Ronald Graham and the Magic of Math

by Tom Leighton on July 8, 2020

Late Monday night, I received an email sharing the sad news that Ronald Graham had died that evening at the age of 84. For those who never had the pleasure of knowing Ron, he was a brilliant mathematician with a great sense of humor, a circus-level juggler and magician, a mentor of countless students and engineers in the field of discrete mathematics, chief scientist at Bell Labs in the 1960s, and a member of Akamai’s board of directors from 2001 to 2010.

Most Americans have heard of the parlor game “Six Degrees of Kevin Bacon,” which begins with the premise that everyone who is anyone in Hollywood can be linked to the actor Kevin Bacon in six or fewer personal connections. But few are aware that the game grew out of a paper that Ron wrote in 1979, popularizing “the Erdős number,” a concept attributed to the mathematician Casper Goffman 10 years before.

Ron was a chief sponsor in the U.S. of the world renowned, nomadic Hungarian mathematician Paul Erdős (pronounced AIR-dosh), who died in 1996. Erdős effectively founded the field of discrete mathematics, the underpinning of computer science, and wrote at least 1,525 papers by one published count. Ron showed that nearly 500 people had co-authored papers with Erdős, making them one degree of separation away (Erdős Number 1). The number of mathematicians who in turn had written papers with Number 1s was 10x greater, making them Erdős Number 2s, and so on. Within 15 years, the Erdős number had morphed into Kevin Bacon. I’m sure Ron laughed about it for years, for he could find humor in anything.

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He held many professional honors, including being one of the first awardees of the Pólya Prize, a recipient of the Lester R. Ford Award from the Mathematical Association of America, as well as president of the American Mathematical Society, and president of the International Jugglers Association. Ron could juggle half a dozen balls effortlessly while carrying on a conversation, but he always seemed to have trouble making bogey on a hole with a single golf ball. “Golf is always a challenge,” he once confessed to me on the links. Ron loved challenges. A tall, trim man 6’2″ in height, he could do a triple somersault on a trampoline into his 60s. “The best way to crack a complex problem, whether a triple somersault or a conundrum in graph theory,” he told John Horgan for a March 1997 profile in Scientific American, “is to break it down into component parts, learn each of the parts and learn how the parts go together.”

I got to know Ron as a mentor and teacher to me when I was a summer graduate student at Bell Labs, where he worked for 37 years and led one of the greatest team of innovators in U.S. corporate history. We both shared a childhood interest in proving the conjecture that there are infinite pairs of prime numbers separated by 2 (the numbers 11 and 13, for example), although neither of us was ever successful in proving it. Later, at MIT, I taught students from his book, Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks. Like Ron himself, it made math accessible and exposed its magic and beauty to a wide audience.

In awarding him the prestigious Steele Prize for Lifetime Achievement in 2003, the American Mathematical Society called Ron “one of the principal architects of the rapid development worldwide of discrete mathematics in recent years. He has made many important research contributions to this subject, including the development, with [his wife] Fan Chung, of the theory of quasirandom combinatorial and graphical families, Ramsey theory, the theory of packing and covering, etc., as well as to the theory of numbers, and seminal contributions to approximation algorithms and computational geometry (the ‘Graham scan’). Furthermore, his talks and his writings have done much to shape the positive public image of mathematical research in the USA, as well as to inspire young people to enter the subject. He was chief scientist at Bell Labs for many years and built it into a world-class center for research in discrete mathematics and theoretical computer science.”

As an editor on the boards of 40 different mathematics and computer journals at the same time, Ron’s energy was indefatigable. He was a professor at the University of California at San Diego, where he held the Chair of Computer and Information Science and was Chief Scientist of the California Institute for Telecommunications and Information Technology, created to fund research related to the next generation of internet technologies. He served for two years on a National Research Council committee on cryptography. He joined the Akamai board in 2001, just before the tragedy of September 11 struck Akamai hard. Lending his organizational and technical gravitas, Ron dug in with us and helped to guide our three-year-old company through our worst nightmare. He also worked with us to establish the Akamai Foundation and its focus on supporting STEM education in collaboration with the MAA. With shares in Akamai that he earned as a director, he endowed the Akamai Professor in Internet Mathematics at UC San Diego, where his wife has taught mathematics since 1998. As collaborators, Ron and Fan showed how to solve congestion on carrier networks by assigning random routes using quasirandom methods.

In The Man Who Loved Only Numbers, Paul Hoffman’s biography of Erdős, the legendary nomad who never married or settled down, Fan said of her husband, Ron: “Many mathematicians would hate to marry someone in the profession. They fear their relationship would be too competitive. In our case, not only are we both mathematicians, we both do work in the same areas. So we can understand and appreciate what the other is working on, and we can work on things together and sometimes make good progress.”

Ron contributed to a lot of progress. The world of mathematics, the field of computer science, and Akamai, are indebted to him. And we will all miss him greatly.