Nikolaus Hofreiter

Nikolaus Hofreiter, who lived from 8 May 1904 to 23 January 1990, was an Austrian mathematician who worked mainly in number theory. He went to school in Linz and studied from 1923 in Vienna with Hans Hahn, Wilhelm Wirtinger and Emil Müller, and with Philipp Furtwängler, under whom he obtained his doctorate in 1927 on the reduction theory of quadratic forms. He habilitated in 1933 and became an associate professor in 1939. His thesis work treated the four variable case of a problem of Minkowski on the product of inhomogeneous linear forms and made significant progress, and in 1934 he proved that there are infinitely many real quadratic number fields without a Euclidean algorithm. He also worked on the geometry of numbers and Diophantine approximation. During the Second World War he worked at the Hermann Goering Aviation Research Institute in Braunschweig, where with Wolfgang Gröbner he began a table of integrals whose two volumes appeared from 1944 and 1950 and stayed in wide use through a fifth edition in 1973 and 1975.