1924, Schönfinkel was a member of David Hilbert
's group at the University of Göttingen. On December 7, 1920 he delivered a talk to the group where he outlined the concept of combinatory logic
. Heinrich Behmann
, a member of Hilbert's group, later revised the text and published it in 1924. In 1929, Schönfinkel had one other paper published, on special cases of the decision problem
("Entscheidungsproblem"), that was prepared by Paul Bernays
.
After he left Göttingen, Schönfinkel returned to Moscow. By 1927 he was reported to be mentally ill and in a sanatorium. His later life was spent in poverty, and he died in Moscow some time in 1942. His papers were burned by his neighbors for heating.
.
His paper also showed that functions of two or more arguments could be replaced by functions taking a single argument. This replacement mechanism simplifies work in both combinatory logic and lambda calculus
and would later be called currying
, after Haskell Curry
. While Curry attributed the concept to Schönfinkel, it had already been used by Frege
.
Dnipropetrovsk
Dnipropetrovsk or Dnepropetrovsk formerly Yekaterinoslav is Ukraine's third largest city with one million inhabitants. It is located southeast of Ukraine's capital Kiev on the Dnieper River, in the south-central region of the country...
(now Dnipropetrovsk
Dnipropetrovsk
Dnipropetrovsk or Dnepropetrovsk formerly Yekaterinoslav is Ukraine's third largest city with one million inhabitants. It is located southeast of Ukraine's capital Kiev on the Dnieper River, in the south-central region of the country...
, Ukraine
Ukraine
Ukraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...
) – 1942, Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
), was a Russian
Russians
The Russian people are an East Slavic ethnic group native to Russia, speaking the Russian language and primarily living in Russia and neighboring countries....
logician and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for the invention of combinatory logic
Combinatory logic
Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...
.
Life
Schönfinkel attended the Novorossiysk University of OdessaOdessa
Odessa or Odesa is the administrative center of the Odessa Oblast located in southern Ukraine. The city is a major seaport located on the northwest shore of the Black Sea and the fourth largest city in Ukraine with a population of 1,029,000 .The predecessor of Odessa, a small Tatar settlement,...
, studying mathematics under Samuil Osipovich Shatunovskii (1859–1929), who worked in geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and the foundations of mathematics
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
. From 1914 to 1924, Schönfinkel was a member of David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
's group at the University of Göttingen. On December 7, 1920 he delivered a talk to the group where he outlined the concept of combinatory logic
Combinatory logic
Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming...
. Heinrich Behmann
Heinrich Behmann
Heinrich Behmann was a German mathematician. He performed research in the field of set theory and predicate logic....
, a member of Hilbert's group, later revised the text and published it in 1924. In 1929, Schönfinkel had one other paper published, on special cases of the decision problem
Decision problem
In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters. For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem...
("Entscheidungsproblem"), that was prepared by Paul Bernays
Paul Bernays
Paul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...
.
After he left Göttingen, Schönfinkel returned to Moscow. By 1927 he was reported to be mentally ill and in a sanatorium. His later life was spent in poverty, and he died in Moscow some time in 1942. His papers were burned by his neighbors for heating.
Work
Schönfinkel developed a formal system that avoided the use of bound variables. His system was essentially equivalent to a combinatory logic based upon the combinators B, C, I, K, and S. Schönfinkel was able to show that the system could be reduced to just K and S and outlined a proof that a version of this system had the same power as predicate logicPredicate logic
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified...
.
His paper also showed that functions of two or more arguments could be replaced by functions taking a single argument. This replacement mechanism simplifies work in both combinatory logic and lambda calculus
Lambda calculus
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
and would later be called currying
Currying
In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument...
, after Haskell Curry
Haskell Curry
Haskell Brooks Curry 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...
. While Curry attributed the concept to Schönfinkel, it had already been used by Frege
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
.
Publications
- 1924. "Über die Bausteine der mathematischen Logik", Mathematische Annalen 92, pp. 305–316. Translated by Stefan Bauer-Mengelberg as "On the building blocks of mathematical logic" in Jean van HeijenoortJean Van HeijenoortJean Louis Maxime van Heijenoort was a pioneer historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and from then until 1947, an American Trotskyist activist.-Life:Van Heijenoort was born in Creil, France...
, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 355–66. - 1929. (with Paul BernaysPaul BernaysPaul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...
) "Zum Entscheidungsproblem der mathematischen Logik," Mathematische Annalen 99: 342–72.