# Theodore G. Ostrom

## 1916-2011

Professor Emeritus Theodore G. Ostrom passed away early on 12 May 2011. A mathematician with international fame, Ostrom made fundamental and outstanding contributions to the field of finite geometries. Ted was a leading authority on projective and affine planes, and he established the area of translation planes as a viable and rich field of research.

Ted was born prematurely on 4 January 1916 in Minnesota to Lloyd and Blanche Ostrom. Ted frequently remarked that his first crib was a shoebox. Although few expected him to live, he showed tenacity for life that enabled him to live for 95 years. His family moved to St. Paul, Minnesota, where he attended grade school and high school, graduating from the latter at the age of 16. Ted continued his education at the University of Minnesota, working part-time to help cover expenses. While at college, Ted was a card-carrying member of a student socialist party and distributed pacifist literature.

Ted graduated in 1937 from the University magna cum laude with a B.S. in Mathematics. He returned to the University and in 1939 he received both a B.S. and a M.S. in Education. For the next two years Ted taught high school mathematics and science in Granite Falls, Minnesota. Although he was successful, Ted decided that high school teaching was not what he wanted to do. Thus, in 1941 Ted enlisted in the US Navy.

Ted was attending Midshipman’s School in Chicago when Pearl Harbor was attacked. He was commissioned as a Lieutenant and served as a Communications Officer on two destroyers during World War II: the USS Dewey (DD-349) and the USS Porter (DD-800). During his service Ted received five Battle Stars.

After the war Ted returned to the University of Minnesota, graduating in 1947 with a Ph.D. in Mathematics. His thesis advisor was Robert H. Cameron and the title of the thesis was: The Solution of Integral Equations by Means of Wiener Integrals. Ted moved to the Mathematics Department at the University in Missoula, Montana. (At that time its name was Montana State University.) From 1954 to 1960 Ted also served as Chair of the Department. At Missoula Ted met Charlotte E. Williams, a member of the Music faculty. They were married on 19 June 1949 and over the next ten years they had four children: Katherine, David, Nancy, and Susan.

In 1960 Ted moved to the Mathematics Department at Washington State University, where he remained until his retirement in 1981. During his time at WSU he mentored five Ph.D. students: Gavin Bjork, Ronald Fryxell, Ranjit Sabharwal, Norman Johnson, and Anthony Evans (co-advisor with Michael Kallaher). Ted also served as Chair of the Department from 1968-1970. During his brief reign as Chair, the department increased its emphasis on research in both theoretical and applied mathematics.

After retirement Ted continued to come to his office every day. He continued his research on affine and projective planes, attended conferences, consulted with colleagues, and performed editorial duties for mathematical journals until his late 80‘s. Ted and Charlotte traveled extensively after his retirement visiting Europe, Asia, and United States. They were together until she passed away in June 2010. Although his physical health showed signs of aging, he was mentally sharp and enjoyed reading, especially nonfiction, and visiting with friends and family.

In the early 1950’s Ted became interested in finite affine and projective planes after hearing a talk on difference sets. Thus began his long and fruitful investigation into the nature of such geometries. Early in his researches Ted and Ascher Wagner proved the famous Ostrom-Wagner Theorem, which says that a finite projective plane with a doubly transitive collineation group must be Desarguesian. In the mid 1960’s Ted discovered the method called derivation for constructing new affine planes from known planes of square order. Under suitable conditions certain sets of lines are each replaced with an appropriate Baer subplane; thereby creating a different plane. As a corollary, this showed that there were many more types of affine planes than previously thought.

In particular, Ted’s work showed that the class of translation planes, a special type of affine plane, was bigger and richer than previously believed. As a result Ted began investigating translation planes with the goal of finding a reasonable description of the various types. He considered translation planes with collineation groups which neither were known groups, contained collineations acting in a certain way, or had certain transitivity properties. He then determined the nature of the plane.

Ted’s research was original, far-reaching, and the basis of much research on finite geometries. He opened up many avenues of research which others traveled. Ted was always willing to discuss with others problems and possible solutions. He gave freely of his time and was generous with his ideas. As his student Norman Johnson said, “Nobody knows why but every one of Ted’s simple and ingenious ideas just worked."

Ted was the author and coauthor of approximately 100 articles and the author of a monograph in the Springer series: Lecture Notes in Mathematics.