Gilman attended local elementary school in White Plains. Hoping for better education, in 1955 his parents sent him to The Taft School in Watertown, Connecticut, where he completed grades 10 to 12. The school was known for its Sports activity, and he described it as "a strict, monastic, and frankly unpleasant environment in the 1950s: academic boot camp." He recalled that he was "the worst 120-pound lineman on the intramural tackle football team." He studied science at Yale University. His first research project was to test the adaptor hypothesis of Francis Crick. He worked in the laboratory of Melvin Simpson, where he met his Future wife Kathryn Hedlund. (They were married in 1963.) He graduated in 1962 receiving a BA in biology with major in biochemistry. During summer break in 1962, he briefly worked at Burroughs Wellcome & Company in New York, under with Allan Conney. With Conney he published his first two research papers in 1963. He then entered a combined MD-PhD program at Case Western Reserve University School of Medicine in Cleveland, Ohio where he wanted to study under Nobel laureate Pharmacologist Earl Sutherland, who was a close friend of his Father. It was Sutherland who had introduced the combined MD-PhD course, and invited Gilman to join course. But to Gilman, a seven-year program was like "an eternity in purgatory" and that he preferred not to have a degree in pharmacology, so he refused. Sutherland later persuaded him by explaining that pharmacology was "just biochemistry with a purpose." However, Sutherland was departing for Vanderbilt University, so Gilman studied with Sutherland's collaborator, Theodore Rall. Gilman graduated from Case Western in 1969, then did his post-doctoral studies at the National Institutes of Health with Nobel laureate Marshall Nirenberg from 1969 to 1971. Nirenberg assigned him to work on the study of nerve endings (axons from cultured neuroblastoma cells), which he considered as "a truly boring project." Instead, against the advice of Nirenberg, he worked on a new method for studying protein binding. After six weeks of working, he showed his result to Nirenberg, who immediately communicated it and get it published in 1970. The work was a simple and vital biochemical assay for studying cyclic AMP.