Minkowski in K?nigsberg 1884: A talk in Lindemann's colloquium

摘要

The mathematical-physico seminar at the university of K?nigsberg in the 1880s shaped the early scientific career of both David Hilbert and Hermann Minkowski. The cover of this issue of the Bulletin of the American Mathematical Society displays a page from the Protokollbuch of the colloquium at K?nigsberg, written in Minkowski's own hand on the day of his talk in May 1884. That a seminar even existed at this time and in this place is a tribute to the reforms in the German educational system earlier in the century. This paper briefly traces those developments and their influence on scientific education in general to provide a frame for understanding Minkowski and his mathematical training. This broader context allows a more meaningful survey of Minkowski's talk where he established an estimate for the minimum of a positive definite quadratic form depending only on its discriminant and degree and interpreted this result geometrically. This geometric approach reveals the first glimpse of Minkowski's later work in the geometry of numbers.