Emanuel Sperner
| Emanuel Sperner | |
|---|---|
 | |
| Born |
9 December 1905 Waltdorf, Upper Silesia, German Empire (now in Poland) |
| Died |
17 March 1980 (aged 74) Sulzburg-Laufen, Germany |
| Nationality | German |
| Alma mater | University of Hamburg |
| Known for |
Sperner's theorem Sperner's lemma |
| Scientific career | |
| Fields | Mathematics |
| Institutions |
University of Königsberg University of Bonn University of Freiburg University of Hamburg |
| Doctoral advisor | Wilhelm Blaschke |
| Doctoral students |
Kurt Leichtweiss Gerhard Ringel |
Emanuel Sperner (9 December 1905 – 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Neiße, Upper Silesia, now Nysa, Poland), and died in Sulzburg-Laufen, West Germany. He was a student at Carolinum in Nysa and then Hamburg University where his advisor was Wilhelm Blaschke. He was appointed Professor in Königsberg in 1934, and subsequently held posts in a number of universities until 1974.
Sperner's theorem, from 1928, says that the size of an antichain in the power set of an n-set (a Sperner family) is at most the middle binomial coefficient(s).[1] It has several proofs and numerous generalizations, including the Sperner property of a partially ordered set.
Sperner's lemma, from 1928, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.[2] It was proven by Sperner to provide an alternate proof of a theorem of Lebesgue characterizing dimensionality of Euclidean spaces. It was later noticed that this lemma provides a direct proof of the Brouwer fixed-point theorem without explicit use of homology.
Sperner's students included Kurt Leichtweiss and Gerhard Ringel.
