Max Dehn

Max Dehn
Max Dehn

Born November 13, 1878(1878-11-13)
Died June 27, 1952(1952-06-27) (aged 73)
Nationality German American
Fields Mathematics
Institutions University of Münster
Goethe University Frankfurt
Black Mountain College
Alma mater University of Göttingen
Doctoral advisor David Hilbert
Doctoral students Ott-Heinrich Keller
Wilhelm Magnus
Ruth Moufang

Max Dehn (November 13, 1878 – June 27, 1952) was a German American mathematician and a student of David Hilbert. He is most famous for his work in geometry, topology and geometric group theory. Dehn's students include Ott-Heinrich Keller, Ruth Moufang, Wilhelm Magnus and the artist Dorothea Rockburne.



Dehn was born in Hamburg, Imperial Germany.

He studied the foundations of geometry with Hilbert at Göttingen in 1899, and obtained a proof of the Jordan curve theorem for polygons. In 1900 he wrote his dissertation on the role of the Legendre angle sum theorem in axiomatic geometry. From 1900 to 1911 he was an employee and researcher at the University of Münster. In his habilitation at the University of Münster in 1900 he resolved Hilbert's third problem, by introducing what was afterwards called Dehn invariant.

Dehn's interests later turned to topology and combinatorial group theory. In 1907 he wrote with Poul Heegaard the first book on the foundations of combinatorial topology, then known as analysis situs. Also in 1907, he described the construction of a new homology sphere. In 1908 he believed that he had found a proof of the Poincaré conjecture, but Tietze found an error.

In 1910 Dehn published a paper on three dimensional topology in which he introduced Dehn surgery and used it to construct homology spheres. He also stated Dehn's lemma, but an error was found in his proof by Hellmuth Kneser in 1929. The result was proved in 1957 by Christos Papakyriakopoulos. The word problem for groups, also called the Dehn problem, was posed by him in 1911.

In 1912 Dehn invented what is now known as Dehn's algorithm and used it in his work on the word and conjugacy problems for groups. The notion of a Dehn function in geometric group theory, which estimates the area of a relation in a finitely presented group in terms of the length of that relation, is also named after him. In 1914 he proved that the left and right trefoil knots are not equivalent. In the early 1920s Dehn introduced the result that would come to be known as the Dehn-Nielsen theorem; its proof would be published in 1927 by Jakob Nielsen.

In 1922 Dehn succeeded Ludwig Bieberbach at Frankfurt, where he stayed until he was forced to retire in 1935. He stayed in Germany until January 1939, when he fled to Copenhagen, and then to Trondheim, Norway, where he took a position at the Norwegian Institute of Technology. In October 1940 he left Norway for America by way of Siberia and Japan (the Atlantic crossing was considered too dangerous).

In America, Dehn obtained a position at Idaho Southern University (now Idaho State University). In 1942 he took a job at the Illinois Institute of Technology, and in 1943 he moved to St. John's College in Annapolis, Maryland. Finally in 1945, he moved to Black Mountain College, where he was the only mathematician. He and his wife regularly had long breakfasts with Buckminster Fuller and his wife.

He died in Black Mountain, North Carolina in 1952.

See also


  • Max Dehn, Papers on group theory and topology. Translated from the German and with introductions and an appendix by John Stillwell. With an appendix by Otto Schreier. Springer-Verlag, New York, 1987. viii+396 pp. ISBN 0-387-96416-9

External links

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Look at other dictionaries:

  • Max Dehn — Max Wilhelm Dehn (* 13. November 1878 in Hamburg; † 27. Juni 1952 in Black Mountain, North Carolina) war ein deutscher Mathematiker. Er löste als erster eines (das dritte) von Hilberts 23 mathematischen Problemen. Inhaltsverzeichnis 1 Leben 2… …   Deutsch Wikipedia

  • Max Dehn — (13 novembre 1878 – 27 juin 1952) est un mathématicien allemand. Il a étudié les fondations de la géométrie avec Hilbert à Göttingen en 1899, et obtenu une preuve du théorème de Jordan pour les polygones. En 1900, il a soutenu …   Wikipédia en Français

  • Max Dehn — (13 de noviembre de 1878, Hamburgo, Alemania – 27 de junio de 1952, Black Mountain, Carolina del Norte, EE. UU.) fue un matemático alemán, que lanzó su famoso Lema de Dehn en los años 1930, y que lo descifró el matemático Griego Christos… …   Wikipedia Español

  • Dehn — ist der Nachname folgender Personen: August Wilhelm von Dehn (1716–1776), Baron von Dehn auf Ludwigsburg und Träger des Danebrog Ordens. Friedrich Ludwig von Dehn (1697–1771), dänischer Diplomat; von 1762 bis 1768 Statthalter der Herzogtümer… …   Deutsch Wikipedia

  • Dehn — may refer to: Dehns the trading name for British attorney office Frank B. Dehn Co Adolf Dehn Lili Dehn Max Dehn, mathematician Megan Dehn Mura Dehn Paul Dehn, poet and screenwriter Werner Dehn …   Wikipedia

  • Dehn function — In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the …   Wikipedia

  • Dehn planes — In geometry, Dehn constructed two examples of planes, a semi Euclidean geometry and a non Legendrian geometry, that have infinitely many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle… …   Wikipedia

  • Dehn's lemma — In mathematics Dehn s lemma asserts that a piecewise linear map of a disk into a 3 manifold, with the map s singularity set in the disc s interior, implies the existence of another piecewise linear map of the disc which is an embedding and is… …   Wikipedia

  • Dehn surgery — In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a specific construction used to modify 3 manifolds. The process takes as input a 3 manifold together with a link. Dehn surgery can be thought of as a two stage process …   Wikipedia

  • Dehn twist — A positive Dehn twist applied to a cylinder about the red curve c modifies the green curve as shown. In geometric topology, a branch of mathematics, a Dehn twist is a certain type of self homeomorphism of a surface (two dimensional manifold).… …   Wikipedia

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