Boyd received an undergraduate degree in mathematics and physics from Smith College, Northampton, Mass., in 1945. She received a doctoral degree in mathematics in 1949 from Yale University, New Haven, Connecticut, where she studied under Einar Hille. She was the second African American woman to receive a doctorate in mathematics. From 1949 to 1950 she had a postdoctoral fellowship at New York University, and from 1950 to 1952 she was an associate professor of mathematics at Fisk University, Nashville, Tennessee.
In 1952 Boyd became a mathematician at the National Bureau of Standards (NBS) in Washington, D.C., where she worked on missile fuses. Her division of NBS was later absorbed by the United States Army and became the Diamond Ordnance Fuze Laboratories. There she became interested in the new field of computer programming, which led her to the corporation International Business Machines (IBM) in 1956. She worked on programs in the assembly language SOAP and later in FORTRAN for t