[2] In 1976, Williams became an Official Fellow, Lecturer and Director of Studies in Mathematics at Girton College,[2] positions she held until she retired in 2012.

Williams’ early research was in elementary particle physics, then during her second postdoctoral position she started working in classical general relativity.

Her particular approach, called Regge calculus, is a version of discrete gravity where curved space-times are approximated by collections of flat simplices.

To this end, and encouraged by Dusa McDuff, she started the British Women in Mathematics Day, which is now an annual event.

[12] Williams is the widow of Czech-born British mathematician, Jan Saxl, Professor of Algebra at the University of Cambridge, and they have one daughter, Miriam.