Ernst Witt (26 June 1911 – 3 July 1991) 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 ...

, one of the leading algebraists of his time.

Biography

Witt was born on the island of Alsen, then a part of the

German Empire The German Empire (),Herbert Tuttle wrote in September 1881 that the term "Reich" does not literally connote an empire as has been commonly assumed by English-speaking people. The term literally denotes an empire – particularly a hereditary ...

. Shortly after his birth, his parents moved the family to

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

to work as missionaries, and he did not return to Europe until he was nine. After his schooling, Witt went to the

University of Freiburg The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public university, public research university located in Freiburg im Breisg ...

and 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 ...

. He joined the

NSDAP The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right politics, far-right political party in Germany active between 1920 and 1945 that crea ...

(Nazi Party) and was an active party member. Witt was awarded a

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

at the University of Göttingen in 1934 with a thesis titled: "Riemann-Roch theorem and zeta-Function in hypercomplexes" (Riemann-Rochscher Satz und Zeta-Funktion im Hyperkomplexen) that was supervised by

Gustav Herglotz Gustav Herglotz (2 February 1881 – 22 March 1953) was a German Bohemian physicist best known for his works on the theory of relativity and seismology. Biography Gustav Ferdinand Joseph Wenzel Herglotz was born in Volary num. 28 to a public not ...

with Emmy Noether suggesting the top for the doctorate. He qualified to become a lecturer and gave guest lectures in Göttingen and Hamburg. He became associated with the team led by

Helmut Hasse Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician 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 ...

who led his habilitation. In June 1936 gave his habilitation lecture. During

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

he joined a group of five mathematicians, recruited by

Wilhelm Fenner Wilhelm Fenner (* 14 April 1891 in Saint Petersburg † after 1946) was a German Cryptanalysis, cryptanalyst, before and during the time of World War II in the OKW/Chi, the Cipher Department of the High Command of the Wehrmacht, working within ...

, and which included

Georg Aumann Georg Aumann (11 November 1906, Munich, Germany – 4 August 1980), was a German mathematician. He was known for his work in general topology and regulated functions. During World War II, he worked as part of a group of five mathematicians, rec ...

Alexander Aigner Alexander Aigner (18 May 1909 – 2 September 1988) was number theorist and a full university professor for mathematics at the Karl Franzens University in Graz, Austria. During World War II he was part of a group of five mathematicians, whic ...

Oswald Teichmüller Paul Julius Oswald Teichmüller (; 18 June 1913 – 11 September 1943) was a German mathematician who made contributions to complex analysis. He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfac ...

, Johann Friedrich Schultze and their leader professor Wolfgang Franz, to form the backbone of the new mathematical research department in the late 1930s, which would eventually be called: Section IVc of Cipher Department of the High Command of the Wehrmacht (abbr. OKW/Chi).TICOM reports DF-187 A-G and DF-176, ‘European Axis Signal Intelligence in World War II’ vol 2 From 1937 until 1979, he taught at the

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 died in Hamburg in 1991, shortly after his 80th birthday.

Work

Witt's work has been highly influential. His invention of the Witt vectors clarifies and generalizes the structure of the ''p''-adic numbers. It has become fundamental to ''p''-adic Hodge theory. Witt was the founder of the theory of

quadratic forms 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 ...

over an arbitrary

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

. He proved several of the key results, including the Witt cancellation theorem. He defined the Witt ring of all quadratic forms over a field, now a central object in the theory. The Poincaré–Birkhoff–Witt theorem is basic to the study of

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s. In

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, the

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' ...

of an algebraic curve over a

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

determines the cyclic étale coverings of degree ''p'' of a curve in characteristic ''p''. In the 1970s, Witt claimed that in 1940 he had discovered what would eventually be named the " Leech lattice" many years before John Leech discovered it in 1965, but Witt did not publish his discovery and the details of exactly what he did are unclear; see his collected works .

References

* *

External links

* * {{DEFAULTSORT:Witt, Ernst 20th-century German mathematicians Algebraists 1911 births 1991 deaths German cryptographers

Biography

Work

See also

References

References

External links