[2] Williams received his bachelor's degree from Princeton University in 1955 and on Martin Summerfield's advice, he moved to California Institute of Technology to pursue his PhD, graduating it in 1958 under the supervision of Sol Penner, with Richard Feynman on the thesis committee.

[4] After finishing his PhD, Williams worked in the Division of Engineering and Applied Physics at Harvard University until 1964, after which he joined the faculty at UCSD.

He was the fourth faculty member to be appointed, when Sol Penner founded the Engineering department in University of California, San Diego.

Though Activation Energy Asymptotics were known to Russian scientists forty years ago, it was Williams' call in 1971 in Annual Review of Fluid Mechanics[7] which made the western scientific community to start using the analysis.

[21] He was a member of the National Construction Safety Team Advisory Committee in reporting the Collapse of the World Trade Center.

[22][23] Some of his awards include: A conference titled Symposium on Advancements in Combustion Theory was conducted at UCSD in 2004 in honor of Williams 70th birthday.