Background
Max Dehn was born on November 13, 1878, in a Jewish family in Hamburg, Imperial Germany.
Goethe University Frankfurt from 1921 to 1935.
The University of Idaho.
Illinois Institute of Technology.
Black Mountain College.
Goethe University Frankfurt from 1921 to 1935.
The University of Idaho.
Illinois Institute of Technology.
Black Mountain College.
(The work of Max Dehn has been quietly influential in math...)
The work of Max Dehn has been quietly influential in mathematics since the beginning of the 20th century. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas.
http://www.amazon.com/gp/product/0387964169/?tag=2022091-20
1987
educator mathematician scientist
Max Dehn was born on November 13, 1878, in a Jewish family in Hamburg, Imperial Germany.
Dehn studied at Göttingen under the direction of David Hilbert and received his doctorate in 1900. He wrote his dissertation on the role of the Legendre angle sum theorem in axiomatic geometry.
Dehn taught at several schools, served in the army, and was a professor of pure and applied mathematics at Goethe University Frankfurt from 1921 to 1935, when the Nazi regime forced him to leave. In 1940 he emigrated to the United States, where he taught at the University of Idaho, Illinois Institute of Technology, St. Johns College (Annapolis), and, from 1945 to 1952, at Black Mountain College, North Carolina.
Dehn was an intuitive geometer. Stimulated by Hilbert’s work on the axiomatization of geometry, Dehn showed in his dissertation that without assuming the Archimedean postulate, Legendre’s theorem that the sum of the angles of a triangle is not greater than two right angles is unprovable, whereas a generalization of Legendre’s theorem on the identity of the sums of angles in different triangles is provable. Following this work, Dehn solved the third of the twenty- three unsolved problems that Hilbert had presented in his famous address to the International Congress of Mathematicians in 1900. This problem concerned the congruence of polyhedra, the geometric properties of which Dehn spent much time studying.
In 1907 Dehn and Poul Heegaard contributed a report to the Encyklopadie der mathematischen Wissenschaften on the topic of analysis situs (now called topology or algebraic topology), which had become prominent as a result of the works of Poincare. The article was one of the early systematic expositions of this subject. In 1910 Dehn proved an important theorem concerning topological manifolds that became known as Dehn’s lemma. In 1928, however, Kneser showed that the proof contained a serious gap; a correct proof was finally given by C. D. Papakyriakopoulos in 1957.
Following Poincare, Dehn became interested in the groups that are generated in attempts to characterize topological structures. He formulated the central problems of what was to become an important mathematical field: the word, the transformation, and the isomorphism problems. In the case of fundamental groups these have direct topological significance.
In March 1944, Dehn was invited to give two talks at Black Mountain College on the philosophy and history of mathematics. He noted in a letter that a lecture on an advanced mathematical topic didn't seem appropriate given the audience. He instead offered up the lectures "Common roots of mathematics and ornamentics," and "Some moments in the development of mathematical ideas." Black Mountain College faculty contacted him shortly after concerning a full-time position. After negotiating his salary from $25 to $40 per month, Dehn and his wife moved into housing provided by the school and he began teaching in January 1945.
While at Black Mountain College, Dehn taught courses in Mathematics, Philosophy, Greek, and Italian. In his class "Geometry for Artists," Dehn introduced students to geometric concepts such as points, lines, planes and solids; cones sectioned into circles, ellipses, parabolas, and hyperbolas; spheres and regular polyhedrons. His classes had an emphasis on the way shapes relate to each other, a concept that can be useful in artistic mediums.
Dehn also supervised the work of eight doctoral candidates in Germany and three in the United States.
In the summer of 1952 Dehn was made Professor Emeritus, which allowed him to remain on campus and act as an advisor. Unfortunately he died of an embolism shortly thereafter while overseeing the removal of several dogwood trees from the campus. He is buried in the woods on the campus.
(The work of Max Dehn has been quietly influential in math...)
1987Dehn was a member of the Norwegian Academy of Science, the Strassburger Naturforschung Gesellschaft, and the Indian Mathematical Association.
Dehn enjoyed the forested mountains found in Black Mountain, and would often hold class in the woods, giving lectures during hikes. His lectures frequently drifted off topic on tangents about philosophy, the arts, and nature and their connection to mathematics. He and his wife took part in community meetings and often ate in the dining room. They also regularly had long breakfasts with Buckminster Fuller and his wife.
Dehn married Antonie Landau on August 23, 1912.
