Emil Leon Post (February 11, 1897 – April 21, 1954) was a Polish-born American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory.
Townsend Harris High School,149-11 Melbourne Ave., Flushing, Queens, New York 11367 United States
Post attended the Townsend Harris High School prior to entering the university.
City College of the City University of New York, New York City, New York, United States
Post received the Bachelor of Science degree from the College of the City of New York in 1917.
Columbia University, 116th St & Broadway, New York, New York 10027, United States
Post was a graduate student, and later lecturer, in mathematics at Columbia University from 1917 to 1920, receiving the Ph.D. in 1920.
Townsend Harris High School,149-11 Melbourne Ave., Flushing, Queens, New York 11367 United States
Post attended the Townsend Harris High School prior to entering the university.
City College of the City University of New York, New York City, New York, United States
Post received the Bachelor of Science degree from the College of the City of New York in 1917.
Columbia University, 116th St & Broadway, New York, New York 10027, United States
Post was a graduate student, and later lecturer, in mathematics at Columbia University from 1917 to 1920, receiving the Ph.D. in 1920.
Jan Łukasiewicz (21 December 1878 – 13 February 1956) was a Polish logician and philosopher.
(Volume 43)
Volume 43
https://www.amazon.com/American-Journal-Mathematics-Hopkins-University/dp/117909493X/?tag=2022091-20
1921
logician mathematician scientist
Emil Leon Post was born on February 11, 1897, in Augustow, Suwałki Governorate, Congress Poland, Russian Empire (now Poland). Post was the son of Arnold J. and Pearl D. Post. In May 1904 he arrived in America, where his father and his uncle, J. L. Post, were in the fur and clothing business in New York.
As a child Post’s first love was astronomy, but the loss of his left arm when he was about twelve ruled that out as a profession. He early showed mathematical ability, however; and his important paper on generalized differentiation, although not published until 1930, was essentially completed by the time he received the Bachelor of Science from the College of the City of New York in 1917. Prior to that Post attended the Townsend Harris High School.
Post was a graduate student, and later lecturer, in mathematics at Columbia University from 1917 to 1920, receiving the Master of Arts in 1918 and the Ph.D. in 1920.
After receiving the doctorate, Post was a Proctor fellow at Princeton University for a year and then returned to Columbia as an instructor, but after a year he suffered the first of the recurrent periods of illness that partially curtailed his scientific work. In the spring of 1924, he taught at Cornell University but again became ill. He resumed his teaching in the New York City high schools in 1927. Appointed to City College in 1932, he stayed there only briefly, returning in 1935 to remain for nineteen years.
Post was the first to obtain decisive results in metamathematics when, in his Ph.D. dissertation of 1920 (published in 1921), he proved the consistency as well as the completeness of the propositional calculus as developed in Whitehead and Russell’s Principia mathematica. This marked the beginning, in important respects, of modern proof theory. In this paper Post systematically applied the truth-table method, which had been introduced into symbolic logic by C. S. Peirce and Ernst Schroder. From this paper came general notions of completeness and consistency: A system is said to be complete in Post’s sense if every well-formed formula becomes provable if we add to the axioms any well-formed formula that is not provable. A system is said to be consistent in Post's sense if no well-formed formula consisting of only a propositional variable is provable. In this paper Post also showed how to set up multivalued systems of propositional logic and introduced multivalued truth tables in analyzing them. Jan Lukasiewicz was studying three-valued logic at the same time; but while his interest was philosophical, Post's was mathematical. Post compared these multivalued systems to geometry, noting that they seem “to have the same relation to ordinary logic that geometry in a space of an arbitrary number of dimensions has to the geometry of Euclid.”
Post began a scientific diary in 1916 and so was able to show, in a paper written in 1941 (but rejected by a mathematics journal and not published until 1965), that he had attained results in the 1920’s similar to those published in the 1930s by Kurt Godel, Alonzo Church, and A. M. Turing. In particular, he had planned in 1925 to show through a special analysis that Principia mathematica was inadequate but later decided in favor of working for a more general result, of which the incompleteness of the logic of Principia would be a corollary.
Indeed, he showed an increasing interest in the creative process and noted in 1941 that “perhaps the greatest service the present account could render would stem from its stressing of its final conclusion that mathematical thinking is, and must be, essentially creative.” But this is creativity with limitations, and he saw symbolic logic as “the indisputable means for revealing and developing these limitations.”
If other mathematicians failed to recognize the power of this theory, it was forcefully shown to them in 1947, when Post demonstrated the recursive unsolvability of the word problem for semigroups, thus solving a problem proposed by A. Thue in 1914.
Emil Post was a pioneer of twentieth-century mathematical logic whose influence on what has come to be called computer science is particularly remarkable considering his lack of any contact with computing machines.
Post's major achievement was in proving, among other things, that the propositional calculus of Principia Mathematica was complete: all tautologies are theorems, given the Principia axioms and the rules of substitution and modus ponens. Post also devised truth tables independently of Wittgenstein and C.S. Peirce and put them to good mathematical use.
Also, Post raised the question of the existence of an uncomputable recursively enumerable set whose Turing degree is less than that of the halting problem. This question, which became known as Post's problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
Two notions are particularly associated with his name: Post-completeness and Post-consistency as applied to systems of logic. Briefly, such a system is Post-complete if every well-formed formula becomes provable once we adjoin to the axioms any well-formed formula that is not provable. A system containing propositional variables is Post-consistent if no well-formed formula consisting of a single propositional variable is provable.
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1921(Volume 48)
1940Post, while not orthodox in his adult years, was a religious man and proud of his Jewish heritage.
Quotations: “I study Mathematics as a product of the human mind and not as absolute.”
Post was a member of the American Mathematical Society from 1918 and a member of the Association for Symbolic Logic from its founding in 1936.
Post’s extra-scientific interests included sketching, poetry, and stargazing.
Post married Gertrude Singer in 1929, with whom he had a daughter, Phyllis Goodman.
Jan Łukasiewicz (21 December 1878 – 13 February 1956) was a Polish logician and philosopher born in Lemberg, a city in the Galician kingdom of Austria-Hungary (now Lviv, Ukraine). His work centred on philosophical logic, mathematical logic, and history of logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle.
In 1936, Post developed, independently of Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1.
