# Helmut Hasse

Helmut Hasse | |
---|---|

Born | |

Died | 26 December 1979 | (aged 81)

Nationality | German |

Alma mater | University of Marburg University of Göttingen |

Known for | Conductor-discriminant formula |

Scientific career | |

Fields | Mathematics |

Thesis | Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen (1922) |

Doctoral advisor | Kurt Hensel |

Doctoral students | Cahit Arf Wolfgang Franz Paul Lorenzen Curt Meyer Peter Roquette Otto Schilling Oswald Teichmüller |

Other notable students | Paul Lorenzen |

**Helmut Hasse** (German: [ˈhasə]; 25 August 1898 – 26 December 1979) was a German mathematician^{[1]} working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions.

## Life[edit]

Hasse was born in Kassel, Province of Hesse-Nassau,^{[2]} the son of Judge Paul Reinhard Hasse aka Haße (12 April 1868 – 1 June 1940,^{[3]} son of Friedrich Ernst Hasse and his wife Anna Von Reinhard) and his wife Margarethe Louise Adolphine Quentin (born 5 July 1872 in Milwaukee, daughter of retail toy merchant^{[4]} Adolph Quentin (b. May 1832, probably Berlin, Kingdom of Prussia) and Margarethe Wehr (b. about 1840, Prussia),^{[5]} then raised in Kassel).^{[6]}

After serving in the Imperial German Navy in World War I, he studied at the University of Göttingen, and then at the University of Marburg under Kurt Hensel, writing a dissertation in 1921 containing the Hasse–Minkowski theorem, as it is now called, on quadratic forms over number fields, he then held positions at Kiel, Halle and Marburg. He was Hermann Weyl's replacement at Göttingen in 1934.

Hasse was an Invited Speaker of the ICM in 1932 in Zurich and a Plenary Speaker of the ICM in 1936 in Oslo.^{[7]}

In 1933 Hasse had signed the *Loyalty Oath of German Professors to Adolf Hitler and the National Socialist State*.

Politically, he applied for membership in the Nazi Party in 1937, but this was denied to him due to his Jewish ancestry.^{[8]} After the war, he briefly returned to Göttingen in 1945, but was excluded by the British authorities. After brief appointments in Berlin, from 1948 on he settled permanently as professor in Hamburg.

He collaborated with many mathematicians, in particular with Emmy Noether and Richard Brauer on simple algebras, and with Harold Davenport on Gauss sums (Hasse–Davenport relations), and with Cahit Arf on the Hasse–Arf theorem.

## Publications[edit]

*Mathematische Abhandlungen*, H.W.Leopoldt, Peter Roquette (ed.), 3 vols., de Gruyter 1975*Number theory*, Springer, 1980, 2002 (Eng. trans. of*Zahlentheorie*, 3rd edn., Akademie Verlag 1969)^{[9]}*Vorlesungen über Zahlentheorie*, Springer, 1950^{[9]}*Über die Klassenzahl abelscher Zahlkörper*, Akademie Verlag, Berlin, 1952.^{[10]}*Höhere Algebra*vols. 1, 2, Sammlung Göschen, 1967, 1969*Vorlesungen über Klassenkörpertheorie*, physica Verlag, Würzburg 1967- Hasse, H. (1926), "Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. I: Klassenkörpertheorie.",
*Jahresbericht der Deutschen Mathematiker-Vereinigung*(in German),**35**: 1–55 - Hasse, H. (1927), "Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Teil Ia: Beweise zu I.",
*Jahresbericht der Deutschen Mathematiker-Vereinigung*(in German),**36**: 233–311 - Hasse, H. (1930), "Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Teil II: Reziprozitätsgesetz",
*Jahresbericht der Deutschen Mathematiker-Vereinigung*(in German), Ergänzungsband 6 *Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper*, 1965 (reprint from Berichts aus dem Jahresbericht der DMV 1926/27)- New edn. of
*Algebraische Theorie der Körper*by Ernst Steinitz, together with Reinhold Baer, with a new appendix on Galois theory. Walter de Gruyter 1930. - Hasse
*Mathematik als Wissenschaft, Kunst und Macht*, DMV Mitteilungen 1997, Nr.4 (Published version of a lecture given at the University of Hamburg 1959) - Hasse „Geschichte der Klassenkörpertheorie“, Jahresbericht DMV 1966
- Hasse „Die moderne algebraische Methode“, Jahresbericht DMV 1930
- Brauer, Hasse, Noether „Beweis eines Hauptsatzes in der Theorie der Algebren“, Journal reine angew.Math. 1932
- Hasse „Theorie der abstrakten elliptischen Funktionenkörper 3- Riemann Vermutung“, Journal reine angew. Math., 1936
- Hasse „Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen“, Journal reine angew.Math. 1923

## See also[edit]

- Hasse diagram
- Hasse invariant of an elliptic curve
- Hasse invariant of a quadratic form
- Artin–Hasse exponential
- Hasse–Weil L-function
- Hasse norm theorem
- Hasse's algorithm
- Hasse's theorem on elliptic curves

## References[edit]

**^**Helmut Hasse at the Mathematics Genealogy Project**^**Hellmuth Haße in the Hesse, Germany, Births, 1851-1901; Hessisches Hauptstaatsarchiv; Wiesbaden, Deutschland; Personenstandsregister Geburtenregister; Bestand: 910; Signatur: 910_5132; accessed 31 March 2018 Ancestry.com. Hesse, Germany, Births, 1851-1901. Lehi, UT, USA: Ancestry.com Operations, Inc., 2016.**^**Paul Reinhard Hasse in the Hesse, Germany, Deaths, 1851-1958, Personenstandsregister Sterberegister; Bestand: 910; Signatur: 5683; Ancestry.com. Hesse, Germany, Deaths, 1851-1958 paid subscription website. Provo, UT, USA: Ancestry.com Operations, Inc., 2016.**^**1870 U.S. Federal Census: Adolph Quentin, accessed 31 March 2018, paid subscription ancestry.com website.**^**Margarethe Louise Adolphine Quentin in the Hesse, Germany, Marriages, 1849-1930; Hessisches Hauptstaatsarchiv; Wiesbaden, Deutschland; Personenstandsregister Heiratsregister; Bestand: 910; Ancestry.com. Hesse, Germany, Marriages, 1849-1930. Lehi, UT, USA: Ancestry.com Operations, Inc., 2016.**^**Harold Edwards, Artikel Helmut Hasse in Dictionary of Scientific Biography**^**Hasse, H. (1937). "Über die riemannsche Vermutung in Funktionenkörpern".*In:**Comptes rendus du Congrès international des mathématiciens: Oslo, 1936*. vol. 1. pp. 189–206.**^**Helmut Hasse und die Familie Mendelssohn, By Peter Roquette. The Nazi mathematician Prof. Erhard Tornier pointed out that Helmut Hasse had a Jewish great grandmother.- ^
^{a}^{b}Kaplansky, Irving (1981). "Review:*Number theory*, by Helmut Hasse".*Bull. Amer. Math. Soc. (N.S.)*.**4**(2): 249–250. doi:10.1090/s0273-0979-1981-14899-0. **^**Chevalley, C. (1953). "Review:*Über die Klassenzahl abelscher Zahlkörper*, by Helmut Hasse".*Bull. Amer. Math. Soc*.**59**(3): 281–282. doi:10.1090/s0002-9904-1953-09709-9.

## External links[edit]

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- 1898 births
- 1979 deaths
- People from Kassel
- People from Hesse-Nassau
- Number theorists
- 20th-century German mathematicians
- University of Marburg faculty
- University of Kiel faculty
- Martin Luther University of Halle-Wittenberg faculty
- University of Hamburg faculty
- University of Göttingen faculty
- University of Göttingen alumni
- University of Marburg alumni
- German people of Jewish descent
- German military personnel of World War I
- Imperial German Navy personnel
- Members of the German Academy of Sciences at Berlin