Douglas was educated at Marr College, Troon. Both his parents were artistic, but his own creative drive was to express itself in a somewhat different form and he acquired an early interest in the two disciplines that were to become his lifelong passions: mathematics and music. He studied mathematics and natural philosophy at the University of Glasgow, graduating in 1951, and went on to take a PhD at Cambridge.
After a short spell at GCHQ in Cheltenham he returned to Glasgow as a member of staff. In 1966, he became the first professor of mathematics at the new University of Stirling and was one of a small group of people entrusted with the task of designing teaching courses and setting up the necessary procedures.
Seven years later he returned to the Thomas Muir chair of mathematics at Glasgow and he remained in that post for the rest of his career.
Semigroup theory was in 1955 a relatively young branch of mathematics. There was a good deal of scope there for someone with enough mathematical insight and power to take the subject forward, and it was an area for investigation tailor-made for Douglas. He gave himself the best possible start by spending the 1958-59 session at Tulane University in Louisiana, working with AH Clifford, the most eminent figure in the field.
Following this formative experience his research gathered momentum. He went from strength to strength and by the mid-1960s he was unstoppable. From that time on each of his papers would attract a surge of interest from colleagues worldwide and they would frequently dictate the future direction for the topic under discussion. He had taken centre stage in his subject and would remain there for many years to come.
His achievements were recognised by his home university, which awarded him a DSc, and by the Royal Society of Edinburgh, which elected him to a fellowship in 1965.
Douglas's success was largely due to his possessing two quite different but complemetary qualities: creativity, and a fastidious regard for detail. Each of his papers was rewritten several times, highly crafted arguments giving way in their turn to even more highly crafted ones, until he obtained a version that satisfied him. The end result was that his published papers were always stylish, with a flawless clarity and precision that became his trademark.
It often seemed that Douglas was acquainted with every semigroup theorist in the world and that he looked on all of them as friends. Certainly, he had an impressive network of contacts, augmented on each occasion that he travelled away to lecture, and he corresponded regularly with many of them.
He was always in demand as a speaker at conferences and seminars, and a typical snapshot of one of these semigroup gatherings would show the tall figure of Douglas hemmed into a corner by people wishing to speak to him. These would often be young research students, and they would be very pleased indeed to discover that the man behind the papers was a kindly and good-natured one, with whom they were at ease, and who was interested in what they had to say.
Throughout his career Douglas played a full part in the Scottish mathematical community. He was an active member of the Edinburgh Mathematical Society and served as president in 1984-85. He was for three years the convener of the mathematics panel of the Scottish Universities Council on Entrance.
Douglas was a much-valued and highly conscientious member of the Glasgow staff. He took his teaching duties seriously and prepared all his lectures to exacting standards. A generation of Glasgow students will remember him as an excellent lecturer and dedicated teacher who was determined their mathematical education should be the finest possible and who would not settle for second best.
By his early twenties, Douglas, an accomplished pianist, had composed a selection of pieces of music for the piano. Seven of his pieces are now held in the archive of the Scottish Music Centre.
Music was an essential part of his life, just as important to him as mathematics. Neither were ever far from his thoughts and he could switch readily from one to the other. He was active in his university's music club and helped to organise its concerts; these would on occasion feature Douglas playing piano duets with his wife, Clare.
Whatever his situation, he gravitated towards musical people, being never happier than when in their company, and he served for many years as a director of St Mary's Music School in Edinburgh.
Douglas's wife, herself an acccomplished musician, survives him.
Born: 24 April, 1929, in Kilbarchan, Renfrewshire. Died: 26 October, 2008, in Troon, Ayrshire, aged 79.
12 November 2008 © Scotsman Newspapers Limited