# Ernst Witt

Ernst Witt ( born June 26, 1911 Alsen, German Empire, now Denmark, † July 3, 1991 in Hamburg ) was a German mathematician.

## Life

Witt was born on until 1920 to Prussia belonging island of Als. His father, Heinrich (1871-1959) was a missionary since 1900 for the Liebenzeller mission in China, and Witt was born during a home leave his father from 1911 to 1913. His mother, Charlotte Jepsen came from Sønderborg Als. Shortly after his birth he moved with his parents to China, where his father headed the Liebenzeller Mission in Changsha. Witt learned there Mandarin by his nanny. He returned only at the age of nine years from China back to Germany, where he lived with his brother with an uncle in garbage home. After his schooling in garbage home and graduating from high school in 1929 in Freiburg, he studied at the Albert- Ludwigs- University of Freiburg and from 1930 at the Georg -August- University of Göttingen, where he in 1934 with Gustav Herglotz with a proposed by Emmy Noether topic, Riemann -Roch theorem and Z- function in hyper complexes doctorate. He transferred in the theorem of Riemann -Roch on algebras over function fields. Emmy Noether was already suspended, so he earned his doctorate at Herglotz, but they continued to hold a seminar at his home from which also visited Witt. In addition, he also heard by Emil Artin in 1932, when he held in Göttingen guest lectures on class field theory and at the invitation of Artin in Hamburg, where he transferred the class field theory for function fields. In Göttingen, he later belonged to the working group of the algebraists Helmut Hasse, whose assistant he was from 1934 and where he habilitated in 1936. Since 1938, Witt was a lecturer at the University of Hamburg, where he remained until his retirement in 1979. In 1939 he became associate professor in 1954 and full professor, interrupted by two years from 1945 due to the de-Nazification proceedings before the British occupation authorities, in which he was fully rehabilitated in 1947. Witt initiated in Hamburg a private seminar with Max Deuring and 1951 with Hasse. He had in the 1940s also offers to teach at the Humboldt University of Berlin, where Hasse was, and he gave lectures. He also appeared in the 1950s ( partly due to mediation by Wilhelm Blaschke, who sought the resumption of international contacts of the Hamburg mathematician ) Guest Lecturer in Barcelona, Madrid ( which he learned Spanish ) and Rome ( with Francesco Severi ). From the early 1950s he rezipierte with his students the beginnings of time spreading from France Bourbaki movement, particularly corresponded to his mathematical style.

His doctoral include Kay Wingberg, Ina Kersten, Walter Borho, Günter Harder, Bernard Banaschewski (Professor at McMaster University ), Jürgen Rohlfs (Vienna ), Manfred Knebusch.

He was married to the mathematician Erna Bannow since 1940, also a student of Emil Artin, 1939 in Hamburg doctorate at Witt ( The automorphism group of the Cayley numbers). With her he had two daughters.

The grave of Ernst Witt is located on the Nienstedtener Cemetery in Hamburg.

## Witt in the era of National Socialism

During the period of National Socialism from 1933 he was a member of the SA, which then caused irritation after Richard Courant at Göttingen him and other mathematics professors. Courant (as long as he could still remain in Göttingen ) promoted Witt, who had great financial difficulties to complete his studies and had to restrict very much. As the (well-known because of its oppositional stance to the Nazis in Hamburg) Erich Hecke and others testified in the denazification process, the setting of Witt was not anti-Semitic. He was rather characterized as " quixotic " and apolitical, with an almost complete focus on mathematics. At the excesses of Nazi students and his friend Oswald Teichmüller at the University of Göttingen he was not involved. It is unclear whether it was himself or his friend Teichmüller, the Emmy Noether in seminar ( which they held with him at home in 1933 ) in SA uniforms was sitting. Emmy Noether even preferring them to take no public notice, and continued to teach her seminar, Witt served as graduate students and made sure that thesis further supervised after their release Herglotz Witts.

In his own words Witt joined the SA, because he saw this as a national duty as a foreign German, participated in nightly Luggage marches of the SA, but avoided gatherings of his comrades and turned away by the Nazis, as he perceived them as uninterested in scientific matters. When the Nazi students in 1934, a scientifically insignificant contender favored as head of the Göttingen Mathematical Institute in Göttingen, he spoke out against it. In 1938 he resigned from the SA and he was not even a member of the Nazi Student League and the National Socialist Federal lecturers. In a review of the National Socialist German lecturers of 1937, he was judged to be quiet and reserved, honest and straightforward, but also as an eccentric and naive and politically indifferent and denies his leadership qualities. During the war he was in 1941 briefly used as a remote indicator on the Eastern Front, but became ill and returned to the recovery not go back to the front, where his unit had since been wiped out, but worked in Berlin in Decipher, where he optical inter alia Machinery method developed.

## Work

The work of Witt dealt mainly with square shapes and various related fields such as algebraic function fields. He also developed a classification Liescher algebras of geometric basis. In 1938 he described the eponymous Wittschen block plans whose existence had already been published in 1931 by Robert Daniel Carmichael. He realized that the automorphism groups of these and derived block plans are the simple Mathieugruppen. Witt said to have found some new finite simple groups in his study of Mathieugruppen, but the unpublished. He planned in the 1950s, a book on Lie groups in the basic teachings of the Springer Verlag series, but nothing came of it. Characteristic of his work are clarity and brevity. He was concerned in the 1940s and 1950s, with intuitionistic logic.

Named after him are the Witt vectors, infinite sequences of elements of a commutative ring. Witt constructed a ring structure on the set of such vectors such that the ring of Witt vectors corresponds to over a finite field of order the ring of p- adic numbers. In his habilitation on quadratic forms in arbitrary fields, he led after him named Witt -rings and Witt groups.