This is a story about Max Dehn’s life – told by many voices as the title suggests – and it includes discussions of his history, his mathematical work, and his students. His was a varied and unusual career. Many who recognize his name do so in connection with mathematical contributions he made: the Dehn invariant, Dehn surgery, Dehn twists, and more.

The book is a collection of essays that address several areas of his life and work. Dehn was a student of Hilbert, and the first to solve one of Hilbert’s famous problems (the third, about reassembling pieces of polyhedra of equal volume). After this, he did significant work in the foundations of geometry, then moved to other notable work in topology, geometric group theory and the word problem. Although he did a good deal of noteworthy work as a mathematician, he is recognized almost equally for his long career as a teacher and scholar. 

The book interweaves chapters that tell the story of Dehn’s life with chapters that identify and describe the themes of his mathematical work. His time in Germany ended when he was dismissed from a position at Frankfurt following imposition of the Nazi racial laws. He moved on to England and Norway before coming to the USA. After a variety of positions at several different schools, he spent seven years as professor of mathematics and philosophy at Black Mountain College, a short-lived experimental college in North Carolina. During that time he seems to have been an inspiration for several renowned artists. He taught a very popular course on geometry for artists, as well a philosophy, Greek, Italian and other mathematics courses. This period seems to have been among the happiest times of his life.

One of Dehn’s many talents was his skill in picturing mathematical concepts, and his ability to convey this to artists, as he did at Black Mountain College. One of the articles about his work there describe him as “a mathematician among artists and an artist among mathematicians”.

This is an attractively written portrait of a fascinating man, but not by any means a biography. Yet the story it tells might just encourage someone to prepare a full biography to give a complete portrait of Dehn’s compelling life story.

Because it is assembled from several pieces, any future edition would benefit from an index to give the reader the ability to search for specific elements among Dehn’s multivariate life.  A bibliography would also be useful.

Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.