Axiomatik. Wintersemester 1930/31. [With:] Vorlesung uber Invariantentheorie, Sommersemester 1931. University of Göttingen, [1931]

WEYL, Hermann

Published by University of Göttingen, [Göttingen, 1931

WEYL S OWN ANNOTATED COPIES OF HIS GÖTTINGEN LECTURE NOTES. First edition, Weyl s own annotated copies, of these two extremely rare sets of lecture notes for Weyl s courses at the University of Göttingen on Axiomatik and Invariant theory. Both sets have numerous formulae written by hand, and Axiomatik has additional annotations and deletions all of these are probably by Weyl himself. These deletions include the crossing out of whole paragraphs, possibly indicating that Weyl had intended to produce a new edition, perhaps for publication, but it appears that no other editions exist. Both sets of notes are from Weyl s short second period in Göttingen. He became Hilbert s successor there in 1930 and then fled with his Jewish wife to the Institute for Advanced Study at Princeton in 1933, where he remained until his death in 1951. The Axiomatik is in five chapters, dealing with Euclidean geometry, the space-time formulation of special relativity, space and number, algebra, and topology. "Weyl understood axiomatics as the defining basis of a conceptual framework on which a mathematical theory could be built. He saw no opposition between axiomatics and the construction of mathematical object fields. The task of an axiomatics formulation was to clarify the structure of some field of mathematical thought; its objects were to be constructed and dealt with symbolically … Weyl s axiomatization of the 2-dimensional manifold and of Riemann surfaces [treated in Chapter V of Axiomatik] was an early example … [Weyl s] view of the continuum was deeply influenced by the long tradition in mathematical and philosophical thought upon this subject. Riemann s concept of manifold appeared to him as the most promising modern clue to the topic. Its logical and formal foundations remained an open question for him until the end of his life, although he himself made at least three attempts to come to grips with it: a constructive approach in [Das Kontinuum, 1918], influenced by E. Borel and H. Poincaré, an intuitionistic one (1921), and a combinatorial topological one in his lecture course on Axiomatics in Göttingen 1930/31" (Scholz, pp. 12-13). The lectures on invariant theory can be seen both as a synthesis of his important papers on groups theory published in 1925-27 and as an precursor of his most famous book, The Classical Groups (Princeton, 1939). "Weyl s use of tensor calculus in his work on relativity led him to re-examine the basic methods of that calculus and, more generally, of classical invariant theory that had been its forerunner but had fallen into near oblivion after Hilbert s work of 1890. On the other hand, his semi-philosophical, semi-mathematical ideas on the general concept of space in connection with Einstein s theory had directed his investigations to generalizations of Helmholtz s problem of characterizing Euclidean geometry by properties of free mobility. From these two directions Weyl was brought into contact with the theory of linear representations of Lie groups; his papers on the subject (1925-1927) certainly represent his masterpiece and must be counted among the most influential ones in twentieth-century mathematics" (DSB). We have been able to locate only two other copies of Axiomatik (ETH Zürich and Göttingen), and none of Invariantentheorie. No copies in auction records. "Weyl attended the Gymnasium at Altona and, on the recommendation of the headmaster of his Gymnasium, who was a cousin of Hilbert, decided at the age of eighteen to enter the University of Göttingen. Except for one year at Munich he remained at Gottingen, as a student and later as Privatdozent, until 1913, when he became professor at the University of Zürich. After Klein s retirement in 1913, Weyl declined an offer to be his successor at Göttingen but accepted a second offer in 1930, after Hilbert had retired. In 1933 he decided he could no longer remain in Nazi Germany and accepted a position at the Institute for Advanced Study at Princeton, wher. Seller Inventory # 6236

Bibliographic Details

Title: Axiomatik. Wintersemester 1930/31. [With:] ...
Publisher: University of Göttingen, [Göttingen
Publication Date: 1931
Edition: First edition.