Professor Williams received his S.B., S.M, and Ph.D. in Computer Science and Electrical Engineering at MIT, and worked at the Xerox Palo Alto Research Center and NASA  Ames Research Center, prior to joining the faculty at MIT.

He received a NASA Space Act Award for Remote Agent, the first fully autonomous, self-repairing space explorer, demonstrated onboard the NASA Deep Space One probe in May, 1999.

He was a member of the Tom Young Blue Ribbon Team in 2000, assessing future Mars missions in light of the Mars Climate Orbiter and Polar Lander incidents, and is currently a member of the Advisory Council of the NASA Jet Propulsion Laboratory at Caltech.

He has won four best paper prizes for his research in diagnosis, qualitative algebras, propositional inference and soft constraints.

He is a fellow of AAAI, has served as guest editor of the Artificial Intelligence Journal and has been on the editorial boards of the Journal of Artificial Intelligence Research, and MIT Press.

He was elected as member of the Euorpean Academy of Engineering in 2021.