**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.

- Max was brought up in Hamburg where he attended the Wilhelm Gymnasium.
- This school prepared students for university and, after graduating, Dehn entered the University of Freiburg.
- At Freiburg, Dehn studied mathematics but, as was common for students at this time, he did not spend his whole time at one university.
- Dehn showed that the answer to this question is "no", constructing a counterexample using what is today called the 'Dehn invariant'.
- Dehn next attempted to solve the Poincaré conjecture but, of course, he failed.
- In 1911 Dehn was appointed as an extraordinary professor at Kiel, and from 1913 until 1921 he was a full professor at the University of Breslau.
- In 1914 Dehn published the paper Die beiden Kleeblattschlingen Ⓣ(The two trefoil knots).
- The fundamental group, very new in 1914, was used by Dehn in a sophisticated fashion, via the investigation of its outer automorphism group.
- Having used it to prove the trefoil is not amphicheiral, Dehn's paper concludes with a brief investigation of the outer automorphism group of the fundamental group of the figure eight knot, which is amphicheiral.
- before 1984 we really didn't have any simple tests for non-amphicheirality, so that Dehn's work (which at first glance looks like the use of a cannon to kill a sparrow) remained central to the subject for nearly 70 years.
- According to Dehn, only a few preconditions are necessary to bring about mathematics.
- Dehn thus positioned "mathematical ability" at a basic anthropological level.
- Dehn qualified under this exemption clause so continued to head the mathematics seminar at University of Frankfurt.
- Dehn was forced to resign but remained in Frankfurt.
- On 11 November 1938 Dehn was arrested but, with so many Jews being held, the prisons were full and he was released later on the same day.
- Immediately Dehn and his wife, fearing re-arrest, fled to the home of Willi Hartner, friends in Bad Homburg north of Frankfurt.
- Dehn was soon given a temporary position at he Technische Hochschule in Trondheim as a replacement for Viggo Brun (1885-1978) who was on leave.
- Dehn fled the city but, despite the great risks, was back in the city by June and began to plan his move to the United States.
- In October 1940 the Dehns emigrated to the USA, travelling from Norway to Stockholm in Sweden, then on to Moscow in Russia from where they took the trans-Siberian train to Vladivostok.
- Once in the USA Dehn taught at several universities and colleges, for instance at the University of Idaho in Pocatello, the Illinois Institute of Technology and St John's College in Annapolis, Maryland.
- Prof Dehn came to teach several graduate courses.
- There was no trained mathematician on the staff when Dehn was invited to give two lectures there in 1944.
- Dehn joined the Faculty in 1945 and remained there until his death.
- Dehn was the only mathematician ever to teach at the College which closed in 1956.
- Dehn's outstanding research record is in stark contrast with the low level of his final post.
- In his 1911 paper Über unendliche diskontinuierliche Gruppen Ⓣ(On infinite discontinuous groups), Dehn formulated important problems on group presentations, namely the word problem and the isomorphism problem.
- Dehn also wrote on statics, projective planes and, as we have noted above, on the history of mathematics.
- Dehn retired at the end of the academic year 1951-1952 and was made Professor Emeritus.

Born 13 November 1878, Hamburg, Germany. Died 27 June 1952, Black Mountain, North Carolina, USA.

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Algebra, Group Theory, Origin Germany, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive