He was born in Chicago, and attended Wheaton College, Illinois, whence he graduated in 1952. He earned a Ph.D. from Columbia University in 1957. After graduation, he taught at the University of Minnesota until 1965 when he became professor of geology at Columbia.
In 1969 Paul Gast assumed leadership of the geo-science management of the Manned Spacecraft Center in preparation for Apollo mission sample return from the Moon. He served as chief scientist of the Apollo Lunar Science Staff. He was one of the science consultant group known unofficially as the "Four Horsemen", along with Jim Arnold, Bob Walker and Gerry Wasserburg.
He died at the age of 43, being survived by his wife, Joyce Rinehart, and two sons and a daughter. During his career he pioneered the study of rare earth elements in examining the crust, mantle, and interior of the planet. He led the development of the use of rubidium-strontium and uranium-lead radiometric dating methods for rocks, particularly for samples returned from the Moon. His examinations of trace elements resulted in new understanding of how volcanic fluids originate.
He was also co-author of multiple papers on Geology.