Emil Leon Post

Source: Wikipedia, the free encyclopedia.
Emil Leon Post
Post's inversion formula
Post's lattice
Post's theorem
Scientific career
FieldsMathematics, logic
InstitutionsPrinceton University
Thesis Introduction to a General Theory of Elementary Propositions  (1920)
Doctoral advisorCassius Jackson Keyser

Emil Leon Post (

logician. He is best known for his work in the field that eventually became known as computability theory
.

Life

Post was born in

Polish-Jewish family that immigrated to New York City in May 1904. His parents were Arnold and Pearl Post.[2]

Post had been interested in astronomy, but at the age of twelve lost his left arm in a car accident. This loss was a significant obstacle to being a professional astronomer, leading to his decision to pursue mathematics rather than astronomy.[3]

Post attended the Townsend Harris High School and continued on to graduate from City College of New York in 1917 with a B.S. in mathematics.[1]

After completing his

Ph.D. in mathematics in 1920 at Columbia University, supervised by Cassius Jackson Keyser, he did a post-doctorate at Princeton University
in the 1920–1921 academic year. Post then became a high school mathematics teacher in New York City.

Post married Gertrude Singer in 1929, with whom he had a daughter, Phyllis Post Goodman (1932–1995).[4] Post spent at most three hours a day on research on the advice of his doctor in order to avoid manic attacks, which he had been experiencing since his year at Princeton.[5]

In 1936, he was appointed to the mathematics department at the City College of New York. He died in 1954 of a heart attack following electroshock treatment for depression;[5][6] he was 57.

Early work

In his doctoral thesis, later shortened and published as "Introduction to a General Theory of Elementary Propositions" (1921), Post proved, 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 C. S. Peirce and Ludwig Wittgenstein and put them to good mathematical use. Jean van Heijenoort's well-known source book on mathematical logic (1966) reprinted Post's classic 1921 article setting out these results.

While at Princeton, Post came very close to discovering the incompleteness of Principia Mathematica, which Kurt Gödel proved in 1931. Post initially failed to publish his ideas as he believed he needed a 'complete analysis' for them to be accepted.[2] As Post said in a postcard to Gödel in 1938:

I would have discovered Gödel's theorem in 1921—if I had been Gödel.[7]

Recursion theory

In 1936, Post developed, independently of

string rewriting and developed by Post in the 1920s but first published in 1943. Post's rewrite technique is now ubiquitous in programming language specification and design, and so with Church's lambda calculus
is a salient influence of classical modern logic on practical computing. Post devised a method of 'auxiliary symbols' by which he could canonically represent any Post-generative language, and indeed any computable function or set at all.

Correspondence systems were introduced by Post in 1946 to give simple examples of

formal languages
.

In an influential address to the

Post's problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in computability theory
.

Polyadic groups

Post made a fundamental and still-influential contribution to the theory of polyadic, or n-ary, groups in a long paper published in 1940. His major theorem showed that a polyadic group is the iterated multiplication of elements of a normal subgroup of a group, such that the quotient group is cyclic of order n − 1. He also demonstrated that a polyadic group operation on a set can be expressed in terms of a group operation on the same set. The paper contains many other important results.

Selected papers

  • Post, Emil Leon (1919). "The Generalized Gamma Functions".
    JSTOR 1967871
    .
  • Post, Emil Leon (1921). "Introduction to a General Theory of Elementary Propositions".
    JSTOR 2370324
    .
  • Post, Emil Leon (1936). "Finite Combinatory Processes – Formulation 1".
    S2CID 40284503
    .
  • Post, Emil Leon (1940). "Polyadic groups".
    JSTOR 1990085
    .
  • Post, Emil Leon (1943). "Formal Reductions of the General Combinatorial Decision Problem". American Journal of Mathematics. 65 (2): 197–215.
    JSTOR 2371809
    .
  • Post, Emil Leon (1944). "Recursively enumerable sets of positive integers and their decision problems". Bulletin of the American Mathematical Society. 50 (5): 284–316.
    doi:10.1090/s0002-9904-1944-08111-1. Introduces the important concept of many-one reduction
    .

See also

Notes

  1. ^ a b Urquhart (2008)
  2. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Emil Leon Post", MacTutor History of Mathematics Archive, University of St Andrews
  3. ^ Urquhart (2008), p. 429.
  4. ^ "Phyllis Post Goodman Park". NYC Parks.
  5. ^ a b Urquhart (2008), p. 430.
  6. ISBN 9781139498432
    .
  7. JSTOR 3219226
    .
  8. doi:10.1090/s0002-9904-1946-08555-9
    .

References

  • JSTOR 3219226
  • Urquhart, Alasdair (2008). "Emil Post" (PDF). In Gabbay, Dov M.; Woods, John Woods (eds.). Logic from Russell to Church. Handbook of the History of Logic. Vol. 5. Elsevier BV.
  • Neary, Turlough (2015), "Undecidability in binary tag systems and the post correspondence problem for five pairs of words", International Symposium on Theoretical Aspects of Computer Science, Leibniz International Proceedings in Informatics (LIPIcs), pages 649–661, 2015.

Further reading

External links
Retrieved from "https://en.wikipedia.org/w/index.php?title=Emil_Leon_Post&oldid=1184671504"