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A Rememberance of Victor Klee (1925 - 2007) by Branko Grünbaum

Submitted by Rose Choi on August 1, 2007 - 5:00am
Victor Klee

The passing of Vic Klee should be an occasion to remember him, his character and his work, and the help of various kinds he has given to so many of us.

More than fifty years ago, while still a student in Jerusalem, I first came in contact with Vic. During the second round of letters he suggested shortening my addressing him from "Professor Klee" to "Klee", and in the next round, to replace "Klee" by "Vic". This is just a small example of his friendly and open approach to people.

One of Vic's very impressive traits was the care he devoted to his students, and the help he was ready to give them throughout their career. His doctoral students had weekly conferences with him, at which he most actively helped them formulate their thoughts in an effective way, provided them with suggestions, and tried to cheer them up when the problems seemed to be overwhelming. I believe that every single student that started research with Vic did finish with a degree.

Vic was a very helpful colleague, always ready with references and other information about a variety of topics. He was also fair to a fault, happy to help out with classes if emergencies arose, and most thoughtful and meticulous in letters of recommendation he wrote. His lectures — whether in class, at the seminar, or in various meetings and colloquia — were always carefully thought out, and delivered in an inspiring and captivating manner.

One of Vic's lasting contributions to the department was the seminar he organized in the 1950s and led for many years. The seminar continues to this day. Over the decades, it went under various names — Convexity, Geometry, Geometry and Combinatorics, Combinatorics and Geometry, Combinatorics, reflecting the preferences and interests of its organizers — but the spirit did not change much. The regular participants formed a community with frequent contacts and exchanges. Often the attendance shot up during the Summer Quarter, as this was one of very few offerings that presented new ideas and recent results.

Vic's mathematical interests and achievements span a large number of fields. He made important contributions to the theory of linear spaces (of finite and infinite dimensions) and convex sets in them. He also wrote interesting papers in graph theory, in combinatorics, in questions of computational complexity of geometric constructions, and on many other topics. In most of these works he presented original ideas, as well as stimulating open problems.

However, his most valuable mathematical achievement was in the theory of convex polytopes. It is my firm belief that Klee's path-breaking and seminal papers on polytopes, published in the 1960s, mark the beginning of the theory that flourishes at present, and that he has to be considered the father of the whole field. He retained an interest in convex polytopes to the end, and had over the years many students exploring the topic.

Vic was also interested in popularizing mathematics among wider circles. He wrote several general surveys, made a film, initiated and edited for several years an "Unsolved Problems" section in the American Mathematical Monthly, and gave literally hundreds of lectures in many different forums. He was also the recipient of many honors — unfortunately I have no list.

Although ill health slowed Vic down over the last few years, till very recently he was still a very valuable member of the department, and of the wider mathematical community.

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