Talmage was born to American Presbyterian missionaries in Japanese-controlled Korea. He was educated by home school and mission school until attending a boarding school in Pyongyang for secondary education. Talmage received his BS from Davidson College in 1941 and his MD from Washington University in St. Louis in 1944. From 1952 to 1959 he was Associate Professor of Medine at the University of Chicago. From 1959 he was Professor of medicine at the University of Colorado, Professor of microbiology from 1960 to 1986, and distinguished professor starting in 1986. Between 1973 and 1983 he served as director of Webb-Waring Lung Institute and as Associate Dean of Research from 1983 to 1986.