Ronald L. Graham, who unlocked the magic of numbers, dies at age 84

Ronald L. Graham, who gained renown with wide-ranging theorems in a field known as discrete mathematics that have found uses in diverse areas, ranging from making telephone and computer networks more efficient to explaining the dynamics of juggling, died on July 6 at his home in the La Jolla section of San Diego. He was 84.

The cause was bronchiectasis, a chronic lung condition, according to a statement from the University of California, San Diego, where Graham was an emeritus professor.

“He created a lot of mathematics and some really pretty cool stuff,” said Peter Winkler, a mathematician at Dartmouth College. “This occurred over many years, and so it’s only now that we get to sort of look back and see all the stuff that he did.”

One thing he did was develop methods for worst-case analysis in scheduling theory — that is, whether the order in which actions are scheduled wastes time. On another front, with his wife and frequent collaborator, Fan Chung, an emeritus mathematician at the University of California, San Diego, he developed the idea of quasi-random graphs, which applied numerical preciseness in describing the random-like structure of networks.

Graham’s research was detailed in about 400 papers, but he never fit the stereotype of a nerdy mathematician. Soft-spoken but garrulous, he leavened his talks on high-level equations with silly jokes and sight gags. He was also an expert trampoline gymnast and juggler, a side pursuit — he was elected president of the International Jugglers’ Association in 1972 — that in his hands also lent itself to mathematical analysis. At one point Graham and three other juggling mathematicians proved an equation for the number of possible ball-juggling patterns before a pattern repeats.