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Peter A. Loeb was a quintessentially nonstandard human, father, husband, and friend鈥嬧�嬧�攁nd the originator of the Loeb measure, which has been used by mathematicians worldwide.

Peter Loeb 鈥�59

Nov. 20, 2024, in Urbana, Illinois.

A professor emeritus at the University of Illinois department of mathematics and a pioneer in nonstandard analysis, Peter A. Loeb was a quintessentially nonstandard human, father, husband, and friend​​—and the originator of the Loeb measure, which has been used by mathematicians worldwide.

After studying mathematics at Reed, Peter graduated in the top half of the first graduating class from Harvey Mudd College in 1959. He received his MS at Princeton in 1961 and his PhD from Stanford.

Peter’s first professorship was at UCLA, where he remained until he became an assistant professor at the University of Illinois in 1968. He and his wife, Jane Loeb, remained in Champaign-Urbana for the next 56 years—or, as Peter would say, “more than 1% of recorded human history.”

In 1975, Peter published a mathematical construction that has since been called the “Loeb measure” (though never by him). The Loeb measure has inspired a vast literature in mathematics and beyond, leading to important applications in probability theory, potential theory, number theory, mathematical economics, and mathematical physics.

Peter received international recognition for his work and served as a visiting scholar at institutions around the world (including Yale, Caltech, Chalmers University of Technology in Sweden, Tokyo Science University, and the National University of Singapore). In the last year of his life, he spoke and was honored at a special session of the American Mathematical Society in San Francisco titled “Loeb Measure after 50 Years.”

Peter’s acute brain was not reserved only for academics. He had a phenomenal memory for tunes and his sense of humor was endemic, as was his particularity about word choice. (He would not have approved of the use of “endemic” in the previous sentence.)

A lifelong Democrat, Peter was active in the party for many years, as well as in the local music scene. Always an enthusiastic singer on family car trips and around the campfires of his youth, he joined the Choral Union upon retirement and began taking voice classes, continuing his singing lessons until the day before he became bedridden.

Peter is survived by his wife of 66 years, Jane, and his children, Eric, Gwen, and Aaron.

Appeared in Reed magazine: Winter 2025