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, structure, space, models, and change.
History
On ...
working in
algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
, known for fundamental contributions to
class field theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.
Hilbert is credit ...
, the application of
''p''-adic numbers to
local class field theory In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite re ...
and
diophantine geometry
In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study ...
(
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 eac ...
), and to
local zeta functions.
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 2020 ...
,
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. With a population of 577,222 at the 2020 census, Milwaukee is ...
, daughter of retail toy merchant Adolph Quentin (b. May 1832, probably
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
,
Kingdom of Prussia
The Kingdom of Prussia (german: Königreich Preußen, ) was a German kingdom that constituted the state of Prussia between 1701 and 1918.Marriott, J. A. R., and Charles Grant Robertson. ''The Evolution of Prussia, the Making of an Empire''. Re ...
) and Margarethe Wehr (b. about 1840, Prussia), then raised in Kassel).
After serving in the
Imperial German Navy
The Imperial German Navy or the Imperial Navy () was the navy of the German Empire, which existed between 1871 and 1919. It grew out of the small Prussian Navy (from 1867 the North German Federal Navy), which was mainly for coast defence. Wilhel ...
in
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
, 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 ...
, 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 wor ...
under
Kurt Hensel
Kurt Wilhelm Sebastian Hensel (29 December 1861 – 1 June 1941) was a German mathematician born in Königsberg.
Life and career
Hensel was born in Königsberg, East Prussia (today Kaliningrad, Russia), the son of Julia (née von Adelson) and lan ...
, writing a dissertation in 1921 containing the
Hasse–Minkowski theorem
The Hasse–Minkowski theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only if they are equivalent ''locally at all places'', i.e. equivalent over every completion o ...
, 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 a ...
s over
number field
In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension).
Thus K is a f ...
s. He then held positions at
Kiel
Kiel () is the capital and most populous city in the northern Germany, 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 J ...
,
Halle 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 approximate ...
. 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 assoc ...
'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
Zürich () is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland, at the northwestern tip of Lake Zürich. As of January 2020, the municipality has 43 ...
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 ''
''.
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
The University of Hamburg (german: link=no, Universität Hamburg, also referred to as UHH) is a public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('' Allgemeines Vor ...
.
He collaborated with many mathematicians, in particular with
Emmy Noether
Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noethe ...
and
Richard Brauer
Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular represent ...
on
simple algebra In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field.
The center of a simple ...
s, and with
Harold Davenport
Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory.
Early life
Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accrington Grammar Scho ...
on
Gauss sum
In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically
:G(\chi) := G(\chi, \psi)= \sum \chi(r)\cdot \psi(r)
where the sum is over elements of some finite commutative ring , is a ...
s (
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 f ...
.
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.
* ''Höhere Algebra'' vols. 1, 2, Sammlung Göschen, 1967, 1969
* ''Vorlesungen über Klassenkörpertheorie'', physica Verlag, Würzburg 1967
*
*
*
* ''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 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
In order theory, a Hasse diagram (; ) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set ''(S, ≤)'' one represents ea ...
*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
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. T ...
*Hasse invariant of an elliptic curve Hasse is both a surname and a given name. Notable people with the name include:
Surname:
* Clara H. Hasse (1880–1926), American botanist
* Helmut Hasse (1898–1979), German mathematician
* Henry Hasse (1913–1977), US writer of science fiction ...
*Hasse invariant of a quadratic form
In mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form ''Q'' over a field ''K'' takes values in the Brauer group Br(''K''). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt.
The quadratic form ''Q'' ...
* Artin–Hasse exponential
* Hasse–Weil L-function
*Hasse norm theorem Hasse is both a surname and a given name. Notable people with the name include:
Surname:
* Clara H. Hasse (1880–1926), American botanist
* Helmut Hasse (1898–1979), German mathematician
* Henry Hasse (1913–1977), US writer of science ficti ...
*Hasse's algorithm
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 integ ...
*Hasse's theorem on elliptic curves
Hasse's theorem on elliptic curves, also referred to as the Hasse bound, provides an estimate of the number of points on an elliptic curve over a finite field, bounding the value both above and below.
If ''N'' is the number of points on the ellip ...
*Hasse–Witt matrix In mathematics, the Hasse–Witt matrix ''H'' of a non-singular algebraic curve ''C'' over a finite field ''F'' is the matrix of the Frobenius mapping (''p''-th power mapping where ''F'' has ''q'' elements, ''q'' a power of the prime number ''p' ...
* Albert–Brauer–Hasse–Noether theorem
*Dedekind–Hasse norm In mathematics, in particular the study of abstract algebra, a Dedekind–Hasse norm is a function on an integral domain that generalises the notion of a Euclidean function on Euclidean domains.
Definition
Let ''R'' be an integral domain and ''g' ...
*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 integ ...
*Local class field theory In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite re ...
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