He anticipated such concepts as punctuated equilibrium (in Tempo and Mode) and dispelled the myth that the evolution of the horse was a linear process culminating in the modern Equus caballus.

He was Professor of Zoology at Columbia University, and Curator of the Department of Geology and Paleontology at the American Museum of Natural History from 1945 to 1959.

Simpson was elected to the American Philosophical Society in 1936 and the United States National Academy of Sciences in 1941.

[7] For his work, Tempo and mode in evolution, he was awarded the academy's Daniel Giraud Elliot Medal in 1944.

Simpson also received the Royal Society's Darwin Medal 'In recognition of his distinguished contributions to general evolutionary theory, based on a profound study of palaeontology, particularly of vertebrates,' in 1962.