Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
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 In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each di ...
), and to
local zeta function In number theory, the local zeta function (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as
:Z(V, s) = \exp\left(\sum_^\infty \frac (q^)^m\right)
where is a non-singular -dimensional projective algebr ...
s.
Life
Hasse was born in
Kassel
Kassel (; in Germany, spelled Cassel until 1926) is a city on the Fulda River in northern Hesse, Germany. It is the administrative seat of the Regierungsbezirk Kassel and the district of the same name and had 201,048 inhabitants in December 2 ...
,
Province of Hesse-Nassau
The Province of Hesse-Nassau () was a province of the Kingdom of Prussia from 1868 to 1918, then a province of the Free State of Prussia until 1944.
Hesse-Nassau was created as a consequence of the Austro-Prussian War of 1866 by combining the p ...
, the son of Judge Paul Reinhard Hasse, also written Haße (12 April 1868 – 1 June 1940, son of Friedrich Ernst Hasse and his wife Anna Von Reinhard) and his wife Margarethe Louise Adolphine Quentin (born 5 July 1872 in
Milwaukee
Milwaukee ( ), officially the City of Milwaukee, is both the most populous and most densely populated city in the U.S. state of Wisconsin and the county seat of Milwaukee County, Wisconsin, Milwaukee County. With a population of 577,222 at th ...
, daughter of retail toy merchant Adolph Quentin (b. May 1832, probably
Berlin
Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...
,
Kingdom of Prussia
The Kingdom of Prussia (german: Königreich Preußen, ) constituted the German state of Prussia between 1701 and 1918. Marriott, J. A. R., and Charles Grant Robertson. ''The Evolution of Prussia, the Making of an Empire''. Rev. ed. Oxford: ...
) and Margarethe Wehr (b. about 1840, Prussia), then raised in Kassel).
After serving in the
Imperial German Navy in
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...
, he studied at the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded i ...
, and then at the
University of Marburg
The Philipps University of Marburg (german: Philipps-Universität Marburg) was founded in 1527 by Philip I, Landgrave of Hesse, which makes it one of Germany's oldest universities and the oldest still operating Protestant university in the worl ...
under
Kurt Hensel, writing a dissertation in 1921 containing the
Hasse–Minkowski theorem, as it is now called, on
quadratic form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
:4x^2 + 2xy - 3y^2
is a quadratic form in the variables and . The coefficients usually belong to ...
s over
number fields. He then held positions at
Kiel
Kiel () is the capital and most populous city in the northern German state of Schleswig-Holstein, with a population of 246,243 (2021).
Kiel lies approximately north of Hamburg. Due to its geographic location in the southeast of the Jutland pe ...
,
Halle Halle may refer to:
Places Germany
* Halle (Saale), also called Halle an der Saale, a city in Saxony-Anhalt
** Halle (region), a former administrative region in Saxony-Anhalt
** Bezirk Halle, a former administrative division of East Germany
** Hall ...
and
Marburg
Marburg ( or ) is a university town in the German federal state (''Bundesland'') of Hesse, capital of the Marburg-Biedenkopf district (''Landkreis''). The town area spreads along the valley of the river Lahn and has a population of approx ...
. He was
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ass ...
's replacement at Göttingen in 1934.
Hasse was an Invited Speaker of the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
(ICM) in 1932 in
Zürich
, neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon
, twintowns = Kunming, San Francisco
Zürich () i ...
and a Plenary Speaker of the ICM in 1936 in
Oslo
Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of ...
.
In 1933 Hasse had signed the ''
Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State''.
Politically, he applied for membership in the Nazi Party in 1937, but this was denied to him allegedly due to his remote
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
ancestry. 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 at
University of 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
Cahit Arf (; 24 October 1910 – 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot theory and surgery theory) in topology, the Hasse–Arf theorem ...
on the
Hasse–Arf theorem
In mathematics, specifically in local class field theory, the Hasse–Arf theorem is a result concerning jumps of the upper numbering filtration of the Galois group of a finite Galois extension. A special case of it when the residue fields are ...
.
Publications
* ''(3 vols.)''
* ''Number theory'', Springer, 1980, 2002 (Eng. trans. of ''Zahlentheorie'', 3rd edn., Akademie Verlag 1969)
* ''Vorlesungen über Zahlentheorie'', Springer, 1950
[
* ''Über die Klassenzahl abelscher Zahlkörper'', Akademie Verlag, Berlin, 1952.]
Hasse „Geschichte der Klassenkörpertheorie“, Jahresbericht DMV 1966Hasse „Die moderne algebraische Methode“, Jahresbericht DMV 1930Brauer, Hasse, Noether „Beweis eines Hauptsatzes in der Theorie der Algebren“, Journal reine angew.Math. 1932Hasse „Theorie der abstrakten elliptischen Funktionenkörper 3- Riemann Vermutung“, Journal reine angew. Math., 1936Hasse „Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen“, Journal reine angew.Math. 1923
See also
* Hasse diagram
*Hasse invariant of an algebra In mathematics, the Hasse invariant of an algebra is an invariant attached to a Brauer class of algebras over a field. The concept is named after Helmut Hasse. The invariant plays a role in local class field theory.
Local fields
Let ''K'' be a l ...
* Hasse invariant of an elliptic curve
* Hasse invariant of a quadratic form
*Artin–Hasse exponential In mathematics, the Artin–Hasse exponential, introduced by , is the power series given by
: E_p(x) = \exp\left(x + \frac + \frac + \frac +\cdots\right).
Motivation
One motivation for considering this series to be analogous to the exponential fu ...
* Hasse–Weil L-function
* Hasse norm theorem
* Hasse's algorithm
* Hasse's theorem on elliptic curves
* Hasse–Witt matrix
* Albert–Brauer–Hasse–Noether theorem
* Dedekind–Hasse norm
*Collatz conjecture
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of intege ...
* Local class field theory
References
External links
*
Another biography
{{DEFAULTSORT:Hasse, Helmut
1898 births
1979 deaths
Scientists 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
Imperial German Navy personnel of World War I
Members of the German Academy of Sciences at Berlin