David Williams is a Welsh mathematician who works in probability theory. He was educated at Gowerton Grammar School, winning a mathematics scholarship to Jesus College, Oxford, and went on to obtain a DPhil. He held posts at Stanford (1962–63), Durham, Cambridge (1966–69) and University College of Swansea (1969–85), where he was promoted to a personal chair in 1972. In 1985 he was elected to the Professorship of Mathematical Statistics, University of Cambridge, where he remained until 1992, serving as Director of the Statistical Laboratory between 1987 and 1991. Following this, he held the Chair of Mathematical Sciences jointly with the Mathematics and Statistics Groups at the University of Bath; he returned to Swansea in 1999, where he currently holds a Research Professorship.
Williams's research interests encompass Brownian motion, diffusions, Markov processes, martingales and Wiener–Hopf theory. Recognition for his work includes being elected Fellow of the Royal Society in 1984, where he was cited for his achievements on the construction problem for Markov chains and on path decompositions for Brownian motion, and being awarded the London Mathematical Society's Pólya Prize in 1994.