Born in Glasgow, his early education was at Royal Belfast Academy and Queen's College, Belfast. On moving to Clare College, Cambridge in 1943, his precocious mathematical abilities were recognised and he joined the code-breakers at Bletchley Park (1943-45). After the war, a glittering educational career followed: wrangler in the Mathematical Tripos, MA (Cantab) 1948 and Smith's Prize in 1949. Two years as a Commonwealth fellow in Princeton led to a PhD under Emil Artin, after which a return to Cambridge, marriage to his wife Julie (who survives him) and a post as lecturer at Keele University in 1951. He was appointed professor at Queen's College, Dundee in 1953, and his research broadened from geometry of numbers and convex measure theory into low-dimensional topology. Discrete groups and transformation group theory formed the central core of his work, in particular Fuchsian and non-Euclidean crystallographic groups and finite group actions on Riemann surfaces, where he reactivated and modernised an area largely untouched since the days of Hurwitz and Klein. He moved in 1962 to the Mason Chair at the University of Birmingham and a taxing life as HOD from 1962 until 1979, when he migrated back to the USA to take up the chair at the University of Pittsburgh vacated by his friend Joseph Lehner. On retirement, a conference was held in his honour at Birmingham in 1992, funded by the Society. He maintained over four decades an international reputation in discrete groups and Riemann surfaces, writing seminal papers on geometry of numbers, measure theory, discrete groups and Teichmüller theory, finite group actions on surfaces and algebraic curves, over 55 publications in all, with a final contribution in 1998 to an MSRI volume The Eightfold Way on Klein's quartic curve.
Murray had a broad circle of friends within the international community, ensuring a healthy flow of postdoctoral visitors to Birmingham and lively seminars. The style and quality of his teaching enriched a generation of students at all levels, including the fortunate few postgrads (12 or more) directly supervised by him. His lectures Discontinuous groups and birational transformations from the 1961 Dundee Conference were very influential in fostering interest in finite group actions on surfaces, group presentations and the topology of 2- and 3-dimensional orbifolds. He spent several periods in visiting positions including Caltech and Pittsburgh, St. Andrews and Warwick. He will be greatly missed by all who knew him and his work.
As a postgraduate student of Murray Macbeath in Birmingham from 1962, I was privileged to gain the best possible introduction to research, with fascinating new ideas at play fostered by a friendly and encouraging supervisor. His complete honesty, lack of pretension and unfailing good humour made the transition from undergraduate to research student almost painless. His own innovative work on presentations of discrete groups blended naturally with the development of quasiconformal mappings and moduli of Riemann surfaces at that time by Lars Ahlfors, Lipman Bers and Harry Rauch; these ideas have proved inspirational to a host of researchers around the world.
Murray had a gift for friendship which enriched life among us graduate students and this together with his academic reputation drew many important visitors to the Birmingham department. He had a quietly mischievous sense of humour and a quick line of wit and aphorism delivered in his very own soft highland brogue. This never deserted him and throughout his retirement he and Julie continued to make new friends: his funeral was a standing-room-only affair. For me, with his high intelligence, kindness and innate modesty, he has been a model as mathematician and human being. An independent observer might note the lack of any formal recognition for his achievements from the British science establishment. He would smile and refer us to the bard:
For a' that, and a' thatI can see him still, at a workshop on Dessins d'enfant in Southampton in Millennium year, sitting happily with his old friend Robert Rankin and enjoying the fare: the talks, the chat and the conviviality. RIP, Murray.
Our toils obscure and a' that,
The rank is but the guinea's stamp,
The man's the gowd for a' that.
July 2014 LMS Newsletter