Hermes studied from 1931 mathematics, physics, chemistry, biology and philosophy at the universities of Freiburg, Munich and Münster. In 1937 he passed the state examination in Münster and was there in 1938 when the physicist Adolf scratches and the philosopher and logician Heinrich Scholz doctorate ( An axiomatization of mechanics). After that he went on a scholarship to the University of Göttingen and then became an assistant at the University of Bonn. During World War II, he was a soldier on the Channel Island of Jersey and then at the Chemical- Physical Institute of the Navy in Kiel and at the end of the war Toplitzsee to 1943. In 1947, he was with Ernst Peschl in Bonn habilitation ( Analytical manifolds in Riemannian areas ) and then diet was a lecturer and in 1949 professor at the Westfälische Wilhelms-Universität Münster, where he turned back to the mathematical logic.
Hans Hermes was a pioneer of the Turing machine as a central concept of predictability. In 1937, Hermes reported under the title Definite terms and predictable numbers an article about the Turing machine, which still adheres closely to Turing, but the universal machine and the reference to the decision problem does not contain. In 1954 appeared an informal proof that the options of programmable digital computers include the computable functions, ie, that the concrete calculators have the same cardinality as Turing machines (see Turing - completeness ).
In 1952 he published together with Heinrich Scholz an encyclopedic report, which has significantly influenced and promoted the development of mathematical logic.
In 1953 he took over from Heinrich Scholz management of the influential Institute for Mathematical logic and basic research at the Westfälische Wilhelms-Universität in Münster. Under his leadership the Institute Münstersche became a center for the young discipline, which aired not only to the Federal Republic but also abroad. With Hermes were there, among others, Wilhelm Ackermann and Gisbert rabbits Jaeger. In 1966 he accepted a call to the newly established Chair of Mathematical Logic and the Foundations of Mathematics at the Albert -Ludwigs- University of Freiburg and began to build an eponymous department at the Mathematical Institute. In 1977 he became Professor Emeritus there.
Hermes ' textbooks as well as his scientific work, according to Heinz- Dieter Ebbinghaus convince originality, accuracy and intuitive clarity. He was also an outstanding academic teacher who knew how to convey difficult issues and complicated proofs extremely understandable.
Hermes was also involved in the already initiated by Scholz publication of the works of Gottlob Frege. He was co-editor of the Journal of Symbolic Logic. In 1962 he was one of the founding members of the German Association for mathematical logic and for basic research of the exact sciences ( DVMLG ). In 1950, he was with Arnold Schmidt and Jürgen von Kempski co-founder of the Archive for Mathematical Logic and Foundations of Mathematics.
Among his students Heinz -Dieter Ebbinghaus, Werner Mark Forest, Arnold Oberschelp, Walter Oberschelp, Jörg Flum.
- Definite terms and predictable numbers. Semester reports for the care of the relationship 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, Issue 3, Leipzig, 1938.
- Machines for decision of mathematical problems. Mathematics and Physical semester reports (Göttingen ) ( 1952), 179-189.
- The universality of program-controlled computing machines. Mathematics and Physical semester reports (Göttingen ) 4 ( 1954), 42-53.
- Introduction to lattice 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.
- A Term logic with choice operator, Berlin, 1965.
- With Klaus Heidler and Friedrich -K. Mahn: Recursive functions, Mannheim - Vienna - Zurich 1977.
- Figures and games in Heinz -Dieter Ebbinghaus, Friedrich Hirzebruch, Hermes, among other things: numbers, Springer -Verlag, 3rd edition, 1992
- Decision problem and domino games, in Konrad Jacobs ( ed.) Selecta Mathematica II, Springer, Heidelberg paperbacks, 1970
- With Werner Markwald: foundations of mathematics, in Behnke, sweet, Fladt: Principles 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