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Max Dehn wrote one of the first systematic expositions of topology (1907) and later formulated important problems on group presentations, namely the word problem and the isomorphism problem.
Dehn studied at Göttingen under Hilbert's supervision obtaining his doctorate in 1900. From 1921 until 1935 he held the chair of Pure and Applied Mathematics at the University of Frankfurt but he was forced to leave his post by the Nazi regime. In 1940 he emigrated to the USA where he taught at several universities and colleges.
Dehn was an intuitive geometer, stimulated by Hilbert's axiomatic approach to the subject. Dehn solved the third of Hilbert's 23 problems on the congruence of polyhedra. In 1907 Dehn wrote one of the first systematic expositions of topology. At that time topology was called 'analysis situs'.
Dehn's work in topology led him into the study of groups, particularly group presentations which arise naturally from topological considerations. Dehn formulated important problems on group presentations, namely the word problem and the isomorphism problem.
The word problem asks the fundamental question of whether there is an algorithm to determine whether a word in a group given by a presentation is trivial. It has since been shown that no such algorithm exists in general. Research on questions of this type are still of major importance in the subject.
Dehn also wrote on statics, projective planes and the history of mathematics.
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