Georg Hamel

from Wikipedia, the free encyclopedia

Georg Hamel (born September 12, 1877 in Düren , † October 4, 1954 in Landshut ; full name Georg Karl Wilhelm Hamel ) was a German mathematician .

Life

Georg Hamel studied in Aachen , Berlin and Göttingen , where he did his doctorate in 1901 under David Hilbert on the subject of Geometries, in which the straight lines are the shortest . He received his habilitation in Karlsruhe in 1903. In 1905 he became a full professor in Brno , in 1912 in Aachen and in 1919 at the TH Berlin . Hamel also held the post of rector at TH Berlin in 1928/1929. In 1938 he became a member of the Prussian Academy of Sciences . He is best known for his work on fundamental problems , which led to the concept of the Hamel basis of real numbers (understood as a vector space over the rational numbers), as well as for his work on the axiomatic structure of classical mechanics, which makes an important contribution to technical mechanics represent.

The existence of the Hamel base is not only valid for the real number field. The same conclusion - with the help of the well-ordering rate or Zorn's lemma - shows that every vector space V , a base B has, that is a subset, so that each vector of V is a uniquely determined linear combination of a finite number of vectors from B 's.

Already in his dissertation he made significant progress on Hilbert's fourth problem of characterizing geometries similar to Euclidean geometry, in which, as in Euclidean geometry, the straight line is the shortest connection between two points. Among other things, he showed that after a metrization of a projective geometry that fulfills the postulate mentioned, only two cases occur in the plane: the geometry is valid in the entire projective plane, with the straight lines being a closed line of finite length ( elliptical geometry ), or the geometry is valid in a convex part (or the entire) affine plane, and the lines are the usual Euclidean lines and have infinite length.

In 1935 Hamel was elected a member of the Leopoldina . As emeritus Georg Hamel was appointed a corresponding member of the Bavarian Academy of Sciences in 1953 and in 1954 Dr. rer. nat. hc from RWTH Aachen University. In 1935 he was President of the German Mathematicians Association (DMV), after there had previously been a power struggle in the DMV, with Ludwig Bieberbach on the side of a more National Socialist orientation. In 1921 Hamel founded the Mathematisches Reichsverband (MR) as a society for school mathematicians, while the DMV at that time was primarily aimed at university mathematicians.

Web links

Individual evidence

  1. ↑ G. Hamel: A basis of all numbers and the discontinuous solutions of the functional equation f (x + y) = f (x) + f (y) . In: Mathematical Annals . tape 60 , no. 3 , 1905, pp. 459-462 ( [1] ).
  2. ^ Karl-Eugen Kurrer : The History of the Theory of Structures. Searching for Equilibrium . Ernst & Sohn , Berlin 2018, pp. 895f., ISBN 978-3-433-03229-9 .
  3. ↑ G. Hamel: About the geometries in which the straight lines are the shortest . In: Mathematical Annals . tape 57 , 1903, pp. 231-264 ( [2] ).
  4. ^ IM Jaglom: On the fourth Hilbert problem, in: Pavel S. Alexandrov (Ed.): Die Hilbertschenproblem, Harri Deutsch 1998, p. 122
  5. ^ Remmert, The German Mathematicians Association in the "Third Reich", Part 1, Communications DMV, 2004, p. 159
personal data
SURNAME Hamel, Georg
ALTERNATIVE NAMES Hamel, Georg Karl Wilhelm (full name)
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH September 12, 1877
PLACE OF BIRTH Düren
DATE OF DEATH 4th October 1954
Place of death Landshut