- Nikolaus Hofreiter
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Nikolaus, Hofreiter Born May 8, 1904
Linz, Upper Austria, AustriaDied January 23, 1990 (aged 85) Doctoral advisor Philipp Furtwängler Nikolaus Hofreiter (born 8 May 1904 in Linz, Upper Austria, Austria; died 23 January 1990) was an Austrian mathematician who worked mainly in number theory.
Hofreiter went to school in Linz and studied from 1923 in Vienna with Hans Hahn, Wilhelm Wirtinger, Emil Müller at the Technische Universität Wien on descriptive geometry, and Philipp Furtwängler, with whom he obtained his doctorate in 1927 on the reduction theory of quadratic forms (Eine neue Reduktionstheorie für definite quadratische Formen). In 1928 he passed the Lehramtsprüfung examination and completed the probationary year as a teacher in Vienna, but then returned to the university (first as a scientific assistant at the TU Vienna) where in 1929 he was assistant to Furtwängler and then habilitated in 1933. He was even then an excellent teacher, and gave lectures not only in Vienna but also in Graz.
His dissertation and habilitation thesis dealt with the reduction theory of quadratic forms, which Gauss, Charles Hermite and Hermann Minkowski had worked on previously. Hofreiter treated the case of four variables of a problem of Minkowski (Minkowski had solved the problem for two variables, while Robert Remak had solved it for three variables) on the product of inhomogeneous linear forms and achieved significant progress. The complete solution was only found 15 years later (and the general case is still unresolved). In 1934, he proved the existence of infinitely many real quadratic number fields without a Euclidean algorithm. In addition, he dealt with the geometry of numbers and Diophantine approximation.
In 1939, he was an associate professor and married the mathematician Margaret Dostalík (born 1912). She was also a student of Furtwängler and did important work on algebraic equations and was working as a meteorologist in Berlin at the time. During the Second World War, he moved from Vienna and was a little later at the Hermann Goering Aviation Research Institute in Braunschweig, where his colleagues Wolfgang Gröbner from Vienna, Bernhard Baule from Graz, Ernst Peschl and Josef Laub were already working. Through his work there, together with Gröbner, he started a table of integrals. The first volume, on indefinite integrals, was published by Notdruck (Braunschweig) in 1944 and by Springer in 1949. In 1950, the second volume containing definite integrals appeared. Both parts were widely available through to the 5th 1973/75 edition. His wife, Margaret, assisted with the calculations, as well as the preparation and review of both volumes.
In addition to their work at the Aviation Research Institute, Gröbner and Hofreiter continued to give lectures and seminars at the Technical University of Braunschweig. After the war he returned to Vienna in 1946 and continued to expand on his number theory work. He also worked on linear optimization and numerical mathematics. In 1954, he became a professor, and in 1963/4 became Dean of the Faculty, and in 1965/6, he was Rector of the Universität Wien. In 1974, he retired.
In 1970, he corresponding member of the Austrian Academy of Sciences. He received the Honorary Cross for Science and Art 1st Class, the Medal of Honor of the City of Vienna in gold, the great silver medals for outstanding contributions to the Republic of Austria, the Komturkreuz of Gregory, the ring of honor of the Austrian Mathematical Society and was honorary senator of the University of Linz.
His doctoral students included Edmund Hlawka, Peter Gruber and Leopold Schmetterer.
References
- Edmund Hlawka: Nachruf. In: Almanach der Österreichischen Akademie der Wissenschaften. Band 140, 1989/90
- Edmund Hlawka: Nachruf auf Nikolaus Hofreiter. In: Monatshefte für Mathematik. Band 116, 1993, Nr.3–4, S.263–273
External links
Categories:- 20th-century mathematicians
- Number theorists
- Austrian mathematicians
- People from Linz
- 1904 births
- 1990 deaths
- Vienna University of Technology alumni
- Vienna University of Technology faculty
- Braunschweig University of Technology faculty
- University of Vienna faculty
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