Graham was born in Taft, California, on October 31, 1935;[6] 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.[1] 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.
