Kalmár was of Jewish ancestry.[1] His early life mixed promise and tragedy. His father died when he was young, and his mother died when he was 17, the year he entered the University of Budapest, making him essentially an orphan.
Kalmár's brilliance manifested itself while in Budapest schools. At the University of Budapest, his teachers included Kürschák and Fejér. His fellow students included the future logician Rózsa Péter. Kalmár graduated in 1927. He discovered mathematical logic, his chosen field, while visiting Göttingen in 1929.
Upon completing his doctorate at Budapest, he took up a position at the University of Szeged. That university was mostly made up of staff from the former University of Kolozsvár, a major Hungarian university before World War I that found itself after the War in Romania. Kolozsvár was renamed Cluj. The Hungarian university moved to Szeged in 1920, where there had previously been no university. The appointment of Haar and Riesz turned Szeged into a major research center for mathematics. Kalmár began his career as a research assistant to Haar and Riesz. Kalmár was appointed a full professor at Szeged in 1947. He was the inaugural holder of Szeged's chair for the Foundations of Mathematics and Computer Science. He also founded Szeged's Cybernetic Laboratory and the Research Group for Mathematical Logic and Automata Theory.
In mathematical logic, Kalmár proved that certain classes of formulas of the first-order predicate calculus were decidable. In 1936, he proved that the predicate calculus could be formulated using a single binary predicate, if the recursive definition of a term was sufficiently rich. (This result is commonly attributed to a 1954 paper of Quine's.) He discovered an alternative form of primitive recursive arithmetic, known as elementary recursive arithmetic, based on primitive functions that differ from the usual kind. He did his utmost to promote computers and computer science in Hungary. He wrote on theoretical computer science, including programming languages, automatic error correction, non-numerical applications of computers, and the connection between computer science and mathematical logic.
Kalmar is one of the very few logicians who has raised doubts about Church's thesis that all intuitively mechanistic, algorithmic functions are representable by recursive functions. [2]
In 1933 Kalmár married Erzsébet Arvay; they had four children.
The face on the middle medallion is Kalmár's
Elementary functions
Kalmar defined what are known as elementary functions, number-theoretic functions (i.e. those based on the natural numbers) built up from the notions of composition and variables, the constants 0 and 1, repeated addition + of the constants, proper subtraction ∸, bounded summation and bounded product (Kleene 1952:526). Elimination of the bounded product from this list yields the subelementary or lower elementary functions. By use of the abstract computational model called a register machineSchwichtenberg provides a demonstration that "all elementary functions are computable and totally defined" (Schwichtenberg 58).
Notes
^Reuben Hersh & Vera John-Steiner (1993). "A Visit to Hungarian Mathematics" (PDF). Retrieved 19 October 2012.
^* Kalmar, L. 1959. ‘An Argument Against the Plausibility of Church's Thesis’. In Heyting, A. (ed.) Constructivity in Mathematics. Amsterdam: (1959 North-Holland).
References
Stephen C. Kleene 1952, 1971 6th reprint with emendations, 10th printing 1999, Introduction to Metamathematics, North-Holland Publishing Company, Amsterdam NY. ISBN0-7204-2103-9
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Laszlo Kalmar 27 March 1905 Edde 2 August 1976 Matrahaza was a Hungarian mathematician and Professor at the University of Szeged Kalmar is considered the founder of mathematical logic and theoretical computer science in Hungary Portrait of Laszlo Kalmar This article is about the mathematician For the composer see Laszlo Kalmar composer Contents 1 Biography 2 Elementary functions 3 Notes 4 References 5 External linksBiography EditKalmar was of Jewish ancestry 1 His early life mixed promise and tragedy His father died when he was young and his mother died when he was 17 the year he entered the University of Budapest making him essentially an orphan Kalmar s brilliance manifested itself while in Budapest schools At the University of Budapest his teachers included Kurschak and Fejer His fellow students included the future logician Rozsa Peter Kalmar graduated in 1927 He discovered mathematical logic his chosen field while visiting Gottingen in 1929 Upon completing his doctorate at Budapest he took up a position at the University of Szeged That university was mostly made up of staff from the former University of Kolozsvar a major Hungarian university before World War I that found itself after the War in Romania Kolozsvar was renamed Cluj The Hungarian university moved to Szeged in 1920 where there had previously been no university The appointment of Haar and Riesz turned Szeged into a major research center for mathematics Kalmar began his career as a research assistant to Haar and Riesz Kalmar was appointed a full professor at Szeged in 1947 He was the inaugural holder of Szeged s chair for the Foundations of Mathematics and Computer Science He also founded Szeged s Cybernetic Laboratory and the Research Group for Mathematical Logic and Automata Theory In mathematical logic Kalmar proved that certain classes of formulas of the first order predicate calculus were decidable In 1936 he proved that the predicate calculus could be formulated using a single binary predicate if the recursive definition of a term was sufficiently rich This result is commonly attributed to a 1954 paper of Quine s He discovered an alternative form of primitive recursive arithmetic known as elementary recursive arithmetic based on primitive functions that differ from the usual kind He did his utmost to promote computers and computer science in Hungary He wrote on theoretical computer science including programming languages automatic error correction non numerical applications of computers and the connection between computer science and mathematical logic Kalmar is one of the very few logicians who has raised doubts about Church s thesis that all intuitively mechanistic algorithmic functions are representable by recursive functions 2 Kalmar was elected to the Hungarian Academy of Sciences in 1949 and was awarded the Kossuth Prize in 1950 and the Hungarian State Prize in 1975 In 1933 Kalmar married Erzsebet Arvay they had four children The face on the middle medallion is Kalmar sElementary functions EditKalmar defined what are known as elementary functions number theoretic functions i e those based on the natural numbers built up from the notions of composition and variables the constants 0 and 1 repeated addition of the constants proper subtraction bounded summation and bounded product Kleene 1952 526 Elimination of the bounded product from this list yields the subelementary or lower elementary functions By use of the abstract computational model called a register machine Schwichtenberg provides a demonstration that all elementary functions are computable and totally defined Schwichtenberg 58 Notes Edit Reuben Hersh amp Vera John Steiner 1993 A Visit to Hungarian Mathematics PDF Retrieved 19 October 2012 Kalmar L 1959 An Argument Against the Plausibility of Church s Thesis In Heyting A ed Constructivity in Mathematics Amsterdam 1959 North Holland References EditStephen C Kleene 1952 1971 6th reprint with emendations 10th printing 1999 Introduction to Metamathematics North Holland Publishing Company Amsterdam NY ISBN 0 7204 2103 9 Helmut Schwichtenberg see under Computability at http sakharov net foundation html or http www mathematik uni muenchen de schwicht lectures logic ws03 comp pdf Exact source of this TBD Kalmar L Zuruckfuhrung des Entscheidungsproblems auf den Fall von Formeln mit einer einzigen binaren Funktionsvariablen Comp Math Bd 4 1936 Quine W V Reduction to a Dyadic Predicate J Symbolic Logic 19 1954 no 3 180 182External links Edit Wikimedia Commons has media related to Laszlo Kalmar mathematician Laszlo Kalmar at the Mathematics Genealogy Project MacTutor The source for most of this entry Retrieved from https en wikipedia org w index php title Laszlo Kalmar amp oldid 1133146131, wikipedia, wiki, book, books, library,
