Dr. Brooks, who was raised in Bethesda, taught at the University of Maryland from 1979 to 1984. Since 1995, he had been on the faculty of Technion, the Israel Institute of Technology in Haifa.
He was writing a book on spectral geometry, a field that examines the relationship between the shape of an object and the frequencies at which it vibrates radically. Colleagues said he was one of the world's leading experts in a field that has drawn increasing interest in recent years, yielding applications in physics and computer science.
Dr. Brooks also studied "circle packings" -- searching for the fundamental principles of mathematics expressed in the fitting of circular tiles of various sizes into prescribed areas. A McGill colleague said that Dr. Brooks's circle-packing theorem was used recently by William P. Thurston of Princeton University to prove a deep theorem in modern geometry.
Dr. Brooks was a 1970 graduate of Walt Whitman High School and a 1974 graduate of Harvard University, where he also received master's and doctoral degrees in mathematics.
While undertaking postdoctoral studies at the State University of New York at Stony Brook, Dr. Brooks worked with J. Peter Matelski in creating pictures of fractals -- patterns that reveal greater complexity when enlarged. Fractals can be subdivided into parts that are images of the whole.
The researchers' work was later reflected in the groundbreaking "Mandelbrot set" pictures of mathematician Benoit Mandelbrot, who first defined fractals.
Dr. Brooks went on to become a professor of mathematics at the University of Southern California, after having done research at the Courant Institute of Mathematical Sciences of New York University. He was also a Fulbright senior scholar at Hebrew University in Jerusalem.
Dr. Brooks spoke often at scientific conferences and published 80 mathematical papers in journals that included Topology, American Journal of Mathematics, Duke Mathematical Journal and St. Petersburg Journal.
He was also visiting lecturer at a number of universities internationally. His honors included an Alfred P. Sloan fellowship, a Guastella fellowship and Technion's Taub Prize for Excellence in Research.
The obituary was published in the Washington Post