{{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<br>(now in Poland) | death_date = {{death date and age|1980|03|17|1905|12|9|df=y}} | death_place = Sulzburg-Laufen, Germany | fields = Mathematics | workplaces = University of Königsberg<br>University of Bonn<br>University of Freiburg<br>University of Hamburg | alma_mater = University of Hamburg | doctoral_advisor = Wilhelm Blaschke | doctoral_students = Kurt Leichtweiss<br>Gerhard Ringel | known_for = Sperner's theorem<br>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).<ref>Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928) 544–548.</ref> 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.<ref>Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes. Abh. Math. Sem. Hamburg VI (1928) 265–272.</ref> 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.<ref>{{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 }}</ref>
Sperner's students included Kurt Leichtweiss and Gerhard Ringel.
== References== {{Reflist}}
== External links == * [https://opc.mfo.de/person_detail?id=3954 Sperner's photos] – from the Mathematical Research Institute of Oberwolfach {{commons category-inline|Emanuel Sperner (mathematician)}}
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{{DEFAULTSORT:Sperner, Emanuel}} Category:1905 births Category:1980 deaths Category:People from Nysa County Category:People from the Province of Silesia Category:20th-century German mathematicians Category:Combinatorialists Category:Kolegium Carolinum Neisse alumni Category:University of Freiburg alumni Category:Academic staff of the University of Freiburg Category:University of Hamburg alumni Category:Academic staff of the University of Hamburg Category:Academic staff of the University of Königsberg Category:Academic staff of the University of Strasbourg Category:Academic staff of the University of Bonn Category:Presidents of the German Mathematical Society