He served in the U.S. Navy from 1954 to 1957. While serving in the Navy, he shifted his focus to applied mathematics in operations research. Among his mathematical achievements were founding contributions to the field of integer programming, an active area of research to this day. He was Higgins lecturer and assistant professor at Princeton University, 1957-59. He joined the Research Division of IBM in 1959. In 1964 he was appointed IBM Fellow. In 1970, Gomory became Director of Research with line responsibility for IBM's Research Division. During his tenure IBM researchers made major contributions to the understanding of memory devices (Dennard Scalling), made major advances possible in high-density storage devices and produced advanced silicon processing methods. They also invented the relational database (Codd) and the RISC computer architecture. His researchers also won two successive Nobel Prizes in Physics and it was at IBM Research that Benoit Mandelbrot created the now widely accepted concept of fractals. He continued in a leadership role for the next 20 years eventually becoming IBM Senior Vice President for Science and Technology. In 1979, the book Science and Technology, A Five Year Outlook was published, collaborated with the National Academy of Sciences by W.H. Freeman and Company, with Gomory took the role of Study Chairman.