Ernst Witt

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Ernst Witt
Ernst Witt.jpeg
Ernst Witt in Nice, 1970
Born (1911-06-26)June 26, 1911
Alsen, German Empire (present-day Denmark)
Died July 3, 1991(1991-07-03) (aged 80)
Hamburg, Germany
Fields Mathematics
Institutions University of Hamburg
Alma mater University of Göttingen
Doctoral advisor Emmy Noether
Doctoral students Walter Borho, Günter Harder
Known for Witt algebra, Witt group, Hasse–Witt matrix, Bourbaki–Witt theorem, Poincaré–Birkhoff–Witt theorem, Witt's theorem, Witt vector

Ernst Witt (June 26, 1911 – July 3, 1991) was a German mathematician, one of the leading algebraists of his time. He was born on the island of Als (German: Alsen). Shortly after his birth, he and his parents moved to China, and he did not return to Europe until he was nine.

After his schooling, Witt went to the University of Freiburg and the University of Göttingen. He joined the Nazi party and was an active party member.[1] Witt completed his Ph.D. at the University of Göttingen in 1934 with Emmy Noether and later became a lecturer. He was then a member of a team led by Helmut Hasse.

From 1937 until 1979, he taught at the University of Hamburg. He died in Hamburg in 1991.


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 over an arbitrary field. 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 algebras. In algebraic geometry, the Hasse-Witt matrix of an algebraic curve over a finite field determines the cyclic étale coverings of degree p of a curve in characteristic p.

In the 1970s, Witt claimed that in 1940 he 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 (Witt 1998, pp. 328–329).

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  1. ^ According to Schappacher (letter in Mathematical Intelligencer 1996) it was most certainly him and not Oswald Teichmüller, who attended Emmy Noether's private seminar held in her house while wearing his SA-uniform.

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