Emanuel Sperner

Emanuel Sperner (9 December 1905 - 31 January 1980) was a German mathematician known for his two lemmas. He was born in Waltdorf (near Nysa, now in Poland), and died in Salzburg-Laufen. He was a student at Hamburg University. He was appointed Professor in Königsberg in 1934, and subsequently held posts in a number of universities until 1974.

The two Sperner's lemmas are both combinatorial in nature. One of them (from 1932) is a step in a direct proof of the Brouwer fixed-point theorem without explicit use of homology.

The other (1927) concerns possible anti-chains in the power set of {1,2, ..., n}, giving the largest possible size being that attained by the 'middle' sets (the central binomial coefficient(s)). It can be reduced to the Hall marriage theorem.