Max Dehn

Born in Hamburg on November 13, 1878 to an assimilated Jewish family, Max Wilhelm Dehn studied mathematics at the University of Göttingen under the legendary David Hilbert. In 1900, at age twenty-two, Dehn stunned the international mathematical community by becoming the very first person to solve one of Hilbert's celebrated twenty-three unsolved mathematical problems presented that year at the Paris Congress. Solving Hilbert's third problem, Dehn proved using an ingenious new invariant (the Dehn invariant) that two polyhedra of equal volume cannot always be cut into a finite number of identical polyhedral pieces, disproving a hypothesis that had stood since Euclid. Dehn went on to pioneer low-dimensional topology, inventing "Dehn surgery" on three-dimensional manifolds and formulating foundational questions in combinatorial group theory (the word problem, conjugacy problem, and isomorphism problem). Appointed professor at the University of Frankfurt in 1921, Dehn was dismissed by the Nazi regime in 1935 under antisemitic Nuremberg Laws. Barely escaping Germany during Kristallnacht in 1938, Dehn fled through Norway and the Soviet Union to the United States. In 1945, he found an intellectual home at the experimental, progressive Black Mountain College in North Carolina, where he was revered as the sole mathematician among avant-garde artists, poets, and architects like Buckminster Fuller, Josef Albers, and John Cage. Passing away in Black Mountain in 1952, Max Dehn is celebrated as one of modern geometry's most original minds.