Emanuel Sperner

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.

Key Information

Emanuel Sperner
Born	(1905-12-09)9 December 1905 Waltdorf, Upper Silesia, German Empire (now in Poland)
Died	17 March 1980(1980-03-17) (aged 74) Sulzburg-Laufen, Germany
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
Show more

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.^[3]

Sperner's students included Kurt Leichtweiss and Gerhard Ringel.