Roberts is the son of astronomer and scientist Walter Orr Roberts (a mentor to Jon Krakauer). David Roberts attended Harvard University, where he received a mathematics degree in 1965. He was a member of and former president of the Harvard Mountaineering Club where he led exploratory first ascents of many peaks in Alaska. He also received a Ph.D. in English from the University of Denver in 1970. In thirteen seasons spent in the Alaskan wilderness, Roberts is well known for many first ascents, including the Wickersham Wall on Mount McKinley, the West rib of Mount Huntington, climbing in the Western Brooks Range and the Kichatna Spires, and on the East Face of Mount Dickey. Roberts also named Alaska's Revelation Mountains, giving many of the peaks Biblical names because he had been reading the Bible as part of his English literature studies at the time.