Born: 24 April 1929 in Troon, Scotland

Died: 26 October 2008 in Troon, Scotland

There followed a brief sojourn as a Scientific Officer in the Royal Scientific Naval Service in Cheltenham, but the attraction of the academic life proved too strong to be resisted, and in January 1956 he joined the faculty at his Alma Mater. In fact, apart from a seven year period (1966-73) at the nearby University of Stirling, and various short periods of leave (notably the Session 1958-59 spent with Al Clifford at Tulane University) he was to remain in the University of Glasgow for all of his professional life. He was appointed Thomas Muir Professor of Mathematics in 1973, holding this chair until he retired in 1996.

Douglas did his duty as a committee man, serving for four years on the Council of the London Mathematical Society and for a short period on the Council of the Royal Society of Edinburgh, and taking his turn as President of the Edinburgh Mathematical Society (1984-85). It is fair to say, however, that his heart was never really in that sort of thing, for it took him away from the two great enthusiasms of his life, pure mathematics and music. Those of us who have had the privilege of hearing him play the piano know of his skill and of how committed he was (and indeed still is) to music. All who have read his papers and heard his lectures know also of his ingenuity, of his exceptional gifts as an expositor and of his commitment to mathematics. One female mathematician, who perhaps had better remain anonymous, declared that she had fallen in love with Professor Munn long before she met him, just by reading his papers!

It is possible to discern certain phases in Douglas's mathematical output. His original interest, arising out of his Ph.D. work, was in semigroup algebras and matrix representations, though even then the work involved what might be called 'pure' semigroup theory. While that interest never entirely disappeared, it is clear that by the mid sixties he was concerned primarily with inverse and regular semigroups. The explicit description in A class of irreducible matrix representations of an arbitrary inverse semigroup (1961) of the minimum group congruence on an inverse semigroup, though foreshadowed by work of Vagner and Rees, was a major step forward, and what is now called the Munn semigroup of a semilattice opened a complete new chapter in the study of inverse semigroups. A series of papers between 1966 and 1973 exploring these ideas gave rise to results that are now regarded as classical. Then in 1974 he published his hugely influential paper on free inverse semigroups, laying the foundations of a graphical approach that is now part of the essential armoury of the modern practitioner. Throughout the seventies he continued to make crucial contributions to the understanding of regular and inverse semigroups. His discovery of Passman's books on infinite group rings brought about a further change in the main thrust of his work, and in the eighties, while still writing the occasional paper on pure semigroup theory, he returned to the study of semigroup algebras, publishing a series of remarkable papers linking semigroup properties to ring-theoretic properties of their algebras. It is clear that this phase is not yet at an end, and that we can hope for many more contributions. I would like to end with an excerpt of a letter from Norman Reilly, Douglas's first PhD student. It reveals the quality of mind and level of commitment that lies behind Douglas's achievement:-

When I entered first year at Glasgow University, I was already interested in mathematics, but just as interested in physics and chemistry. Douglas was one of my first year instructors and the contrast between his lectures and those in the other courses that I was taking was like night and day. He brought the same preparation and clarity to his undergraduate lectures then that he still demonstrates in his conference presentations. I have no doubt that that experience was an important factor in my subsequently choosing mathematics over the other sciences and for my later choice of Douglas as a supervisor.

The meticulous care with which he prepared his lectures was typical of how he approached all his tasks, especially the reading and writing of papers. Any paper that he read was considered in the minutest detail for every grain of insight that could be gleaned from it. Each of his own papers would go through many rewritings before reaching a level of presentation that he found acceptable. This was great training for a student and taught me the value of understanding papers thoroughly, not just the stated results, but also the why and the wherefore of their workings.

On visits to Troon, we would occasionally go for walks among the dunes along the front there. It seemed a great place to go when struggling with a piece of mathematics. However, he always gave me the impression that he did his best work on the train going up to Glasgow and back. I think that he did it in the margins of the Glasgow Herald!

Articles:

1. J M Howie, Walter Douglas Munn, Semigroup Forum 59 (1999) 1-7.

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