Wilhelm Grunwald

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Wilhelm Grunwald (born July 15, 1909 in Bad Rastenberg ; † June 7, 1989 ) was a German mathematician and library director.

Life

Grunwald studied mathematics with Helmut Hasse at the University of Halle and followed him in 1930 to the Philipps University of Marburg , where he received his doctorate in 1932 under Hasse ( characterization of the residual norm symbol by the continuity, the front decomposition clause and the product formula ).

He is known from Grunwald-Wang's theorem, which closed a gap in the proof of Brauer-Hasse-Noether's main theorem in algebra theory. It says (in the corrected version, see below) that an element x of an algebraic number field K is an n-th power in K if it is an n-th power in the associated local fields for almost all prime ideals of K. The sentence is an example of Hasse's local-global principle .

The sentence itself could be proven with methods from Grunwald's dissertation, as Hasse recognized, who suggested Grunwald in a letter. Grunwald published the proof, which made extensive use of class field theory , in 1933 and a simplified proof was given by George Whaples in 1942 . In 1948, a student of Emil Artin in Princeton, Shianghao Wang (1915-1993), found a gap in Grunwald's proof (more precisely in a lemma from Grunwald's dissertation, which Grunwald used for the proof). Grunwald's theorem was correct in most cases, but there were exceptional cases (if n was divisible by 8), which were described by Helmut Hasse (after he had found out about it) and Wang (dissertation 1950). Wang's counterexample caused quite a stir at the Artin seminar on class field theory at Princeton, as John T. Tate recalls, because apparently a central proposition of algebraic number theory and algebra theory was affected, the main proposition of Hasse-Brauer-Noether. It then turned out that this was not the case, since a weaker version of Grunwald's theorem was used to prove the theorem.

After completing his doctorate, Grunwald briefly worked in the potash industry and as an assistant at the mathematical seminar at the University of Rostock . In 1932 he turned to a career as a scientific librarian . After completing his traineeship at the University Library in Halle and the Prussian State Library (Berlin), he initially worked as a library assessor at the university libraries in Halle and Kiel from 1934 to 1938 . From 1938 to 1950 he was at the Göttingen University Library . He then went to the library of the Technical University of Hanover as director and in 1957 became the founding director of the technical information library . From 1963 to 1974 he was director of the Göttingen State and University Library . His estate is kept by the Central Archives of German Mathematicians' bequests at the Lower Saxony State and University Library in Göttingen .

Publications

  • Characterization of the residual norm symbol by the p-continuity, the front decomposition theorem and the product formula , Marburg, Univ., Diss. In: Mathematische Annalen, Vol. 107, 1932, pp. 145-164.
  • The library of the Technical University of Hanover . In: News sheet for technical-scientific associations , Vol. 3, 1952, Issue 3.
  • The special librarian: tasks, selection, training proposals . In: Library, Librarian, Library Science: Festschrift Joris Vorstius , Leipzig: Harrassowitz 1954, pp. 182–191.
  • Technical university libraries. Lecture at the Librarian's Day in Düsseldorf on June 3, 1955 . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 2, 1955, Issue 4, pp. 257-279.
  • Tasks of the TH libraries in the library system of their countries: Lecture at the conference of the International Association of Libraries of Technical Universities (IATUL) in the library of the Technical University, Munich, on September 1, 1956 , [Göteborg: Elander] [approx. 1956].
  • The current position, the tasks, the equipment and the development tendencies of the technical university libraries: Lecture at the conference of the boarding school. Association of Libraries of Technical Universities (IATUL) in Fulda on May 28, 1958 , [Göteborg: Elander] [1958].
  • The Technical Information Library - TIB, Hanover . In: News for Documentation: nfd , Vol. 10, 1959, Issue 4, pp. 180-184.
  • The Evaluation Center (AST) for Russian scientific and technical literature at the Technical Information Library in Hanover . In: Osteuropa, Vol. 4, 1960, Issue 2, pp. 141-143.
  • For subject indexing in the field of chemistry . In: From the world of the librarian: Festschrift for Rudolf Juchhoff on his 65th birthday , Cologne: Greven 1961 (publication by the Librarian Training Institute of the State of North Rhine-Westphalia), pp. 393–403.
  • together with Gisela von Busse, Otto Mach and Wolfgang Seuberlich: Reports on a study trip to libraries in Moscow and Leningrad from May 8 to 20, 1961 . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 9, 1962, Issue 2, pp. 97–176.
  • The Institute for Scientific Information: (VINITI) - Vsesojǔznyj Institut naučnoj i techničeskoj informacii. In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 9, 1962, Issue 2, pp. 132-135.
  • The Technical Information Library - objectives and current status of work . In: Report on the conference / working group of technical and economic libraries , vol. 8, 1962, issue pp. 11–24.
  • Budget models for academic libraries . In: Wieland Schmidt (ed.): Fifteen years of library work by the German Research Foundation, 1949–1964 , Frankfurt a. M .: Klostermann 1966, pp. 79–141.
  • Cooperation between university library and university: lecture . In: Mitteilungsblatt / Association of Libraries of the State of North Rhine-Westphalia , Vol. 17, 1967, Issue 3, pp. 131–141.
  • Universal libraries: special libraries . In: Report on the ... Conference / Working Group of Special Libraries , Vol. 11, 1967, pp. 31–40.
  • Classification Theory: Lecture given in 1967 . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 15, 1968, Issue 1, pp. 17–34.
  • The Goettingen State and University Library . In: Georgia Augusta , 1968, No. 9, pp. 119-135.
  • The librarian and his education . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 16, 1969, Issue 2, pp. 154-169.
  • "The library system at the universities and at the Technical University of the State of North Rhine-Westphalia": on the report submitted by Gerhart Lohse . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 19, 1972, Issue 6, pp. 413-428.
  • Tasks and training of librarians in academic libraries (with special focus on Lower Saxony) . In: DFW: Documentation, Information , Vol. 20, 1971/72, Issue 2, pp. 47-49.
  • The library plan for Baden-Württemberg . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 20, 1973, Issue 6, pp. 443-465.
  • Discussion on Oskar Mahrenholtz: a contribution to determining the staffing requirements of academic libraries . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 20, 1973, Issue 3, pp. 151-189.
  • To determine the staffing requirements of academic libraries . In: Zeitschrift für Bibliothekswesen und Bibliographie , Vol. 20, 1973, Issue 3, pp. 151–156.

literature

  • Peter Roquette : The Brauer Hasse Noether Theorem in Historical Perspective , Schriften der Mathem.-Naturwiss. Class of the Heidelberg Academy of Sciences, Volume 15, Springer Verlag 2005 (Section 5.3 The Grunwald Wang Story ).
  • TH Hannover (ed.): Catalogus Professorum. The teaching staff of the Technical University of Hanover 1831–1856 , Hanover: Technical University of Technology 1956, p. 235.

Individual evidence

  1. ↑ Grunwald Mathematische Annalen, Volume 107, 1932, pp. 145-164, online
  2. ↑ Main clause in the sense of the original work by Brauer, Hasse, Noether Proof of a main clause in the theory of algebras (J. Reine Angewandte Mathematik, Volume 167, 1932, pp. 399–404): Every central division algebra over a field K is cyclic. The term cyclic algebra comes from Leonard Dickson and describes a specific construction in a cyclic field extension by K. Today, the Brauer-Hasse-Noether theorem is understood as another result of the work, which follows from the main clause and an existential clause, which later became Grunwald proved, namely the complete characterization of division algebras over a number field by local invariants (Hasse invariants).
  3. ↑ Grunwald A general existence theorem for algebraic number fields , Journal für Reine und Angewandte Mathematik, Volume 169, 1933, pp. 103-107, online
  4. ↑ Whaples Non-analytic class field theory and Grunewalds Theorem , Duke Math. J., Volume 9, 1942, pp. 455-473
  5. ↑ He returned to China after completing his doctorate, turned to control theory and computer science, and was Professor of Mathematics (and Faculty Director) at Jiling University since 1952. In 1980/81 he was its vice-president. He was a member of the Academia Sinica.
  6. ↑ Which also concerned the Whaples proof
  7. ^ Hasse on Grunwald's existence theorem in class field theory , J. Reine Angewandte Math., Volume 188, 1950, pp. 40–64, online
  8. ↑ Wang A counterexample to Grunwald's theorem , Annals of Mathematics, Volume 49, 1948, pp. 1008-1009. Another work followed on this, On Grunwald's Theorem , Annals of Mathematics, Volume 51, 1950, pp. 471-484
  9. ↑ Quoted in Roquette, see literature
  10. ^ Alexandra Habermann, Peter Kittel: Lexicon of German Scientific Librarians. The academic librarians of the Federal Republic of Germany (1981-2002) and the German Democratic Republic (1948-1990) . Klostermann, Frankfurt am Main 2004, ISBN 3-465-03343-4 , pp. 58-59 .
  11. ^ Grunwald, Wilhelm: The Technical Information Library (TIB) Hanover . In: News for Documentation . tape 10 , no. 4 , p. 180-184 .

Web links

personal data
SURNAME Grunwald, Wilhelm
BRIEF DESCRIPTION German mathematician and library director
DATE OF BIRTH July 15, 1909
PLACE OF BIRTH Bad Rastenberg
DATE OF DEATH June 7, 1989