Wilhelm Grunwald

William Grunwald ( born July 15, 1909 in Bad Rastenberg; † 7 June 1989), was a German mathematician and director of the Göttingen State and University Library Göttingen.

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

He is known by the set of Grunwald - Wang, who completed a gap in the proof of the main theorem of Brauer - Hasse -Noether in the Algebrentheorie. He said ( in the corrected version, see below) that an element x of an algebraic number field K is an n -th power in K if there is an n -th power in the relevant local bodies for almost all prime ideals of K. The sentence is an example of Hasse 's local-global principle.

The sentence itself could be proved by methods of Grunwald's dissertation, as Hasse recognized, the Grunwald letter encouraged to do so. Grunwald published evidence, the detail of the class field theory made ​​use in 1933 and a simplified proof was given in 1942 by George Whaples. In 1948 a student of Emil Artin at Princeton, Shianghao Wang ( 1915-1993 ), a gap in the proof of Grunwald (more precisely, in a lemma from the dissertation of Grunwald, to this used for the proof ). Although the set of Grunwald was correct in most cases, but there were exceptions (if n was divisible by 8 ), the by Helmut Hasse ( after he had learned of it) and Wang (PhD 1950) have been described. Wang's counterexample caused quite the Artin - seminar on class field theory in Princeton quite a stir as John T. Tate recalls, as seemingly a central set of algebraic number theory and Algebrentheorie was concerned, the main theorem of Hasse -Brauer- Noether. It turned out then but that was not the case, since the proof of the theorem, a weaker version of the theorem was used by Grunwald.

Later, Grunwald turned to a career as an academic librarian and was from 1963 to 1974 director of the State and University Library Göttingen.