Helmut Hasse

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Helmut Hasse

Helmut Hasse (born August 25, 1898 in Kassel , † December 26, 1979 in Ahrensburg near Hamburg) was a German mathematician and is considered one of the leading algebraists and number theorists of his time.


Hasse was the son of Judge Paul Reinhard Hasse and Margaret Quentin, who was born in Milwaukee but grew up in Kassel. He went to school in Kassel and Berlin (Fichte-Gymnasium) after the family moved to Berlin in 1913. In the First World War he volunteered for the Navy after graduating from high school in 1915 and was stationed in the Baltic States - where he also did cryptographic work and studied the number theory textbook by Dirichlet-Dedekind - and in Kiel, where he also lectured by Otto Toeplitz in 1917/18 visited. After the war he first studied in Göttingen , where he listened to Erich Hecke until he left for Hamburg ; Reading the book “Number Theory” by Kurt Hensel with his new p-adic methods moved him to move to Marburg in 1920 , where he received his doctorate in May 1921 (with the work on quadratic forms in the rational numbers, which the local Global principle ). During his studies he became a member of the Association of German Students in Marburg . In February 1922 the habilitation followed (equivalence of quadratic forms over the rational numbers). In autumn 1922 he got a position as a private lecturer in Kiel , and at the same time he married Clara Ohle. At Easter 1925 he was appointed full professor in Halle and, along with Heinrich Wilhelm Ewald Jung , became director of the Mathematical Institute there. In 1930 he took over from his teacher Kurt Hensel in Marburg .

Helmut Hasse (1930)

After the “ seizure of power ” by the National Socialists , on November 11, 1933, he was one of the signatories of the professors' commitment to Adolf Hitler and the National Socialist state at German universities and colleges . In 1934 he succeeded Hermann Weyl in Göttingen , who was driven into emigration because of his political views and his Jewish wife. During the time of National Socialism, as a board member of the DMV, he was involved in a power struggle with Ludwig Bieberbach , one of the main representatives of German mathematics , because he wanted to maintain the independence of the DMV. Hasse was primarily concerned with maintaining the reputation of German mathematics abroad. During his time in Göttingen, too, he tried to counteract the loss of importance caused by the expulsion of Jewish professors and professors who were hired against the National Socialists by placing high demands on the scientific work at the institute.

Politically, like many former members of the Imperial Navy, Hasse was far to the right. In 1937 he applied for membership in the NSDAP, which was also granted to him in 1939 (backdated to 1937). But since he had a Jewish great-grandmother, this led to resistance in the party, in which some positions stubbornly sought an exclusion procedure, which was temporarily put on hold after Hate entered the Navy. During the war he conducted research for the German Navy on ballistics and high pressure physics in Berlin and acquired it also provides space at the Mathematical Institute in Göttingen, in part, but probably also to prevent to their otherwise seizure. His stance under National Socialism remained controversial. While on the one hand he was credited with advocating for Jewish colleagues such as Hensel and Emmy Noether, on the other hand he wrote an essay on the situation of mathematics in Germany in a commemorative publication on the 50th birthday of Adolf Hitler and he joined a Nazi academy founded in 1937 of the sciences in Göttingen. As a result, some foreign and emigrated colleagues later met him with suspicion.

After the war, Hasse returned to Göttingen. However, he was removed from his chair by the British authorities in September 1945. In an interview with Constance Reid , Hasse admitted that this was possibly due to the fact that he had bluntly expressed right-wing national ideas at, among other things, the first faculty meeting and to American visitors. Godfrey Harold Hardy and others campaigned in vain to keep hatred on his chair. In 1947, as a result of the denazification process, he was banned from teaching, the reason given being NSDAP membership since 1938, and only after the appeal process was now in German hands he was classified as exonerated in 1948 . Meanwhile, Hasse went to Berlin (East), where he first worked at the German Academy of Sciences from 1946 and later at Humboldt University , where he became a professor in 1949. During this time his monograph and his textbook on number theory were written. In 1950 Hasse accepted a position at the University of Hamburg , where he stayed until his retirement in 1966.

His employees and students in Göttingen in the 1930s included Ernst Witt , Friedrich Karl Schmidt , Oswald Teichmüller , Martin Eichler and Harold Davenport . His doctoral students include Peter Roquette , Heinrich-Wolfgang Leopoldt , Cahit Arf , Wolfgang Franz , Günter Pickert , Curt Meyer , Paul Lorenzen , Otto Schilling , Hans Wittich , Günter Tamme , Hans Reichardt (in Marburg), Hermann Ludwig Schmid and Helmut Brückner ( in Hamburg) and he was also in active correspondence with Arnold Scholz , Emil Artin and Harold Davenport , among others . He had an extensive correspondence with Emmy Noether even after her emigration.

From 1926 Hasse was a member of the Leopoldina (whose Cothenius Medal he received), the Academy of Sciences in Göttingen (from 1934 to 1945), the Academia Scientiarum Fennica (in Helsinki, since 1942), the Berlin Academy of Sciences (the GDR, since 1949), the Academy of Sciences and Literature Mainz (since 1952) and the Real Academia de Ciencias Exactas, Físicas y Naturales (in Madrid, since 1956). In 1953 he received the National Prize of the GDR 1st class for science and technology. He was an honorary doctor of the University of Kiel.

From 1929 to 1979 he was editor of the Journal for Pure and Applied Mathematics .


Hasse made fundamental contributions to algebraic number theory, in particular the proof of higher reciprocity laws (with many detailed investigations in special number fields) and class field theory . His famous report for the German Mathematicians Association (DMV) summarizes the development up to 1926/1927. He also worked on the theory of complex multiplication in number fields and, after the war, on the class numbers of Abelian number fields.

With his teacher Kurt Hensel he was a pioneer in the introduction and further development of local (p-adic) methods in algebra and number theory. He proved that for quadratic forms in the rational numbers from the "local" solvability (p-adic and real) of equations follows the "global". In detail: If a quadratic form with rational coefficients in every p-adic field and in the real number field represents the zero nontrivially [ie there are values ​​of the variables (not all zero) which, when inserted, make the value of the form zero], then represents they represent the zero nontrivially even in the rational number field.

In general, this no longer applies to equations of a higher degree and is subject to the “ local-global principle ”.

In 1936 he achieved a great scientific breakthrough with his proof of the Riemann Hypothesis in the case of the function fields of elliptical curves . In 1936 he gave a plenary lecture on this at the International Congress of Mathematicians in Oslo (About the Riemann Hypothesis in Functional Fields).

He also worked on the theory of algebras. In 1932 he investigated the Brauer group , the group of centrally simple algebras over a basic field k, for the case of p-adic basic fields, i.e. in the “local” case, and thus found the local theory of the residual norm symbol of number fields he was looking for. A local-global principle also applies to the brewing group, its global decomposition is equivalent to the local one (“Brauer-Hasse-Noether theorem”).

The Hasse diagram , a graphic representation of semi-ordered sets, and the Hasse-Arf theory , a branching theory (together with the Turkish mathematician Cahit Arf ) are named after him .



  • Harold M. Edwards : Hasse, Helmut . In: Frederic Lawrence Holmes (Ed.): Dictionary of Scientific Biography . tape 17 , Supplement II: Leason Heberling Adams - Fritz H. Laves . Charles Scribner's Sons, New York 1981, p. 385-387 .
  • Günther Frei : Helmut Hasse , Expositiones Mathematicae Vol. 3, 1985, pp. 55-69
  • Günther Frei, Peter Roquette: Helmut Hasse in Halle , 2002, PDF file (172 kB)
  • Frei (editor): Letters from Emil Artin to Helmut Hasse , Collection Mathématique, University of Laval and Research Institute of Mathematics ETH Zurich, 1981, new edition with Peter Roquette, Universitätsverlag Göttingen 2008 ( Die Artin-Hasse Korrespondenz )
  • Frei: Life and work of Helmut Hasse , Collection Mathématique, University of Laval and Research Institute of Mathematics ETH Zurich, 1977
  • Frei: How Hasse was led to the theory of quadratic forms, the local-global principle, the theory of the norm residue symbol, the reciprocity laws and to class field theory , in: Miyake (editor): Class field theory - its centenary and its prospect, Advanced Studies in Pure Mathematics , Tokyo, 2001, p. 31
  • Franz Lemmermeyer, Peter Roquette (eds.): Helmut Hasse and Emmy Noether . The correspondence 1925–1935 . Universitätsverlag Göttingen, Göttingen 2006, ISBN 3-938616-35-0 ( E-Text ; PDF file; 3.84 MB)
  • Franz Lemmermeyer, Peter Roquette (eds.): The mathematical diaries of Helmut Hasse 1923 - 1935 , Universitätsverlag Göttingen 2012
  • Franz Lemmermeyer, Peter Roquette (eds.): The exchange of letters Hasse - Scholz - Taussky , Universitätsverlag Göttingen 2016 (correspondence with Olga Taussky-Todd , Arnold Scholz )
  • Karin Reich : The exchange of letters Emil Artin - Helmut Hasse (1937/38 and 1953 to 1958) The friendship of the two scholars in a historical context , EAGLE Volume 103, Leipzig, 2018
  • Peter Roquette: The Brauer-Hasse-Noether theorem in historical perspective . (= Writings of the mathematical and natural science class of the Heidelberg Academy of Sciences; 15). Springer, Berlin et al. 2005, ISBN 3-540-23005-X
  • on the history of number theory in the thirties , Mathematisch-Physikalische Semesterberichte 1998, No. 1
  • Nobert Schappacher: The mathematical institute of the University of Göttingen 1929-1950 , in: Heinrich Becker, Hans-Joachim Dahms, Cornelia Wegler (eds.): The University of Göttingen under National Socialism , KG Saur, Munich 1998, pp. 523–551
  • Sanford Segal: Mathematicians under the Nazis , Princeton University Press 2003 (biography p. 130ff)

Web links

Individual evidence

  1. Harold Edwards, article Helmut Hasse in Dictionary of Scientific Biography
  2. Louis Lange (Ed.): Kyffhäuser Association of German Student Associations. Address book 1931. Berlin 1931, p. 82.
  3. According to Hans Reichardt's essay on Hensel in Pieper numbers from prime numbers , Berlin 1974, Hasse is said to have prevented his teacher Hensel, who was Jewish, from being sent to a concentration camp
  4. ^ Ernst Klee : The dictionary of persons on the Third Reich. Who was what before and after 1945 . Fischer Taschenbuch Verlag, Second updated edition, Frankfurt am Main 2005, p. 230.
  5. Volker Remmert The DMV in the "Third Reich" , DMV communications 2004
  6. ^ Sanford Segal, Mathematicians under the Nazis, Princeton University Press, pp. 162ff with a detailed description of the procedure.
  7. The information about what his research group dealt with varies. According to Schappacher, The Mathematical Institute of the University of Göttingen 1929–1950, p. 546, she dealt with tracking curves and collaborators were among others Wilhelm Magnus and Karl Willy Wagner and in Göttingen Maximilian Schuler . According to Schappacher, it is unclear whether there was any connection with the work in the requisitioned rooms of the Mathematical Institute, where, according to official information, high pressure physics was carried out. According to Rainer Karlsch, Hitler's bomb, DVA 2005, p. 45, he built up a research institute of the Naval Weapons Office on Wannsee from 1941 (headline Rear Admiral Wilhelm Rhein), where research in nuclear physics was carried out as well as research on remote missile control. In 1945 the institute was relocated to Göttingen. Fritz Houtermans , Otto Haxel and Pascual Jordan also worked for the Berlin naval research .
  8. Schappacher, The Mathematical Institute at the University of Göttingen 1929–1950, p. 538
  9. ^ Siegmund-Schultze, Mathematicians fleeing under the Nazis, p. 324. In 1963 , Lipman Bers and others opposed Hasse's invitation as a keynote speaker at the memorial service for Emil Artin at the Mathematical Association of America in Colorado. On p. 333 reservations of former colleagues such as Courant and Weyl are cited in 1947 on the occasion of the resumption of contacts to Göttingen and p. 335 in a letter from Courant in 1963.
  10. Constance Reid, Hilbert-Courant, Springer 1986, p. 474. He attributed merits to Hitler in the annulment of the Versailles Peace Treaty.
  11. ^ Norbert Schappacher, The Mathematical Institute of the University of Göttingen 1929–1950, p. 539
  12. His suspension as a member of the Academy of Sciences in Göttingen was not withdrawn, see N. Schappacher: Ideology, Science Policy , and the Honor of Being a Member of the Academy .
  13. Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 105.