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Wanda Montlak Szmielew (1918–1976) was a Polish mathematical logician (of Jewish decent) who first proved the decidability of the first-order theory of abelian groups.[1]

LifeEdit

Wanda Montlak was born on April 5, 1918 in Warsaw. She completed high school in 1935 and married, taking the name Szmielew. In the same year she entered the University of Warsaw, where she studied logic under Adolf Lindenbaum, Jan Łukasiewicz, Kazimierz Kuratowski, and Alfred Tarski. Her research at this time included work on the axiom of choice, but it was interrupted by the 1939 Invasion of Poland.[1]

Szmielew became a surveyor during World War II, during which time she continued her research on her own, developing a decision procedure based on quantifier elimination for the theory of abelian groups. She also taught for the Polish underground. After the liberation of Poland, Szmielew took a position at the University of Łódź, which was founded in May 1945. In 1947 she published her paper on the axiom of choice, earned a master's degree from the University of Warsaw, and moved to Warsaw as a senior assistant.[1][2]

In 1949 and 1950, Szmielew visited the University of California, Berkeley, where Tarski had found a permanent position after being exiled from Poland for the war. She completed a Ph.D. at Berkeley in 1950 under Tarski's supervision, with her dissertation consisting of her work on abelian groups.[1][2][3] For the 1955 journal publication of these results, Tarski convinced Szmielew to rephrase her work in terms of his theory of arithmetical functions, a decision that caused this work to be described by Solomon Feferman as "unreadable".[4] Later work by Eklof & Fischer (1972) re-proved Szmielew's result using more standard model-theoretic techniques.[4][5]

Returning to Warsaw as an assistant professor, her interests shifted to the foundations of geometry. With Karol Borsuk, she published a text on the subject in 1955 (translated into English in 1960), and another monograph, published posthumously in 1981 and (in English translation) 1983.[1][2]

She died of cancer on August 27, 1976 in Warsaw.[1]

Selected publicationsEdit

  • Szmielew, Wanda (1947), "On choices from finite sets", Fundamenta Mathematicae, 34: 75–80, MR 0022539 .
  • Szmielew, W. (1955), "Elementary properties of Abelian groups", Fundamenta Mathematicae, 41: 203–271, MR 0072131 .
  • Borsuk, Karol; Szmielew, Wanda (1955), Podstawy geometrii, Warsawa: Państwowe Wydawnictwo Naukowe, MR 0071791 . Translated as Borsuk, Karol; Szmielew, Wanda (1960), Foundations of geometry: Euclidean and Bolyai-Lobachevskian geometry; projective geometry, Revised English translation, New York: Interscience Publishers, Inc., MR 0143072 .
  • Szmielew, Wanda (1981), Od geometrii afinicznej do euklidesowej, Biblioteka Matematyczna [Mathematics Library], 55, Warsaw: Państwowe Wydawnictwo Naukowe (PWN), p. 172, ISBN 83-01-01374-5, MR 664205 . Translated as Szmielew, Wanda (1983), From affine to Euclidean geometry, Warsaw: PWN—Polish Scientific Publishers, ISBN 90-277-1243-3, MR 720548 .
  • Schwabhäuser, W.; Szmielew, W.; Tarski, A. (1983), Metamathematische Methoden in der Geometrie, Hochschultext [University Textbooks], Berlin: Springer-Verlag, ISBN 3-540-12958-8, MR 731370, doi:10.1007/978-3-642-69418-9 .

ReferencesEdit

  1. ^ a b c d e f O'Connor, John J.; Robertson, Edmund F., "Wanda Montlak Szmielew", MacTutor History of Mathematics archive, University of St Andrews .
  2. ^ a b c Kordos, Marek; Moszyńska, Maria; Szczerba, Lesław W. (December 1977), "Wanda Szmielew 1918–1976", Studia Logica, 36 (4): 241–244, MR 0497794, doi:10.1007/BF02120661 .
  3. ^ Wanda Szmielew at the Mathematics Genealogy Project
  4. ^ a b Feferman, Solomon (2008), "Tarski's conceptual analysis of semantical notions", New essays on Tarski and philosophy, Oxford Univ. Press, Oxford, pp. 72–93, MR 2509211, doi:10.1093/acprof:oso/9780199296309.003.0004 . See footnote 28, p. 90.
  5. ^ Eklof, Paul C.; Fischer, Edward R. (1972), "The elementary theory of abelian groups", Annals of Pure and Applied Logic, 4: 115–171, MR 0540003, doi:10.1016/0003-4843(72)90013-7 .