George W. Mackey, the Landon T. Clay Professor of Mathematics Emeritus, died March 15 of complications from pneumonia. He was 90.

George W. Mackey

Mackey worked in the fields of representation theory, group actions, functional analysis, and mathematical physics. One of his best-known contributions was to provide a sound mathematical foundation for the science of quantum mechanics.

Born in 1916 in St. Louis, he earned a bachelor’s degree from the Rice Institute (now Rice University) in 1938. He then began graduate studies in mathematics at Harvard, earning a master’s degree in 1939 and a Ph.D. in 1942.

After teaching for a year at the Illinois Institute of Technology in Chicago, Mackey returned to Harvard in 1943 as an instructor in mathematics. He became a full professor in 1956 and in 1969 received the Landon T. Clay Professorship. He retired in 1985.

As an undergraduate, Mackey majored in physics, but found himself increasingly interested in mathematics. In an autobiographical sketch he wrote later in life, he said, “I was disturbed by the way that mathematics was handled in my physics courses and spent a great deal of time trying to redo things in a more precisely defined and rigorously argued manner.”

In fact, it was to bring mathematical reform to physics that he originally decided to study mathematics on the graduate level. However, his focus soon changed.

“Once in graduate school I became seduced by the beauties of pure mathematics and put my plans for reforming physics aside.”

Mackey never entirely abandoned his interest in physics, however. In the 1940s, while working in the area of representation theory, he formulated what became known as the “imprimitivity theorem,” which played a key role in much of his future work. In the 1950s, he found he could use this theorem to explain certain mysterious features of quantum mechanics.

Clifford Taubes, the William Petschek Professor of Mathematics and department chair, described Mackey as “a very kind, gentle man, and probably the most intellectually honest person I can think of. He was a realist. He believed that people shouldn’t delude themselves. He was a gentleman to a fault, but he wouldn’t let people get away with cozy preconceptions. He didn’t have much patience for people who didn’t think through what they believed in.”

Mackey was a member of the American Academy of Arts and Sciences and the American Philosophical Society. He was vice president of the American Mathematical Society in 1964-65, a member of the Institute for Advanced Study in 1977, and professeur associé at the Université de Paris VI in 1978.

He served as visiting professor at many institutions, including Oxford University, the University of Chicago, the University of California, Los Angeles, the University of California, Berkeley, and the International Center for Theoretical Physics in Trieste, Italy. He received the distinguished alumnus award from Rice University in 1982, and in 1985 received a Humboldt Foundation teaching grant, which he used to teach at the Max Planck Institute in Bonn, Germany.

His published works include “Mathematical Foundations of Quantum Mechanics” (1963), “Mathematical Problems of Relativistic Physics” (1967), “Induced Representations of Groups and Quantum Mechanics” (1968), “Theory of Unitary Group Representation” (1976), “Lectures on the Theory of Functions of a Complex Variable” (1977), and numerous scholarly articles.

He leaves his wife, Alice (Willard) Mackey; a daughter, Ann Sturges Mackey of Hastings-on-Hudson, N.Y.; a sister, Madge Mackey Wintz of Houston; and two grandchildren.

A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.