David Williams FRS 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 under the supervision of David George Kendall and Gerd Edzard Harry Reuter, with a thesis titled Random time substitution in Markov chains.

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,[3] and being awarded the London Mathematical Society's Pólya Prize in 1994.

[4] One of his main discoveries is the decomposition of Brownian paths with respect to their maximum.