Emanuel Sperner

{{Short description|German mathematician (1905–1980)}}

{{Infobox scientist

| name = Emanuel Sperner

| image = Emanuel Sperner.jpg

| image_size =

| caption =

| birth_date = {{birth date|1905|12|9|df=y}}

| birth_place = Waltdorf, Upper Silesia, German Empire
(now in Poland)

| death_date = {{death date and age|1980|03|17|1905|12|9|df=y}}

| death_place = Sulzburg-Laufen, Germany

| nationality = German

| fields = Mathematics

| workplaces = University of Königsberg
University of Bonn
University of Freiburg
University of Hamburg

| alma_mater = University of Hamburg

| doctoral_advisor = Wilhelm Blaschke

| doctoral_students = Kurt Leichtweiss
Gerhard Ringel

| known_for = Sperner's theorem
Sperner's lemma

| awards =

}}

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).Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928) 544–548. 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.Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes. Abh. Math. Sem. Hamburg VI (1928) 265–272. 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.{{cite journal |first=Sehie |last=Park |title=Ninety Years of the Brouwer Fixed Point Theorem |journal=Vietnam Journal of Mathematics |volume=27 |issue=3 |year=1999 |pages=187–222|url=http://www.math.ac.vn/publications/vjm/vjm_27/No.3/187-222_Park.PDF |citeseerx=10.1.1.473.5513 |access-date=2018-11-05 }}

Sperner's students included Kurt Leichtweiss and Gerhard Ringel.