Emanuel Sperner

Who was Emanuel Sperner?

Emanuel Sperner was a German mathematician, best known for two theorems. He was born in Waltdorf, and died in Sulzburg-Laufen, West Germany. He was a student at 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 is at most the middle binomial coefficient. 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. 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.