Muth earned his Ph.D. in mathematical economics from Carnegie Mellon University, and was in 1954 the first recipient of the Alexander Henderson Award. He was affiliated with Carnegie Mellon as a research associate from 1956 until 1959, as an assistant professor from 1959 to 1962, and as an associate professor without tenure from 1962 to 1964. He was a full professor at Michigan State University from 1964 to 1969 and a full professor at Indiana University from 1969 until his retirement in 1994.