Person: Witt, Ernst
Ernst Witt was a German mathematician and a leading algebraist. He proved important results on Lie algebras.
Mathematical Profile (Excerpt):
- He always intended to become a missionary and, after the Liebenzell Mission was set up in Hamburg in November 1899 they appointed Heinrich Witt to be their first missionary in China in March 1900.
- It was during this two years leave that Ernst was born on the island of Alsen.
- The island and was returned to Denmark by plebiscite in 1920, nine years after Witt's birth there, and is now known as Als.
- When Ernst was two years old, his parents returned to China to continue their missionary work.
- Heinrich Witt became head of the Liebenzell Mission in Changsha.
- However, Heinrich Witt was very involved in his missionary work which took him on many long journeys through China.
- The home was strictly run and did not provide a very stimulating environment for the young Witt.
- After graduating from the Realschule in Müllheim, Witt went to Freiburg in 1927 were he attended the Oberrealschule.
- At this time his parents returned from China for another two year leave and they were in Germany for the years when Witt was at the Oberrealschule.
- At this school Witt was fortunate to have a talented mathematics teacher, Karl Öttinger, who quickly realised the extraordinary talent of his pupil and did everything he could to allow him to progress rapidly to advanced topics.
- Witt took his Abitur examination in the same year, then entered the University of Freiburg to study mathematics and physics.
- It was usually for students at German universities at this time to move between institutions and after two terms at Freiburg, Witt moved to Göttingen for the start of the 1930 summer term.
- Herglotz quickly realised that Witt had remarkable mathematical gifts.
- Having seen a remarkably simple proof by Witt of Wedderburn's theorem that every finite skew field is commutative, Herglotz encouraged him to submit it for publication and it became Witt's first paper appearing in 1931.
- Emil Artin, who held the chair at Hamburg, lectured at Göttingen in 1932 and Witt attended his lectures on class field theory and was greatly influenced by them.
- Witt joined the Nazi Party on 1 May 1933 and also the SA, the military wing of the Party.
- It has been claimed that Oswald Teichmüller, who was like Witt a student at Göttingen, convinced him to join.
- At one of the lectures Witt turned up wearing his SA (Sturm Abteilung: Storm Section) uniform.
- This view that Witt put mathematics before Nazi ideology is born out by many, both staunch Nazi supporters and those opposed to the Nazi ideas.
- Witt once explained that all sciences can reshape themselves in accordance with the spirit of the times; only in mathematics must everything remain as before.
- Witt joined Hasse's seminar on congruence function fields and p-adic numbers; he was appointed as Hasse's assistant.
- Oswald Teichmüller and Ludwig Schmid were also members of the seminar, and Schmid collaborated with Witt on ideas which would lead to the Witt vector calculus.
- Witt habilitated with Hasse in 1936.
- In it he introduced what was later named the 'Witt ring' of quadratic forms.
- In the following year Herglotz argued strongly in support of Witt becoming Toeplitz's successor but the chair was not filled until 1939 when Wolfgang Krull was appointed.
- Witt published Treue Darstellung Liescher Ringe Ⓣ(Faithful representations of Lie rings) in 1937, which was inspired by earlier work of Wilhelm Magnus on free Lie algebras.
- In this paper Witt showed that any Lie algebra over a field has a faithful representation in an associative algebra, and that there exists an associative algebra which is universal with respect to this construction.
- Description of his character: Witt has shown himself to be quiet, modest and restrained, with a tendency to keep to himself; characteristic features are a certain naivety and eccentricity.
- Witt was appointed to fill the vacancy at Hamburg in 1938, at first as a lecturer, then from 1 September 1939 as an extraordinary professor.
- Erna Bannow's doctoral dissertation Die Automorphismengruppen der Cayley-Zahlen Ⓣ(The automorphism groups of the Cayley numbers) was published in 1940 as was Witt's report on the thesis.
- Witt was called up for war service in February 1940 but managed to get it deferred for a year.
- Many of his colleagues wrote supporting his reinstatement, all testifying that Witt, despite his membership of the Party, had quickly realised that the aims of the Nazi Party were incompatible with scientific progress which was always the most important thing in his life.
- We note that following the two papers Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe Ⓣ(Reflection groups and enumeration of semisimple Lie rings) and Eine Identität zwischen Modulformen zweiten Grades Ⓣ(An identity between modular forms of second degree), both published in 1941, no further publications by Witt appeared until 1949 when he published Rekursionsformel für Volumina sphärischer Polyeder Ⓣ(Recursion for the volume of spherical polyhedra).
- Witt made many visits to lecture on his work.
- Witt was always completely honest and often rather naive, and he showed this side of his character during his time in Princeton.
- In spring 1961 Kurosh and Witt were introduced in Princeton.
- Witt never quite understood why his openness about such matters led to his colleagues at Princeton avoiding him.
- Witt's work was mainly concerned with quadratic forms and various related fields such as algebraic function fields, Witt vectors, Lie rings and Mathieu groups.
- He is best known for his introduction of Witt vectors which appeared in his paper in 1936 in J.
- Witt received many honours such as membership of the German Mathematical Society (Deutsche Mathematiker-Vereinigung) in 1937, the Hamburg Mathematical Society, the oldest mathematical society in the world which still exists today, in 1954, and the Göttingen Academy of Sciences in 1978.
- Witt is worth consideration because his life seems to show that the caricatures could, in fact, both be true.
Born 26 June 1911, Alsen (German Baltic island) (now Als, Denmark). Died 3 July 1991, Hamburg, Germany.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive