Hoover received a B.A. from Wellesley College in classical and medieval philosophy and history in 1948. After graduating with honors in 1948, she was inducted into Phi Beta Kappa, an honor society of liberal arts and sciences, and was honored as a Durant Scholar. She obtained a Ph.D. from Yale University in philosophy and foundations of mathematics in 1951. She was a professor in Swarthmore College from 1951 to 1954. Upon marrying her husband, Hoover found it difficult to secure a tenure track position, so she joined Bell Labs. Later, she worked on the development of the Safeguard Anti-Ballistic Missile System and subsequently became the first woman to head a technical department in 1978. She spent the next decade working on software applications with a particular focus on Artificial Intelligence (AI) and IMS-IBM/Unix based system communications. In 1987, after three decades of dedication to improving telecommunications as we know it, Dr. Hoover retired.