Ron Graham

Ronald Lewis Graham (October 31, 1935 – July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".

He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.

After graduate study at the University of California, Berkeley, Graham worked for many years at Bell Labs and later at the University of California, San Diego.

He did important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness, and many topics in mathematics are named after him.

He published six books and about 400 papers, and had nearly 200 co-authors, including many collaborative works with his wife Fan Chung and with Paul Erdős.

Graham has been featured in Ripley's Believe It or Not! for being not only "one of the world's foremost mathematicians", but also an accomplished trampolinist and juggler.

He served as president of the International Jugglers' Association.

Graham was born in Taft, California, on October 31, 1935; his father was an oil field worker and later merchant marine.

Despite Graham's later interest in gymnastics, he was small and non-athletic.

He grew up moving frequently between California and Georgia, skipping several grades of school in these moves, and never staying at any one school longer than a year.

As a teenager, he moved to Florida with his then-divorced mother, where he went to but did not finish high school.

Instead, at the age of 15 he won a Ford Foundation scholarship to the University of Chicago, where he learned gymnastics but took no mathematics courses.

After three years, when his scholarship expired, he moved to the University of California, Berkeley, officially as a student of electrical engineering but also studying number theory under Derrick Henry Lehmer, and winning a title as California state trampoline champion.

He enlisted in the United States Air Force in 1955, when he reached the age of eligibility, left Berkeley without a degree, and was stationed in Fairbanks, Alaska, where he finally completed a bachelor's degree in physics in 1959 at the University of Alaska Fairbanks.

Returning to the University of California, Berkeley for graduate study, he received his Ph.D. in mathematics in 1962.

His dissertation, supervised by Lehmer, was On Finite Sums of Rational Numbers.

While a graduate student, he supported himself by performing on trampoline in a circus, and married Nancy Young, an undergraduate mathematics student at Berkeley; they had two children.

After completing his doctorate, Graham went to work in 1962 at Bell Labs and later as Director of Information Sciences at AT&T Labs, both in New Jersey.

In 1963, at a conference in Colorado, he met the prolific Hungarian mathematician Paul Erdős (1913–1996), who became a close friend and frequent research collaborator.

Graham was chagrined to be beaten in ping-pong by Erdős, then already middle-aged; he returned to New Jersey determined to improve his game, and eventually became Bell Labs champion and won a state title in the game.

Graham later popularized the concept of the Erdős number, a measure of distance from Erdős in the collaboration network of mathematicians; his many works with Erdős include two books of open problems and Erdős's final posthumous paper.

In a 1964 paper, Graham began the study of primefree sequences by observing that there exist sequences of numbers, defined by the same recurrence relation as the Fibonacci numbers, in which none of the sequence elements is prime.

The challenge of constructing more such sequences was later taken up by Donald Knuth and others.

Graham divorced in the 1970s; in 1983 he married his Bell Labs colleague and frequent coauthor Fan Chung.

While at Bell Labs, Graham also took a position at Rutgers University as University Professor of Mathematical Sciences in 1986, and served a term as president of the American Mathematical Society from 1993 to 1994.

He became Chief Scientist of the labs in 1995.

He retired from AT&T in 1999 after 37 years of service there, and moved to the University of California, San Diego (UCSD), as the Irwin and Joan Jacobs Endowed Professor of Computer and Information Science.

At UCSD, he also became chief scientist at the California Institute for Telecommunications and Information Technology.

In 2003–04, he was president of the Mathematical Association of America.

A proof was published by Ernie Croot in 2003.

Another of Graham's papers on Egyptian fractions was published in 2015 with Steve Butler and (nearly 20 years posthumously) Erdős; it was the last of Erdős's papers to be published, making Butler his 512th coauthor.

Graham died of bronchiectasis on July 6, 2020, aged 84, in La Jolla, California.

Graham made important contributions in multiple areas of mathematics and theoretical computer science.

He published about 400 papers, a quarter of those with Chung, and six books, including Concrete Mathematics with Donald Knuth and Oren Patashnik.

The Erdős Number Project lists him as having nearly 200 coauthors.

He was the doctoral advisor of nine students, one each at the City University of New York and Rutgers University while he was at Bell Labs, and seven at UC San Diego.

Notable topics in mathematics named after Graham include the Erdős–Graham problem on Egyptian fractions, the Graham–Rothschild theorem in the Ramsey theory of parameter words and Graham's number derived from it, the Graham–Pollak theorem and Graham's pebbling conjecture in graph theory, the Coffman–Graham algorithm for approximate scheduling and graph drawing, and the Graham scan algorithm for convex hulls.

He also began the study of primefree sequences, the Boolean Pythagorean triples problem, the biggest little polygon, and square packing in a square.

Graham was one of the contributors to the publications of G. W. Peck, a pseudonymous mathematical collaboration named for the initials of its members, with Graham as the "G".

Graham's doctoral dissertation was in number theory, on Egyptian fractions, as is the Erdős–Graham problem on whether, for every partition of the integers into finitely many classes, one of these classes has a finite subclass whose reciprocals sum to one.