Wendell Helms Fleming, a mathematician who made seminal contributions in analysis and probability, passed away on February 18, 2023 in Bristol, Rhode Island, USA. He was born March 7, 1928, in Guthrie, Oklahoma, and spent most of his childhood years in southern Indiana. Although starting at Purdue University as an engineering major, he became more interested in the underlying mathematics and refocused in that area. It was also at Purdue that he met his future wife, Flo Tatum. They began a partnership that lasted for 69 years and to which he would attribute his later success.
Upon graduation, mathematics took them first to the University of Wisconsin for his PhD in 1951. Wendell’s first job after receiving his degree was at the Rand Corporation in Santa Monica, California. The Rand Corporation’s purpose was to advise the US Air Force on strategic, operational and technical issues. While there he chose to work on game theory, which led to his long-term interest in the topic of differential games and their connections with risk sensitivity in control systems. However, he eventually concluded that Rand was not the right work environment for him, and that he wanted to do mathematical research and teach in a university. His academic career began with an appointment as Assistant Professor at Purdue University in 1955. In the summer of 1957, he attended an AMS meeting where he met Herbert Federer, and shortly thereafter was invited for a job interview that produced a second appointment as Assistant Professor in Mathematics at Brown University in Providence, Rhode Island. He remained a part of Brown for the next 65 years.
A fascination with variational problems appeared throughout Wendell’s career. His early post-Rand work at Brown focused on geometric measure theory, a topic that emerged from his work with Federer. Later he would add a probabilistic aspect to his work. These new interests overlapped with the faculty in Applied Mathematics at Brown, leading to a second appointment in that department. He was a dedicated and committed colleague to both departments and the university, serving once as chair of Mathematics and twice as chair of Applied Mathematics, and serving as Chair of Brown’s Faculty Policy Group during the tumultuous early 1970s. Although spending most of his years in New England, Wendell never lost his very calm and deliberative Midwestern manner, which served him well in these administrative posts. He did develop an affinity for New England, and in particular the coast of Maine, which was the focal point of family getaways and events.
Wendell was generous with his time to students and junior colleagues of all levels. He provided insightful guidance to undergraduates considering further work in mathematics, thesis supervision to an exceptional cohort of graduate advisees, and wise counsel to a long list of postdocs who spent time at Brown. This practice continued long after he officially retired from Brown, even up to and into his 90s.
Wendell received many awards and honors, including an NSF Senior Postdoctoral Fellowship, a Guggenheim Fellowship, the AMS Steele Prize, and the SIAM Reid Prize. He was a Fellow of the Society of Industrial and Applied Mathematics, a member of the American Academy of Arts and Sciences, and an elected member of the National Academy of Sciences. He also received an honorary Doctor of Science degree from his alma mater Purdue University.
Wendell Fleming was a pioneer in the areas of geometric measure theory, stochastic control theory, differential games, and related topics in the theory of nonlinear partial differential equations. He also worked extensively on risk-sensitive control theory and measure-valued Markov stochastic processes, including applications to mathematical finance.
An extended version of this note—including reviews of his contributions in geometric measure theory (Luigi Ambrosio), stochastic control (Ioannis Karatzas), measure-valued processes (Stewart Ethier) and deterministic differential games (Robert Elliott)—was published in the Quarterly of Applied Mathematics DOI:10.1090/qam/1715.
As colleagues and (in some cases) former students of Wendell, we record here our gratitude for the great and benevolent impact he has had on our personal and professional lives. He will be sorely missed.
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Written by Constantine Dafermos and Paul Dupuis, Brown University