Hans Hermes

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Hans Hermes (born February 12, 1912 in Neunkirchen (Saar) ; † November 10, 2003 ) was a German mathematician who made significant contributions to the foundations of mathematical logic .


From 1931 Hermes studied mathematics, physics, chemistry, biology and philosophy at the universities of Freiburg im Breisgau, Munich and Münster. In 1937 he passed the state examination in Münster and received his doctorate there in 1938 under the physicist Adolf Kratzer and the philosopher and logician Heinrich Scholz ( an axiomatization of mechanics ). He then went to the University of Göttingen on a scholarship and then became an assistant at the University of Bonn . During the Second World War he was a soldier on the Channel Island of Jersey , which had been occupied by the German Wehrmacht since 1940, until 1943 and then at the Chemical-Physical Institute of the Navy in Kiel and towards the end of the war on Lake Toplitz . In 1947 he received his habilitation from Ernst Peschl in Bonn ( Analytical Manifolds in Riemannian Areas ) and was then a dietician and, from 1949, a lecturer at the Westphalian Wilhelms University of Münster , where he turned back to mathematical logic.

Hans Hermes pioneered the Turing machine as the central concept of predictability. As early as 1937, Hermes reported an article on the Turing machine under the title Definite Terms and Calculable Numbers , which still adheres closely to Turing, but does not contain the universal machine and the reference to the decision problem . In 1954 an informal proof then appeared that the possibilities of programmable digital computers include the calculable functions , that the concrete calculating machines have the same power as Turing machines (see Turing completeness ).

In 1952, together with Heinrich Scholz, he published an encyclopedic report that significantly influenced and promoted the development of mathematical logic.

In 1953 he took over the management of the influential Institute for Mathematical Logic and Basic Research at the Westphalian Wilhelms University in Münster from Heinrich Scholz . Under his leadership, the Münster Institute became a center of the young discipline, which not only had an impact on the Federal Republic, but also abroad. Wilhelm Ackermann and Gisbert Hasenjaeger, among others, were there with Hermes . In 1966 he accepted a call to the newly established Chair for Mathematical Logic and Fundamentals of Mathematics at the Albert Ludwig University of Freiburg and began to set up a department of the same name at the Mathematical Institute. In 1977 he was retired there.

In 1967 Hermes was elected to the Heidelberg Academy of Sciences .

According to Heinz-Dieter Ebbinghaus, Hermes' textbooks as well as his scientific work are convincing through their originality, accuracy and intuitive clarity. He was also an outstanding academic teacher who knew how to convey difficult topics and complicated evidence in an extremely understandable manner.

Hermes was also involved in the publication of Gottlob Frege's works, which Scholz had already begun . He was an associate editor of the Journal of Symbolic Logic. In 1962 he was one of the founding members of the German Association for Mathematical Logic and Basic Research in the Exact Sciences (DVMLG) . In 1950 he co-founded the Archive for Mathematical Logic and Fundamentals of Mathematics with Arnold Schmidt and Jürgen von Kempski .

His students include Heinz-Dieter Ebbinghaus , Werner Markwald , Arnold Oberschelp , Walter Oberschelp , Jörg Flum .


  • Definite terms and calculable numbers . Semester reports on maintaining the connection between university and school from the mathematical seminars, Münster 1937, 110–123.
  • An axiomatization of general mechanics . Research on logic and the foundations of the exact sciences, Volume 3, Leipzig 1938.
  • Machines to solve math problems . Mathematical-Physical Semester Reports (Göttingen) (1952), 179–189.
  • The universality of program-controlled calculating machines . Mathematical-Physical Semester Reports (Göttingen) 4 (1954), 42–53.
  • Introduction to Association Theory , Berlin - Göttingen - Heidelberg 1955, 2nd expanded edition 1967
  • Enumerability - decidability - predictability. Introduction to the theory of recursive functions , Berlin - Göttingen - Heidelberg 1961, 2nd edition 1971 (as Heidelberg paperback).
  • Introduction to mathematical logic - Classical predicate logic , Teubner Verlag, Stuttgart 1963, 2nd expanded edition 1969.
  • Term logic with a selection operator , Berlin, 1965.
  • With Klaus Heidler and Friedrich-Karl Mahn: Recursive functions , Mannheim - Vienna - Zurich 1977.
  • Numbers and games , in Heinz-Dieter Ebbinghaus , Friedrich Hirzebruch , Hermes a. a .: Numbers , Springer Verlag, 3rd edition 1992
  • Decision problem and domino games , in Konrad Jacobs (Ed.) Selecta Mathematica II , Springer, Heidelberger Taschenbücher, 1970
  • with Werner Markwald: Fundamentals of Mathematics , in Behnke, Süss, Fladt: Fundamentals of Mathematics , Vol. 1, 1958, Vandenhoeck and Ruprecht
  • with Heinrich Scholz Mathematical Logic , Encyclopedia of Mathematical Sciences, New Series, 1952
  • with Gottfried Köthe : Theory of Associations , Encyclopedia of Mathematical Sciences, New Series, 1939


  • Friedrich Ludwig Bauer : Who invented the von Neumann calculator? , Informatik-Spektrum 21 (1998) 2, 84-88
  • Heinz-Dieter Ebbinghaus: Hans Hermes in memory in: Freiburger Universitaetsblaetter, Heft 162 (2003), pages 219-221.
  • Walter Oberschelp: Hans Hermes , Annual Report DMV, Vol. 112, 2007, pp. 99–109

Web links

Individual evidence

  1. ^ Gabriele Dörflinger: Mathematics in the Heidelberg Academy of Sciences . 2014, pp. 26-27.