David ("Taffy") Williams, mathematician, studied at the University College of Bangor, Wales, where he won an 1851 Exhibition scholarship. He was awarded the degree Bachelor of Science (BSc) by the University of London. By 1900 he was assistant to Arthur Matthews*, teaching mathematics at St Andrews College, Grahamstown. He moved to Cape Town for a few years, for in 1903 he was living in Rondebosch. However, by 1907 he was back in Grahamstown as assistant lecturer in mathematics, again under (now Professor) Matthews, at Rhodes University College. In 1912 he succeeded Matthews as professor of pure and applied mathematics, a position he held until the early nineteen-thirties. He was a lecturer of very few words, writing extensively on the blackboard in a beautifully clear hand.
Williams was admitted to the BSc degree of the University of the Cape of Good Hope in 1901 and the next year one David Williams, presumably him, passed its Survey Certificate examination. He was an examiner for the university for several years - first in mathematics and physics (1900-1902), then in physics only (1903, 1906-1909).
Williams became a member of the South African Association for the Advancement of Science in 1902. In 1907 he was elected joint honorary secretary of Section A (which included mathematics) for the association's annual congress held at Grahamstown in 1908. By 1917 he was a member also of the Royal Society of South Africa. D. Williams, presumably him, was a member of the 1921 Survey Commission.