Professor Bill Parry

11-plus-failure mathematician FRS

William Parry, mathematician: born Coventry 3 July 1934; Lecturer, Birmingham University 1960-65; Senior Lecturer in Mathematics, Sussex University 1965-68; Reader in Mathematics, Warwick University 1968-70, Professor of Mathematics 1970-99 (Emeritus); FRS 1984; married 1958 Benita Teper (one daughter): died Coventry 20 August 2006.

Bill Parry had a meagre school education but went on be an outstanding mathematician in the field of dynamical systems and a Fellow of the Royal Society. He specialised in ergodic theory, which has close connections with probability theory, statistical mechanics, number theory, differential equations and information theory.

Parry was born in Coventry in 1934, the sixth of a family of seven children. He failed his 11-plus examination and at the age of 13 went to a technical school which specialised in woodwork and metalwork but where a teacher noticed his mathematical ability and persuaded him to stay in the sixth form. Because the school was unable to provide proper tuition in mathematics, Parry was obliged to take classes at Birmingham Technical College, and, after obtaining the requisite passes, he was, despite the limitations of his schooling, admitted to University College London to study Mathematics, where he was encouraged by Hyman Kestelman.

After graduating in 1955 he did a one-year MSc course at Liverpool University before studying for his doctorate at Imperial College, London, under the guidance of Yael Dowker. His first post was as a Lecturer in the Mathematics Department at Birmingham University.

The academic year 1962-63, spent at Yale University, was very important in Parry's mathematical development because he had close contact with Shizuo Kakutani and several young American mathematicians who were working in the same area. He returned to Birmingham with an enhanced enthusiasm for mathematics and began to supervise research students.

Parry's early research work was in several areas of ergodic theory that turned out to be of major importance. He was the first to study topological Markov chains, later called subshifts of finite type, and these became significant in some coding theory problems and as models for parts of smooth dynamical systems with hyperbolic behaviour. He showed that each irreducible topological Markov chain has a unique measure of maximal entropy and these measures, which are now called Parry measures, can be described in a simple way using matrix theory.

In 1965 he moved to the newly founded Sussex University as Senior Lecturer. There he worked on entropy theory showing, amongst other things, that each aperiodic measure-preserving transformation could be viewed as the shift on the realisation space of a stationary, countable state, stochastic process indexed by the integers or the natural numbers. He moved to Warwick University, in his home city of Coventry, in the spring of 1968 and spent the remainder of his career there.

Warwick had been founded at much the same time as Sussex and had a thriving research environment through its Mathematical Research Centre, and Parry, who previously had disliked the pretensions of common rooms, was at home in the atmosphere of discussions, both mathematical and general, in the large comfortable space adorned with many large blackboards in the Mathematics Institute.

Among his contributions during these years was fundamental work on codings between symbolic systems. Sometimes the efficiency of a code is very important. For example, in the theory of computing, sentences in English need to be changed into strings of zeros and ones, and conversely strings of zeros and ones need to be translated into sentences in English, and this needs to be done as efficiently as possible. Parry was instrumental in developing a theory of different types of codings between symbolic systems.

In another area he also showed how to use ideas and techniques from analytic number theory to study the distribution of periodic orbits of dynamical systems with hyperbolic properties. He showed that an analogue of the Prime Number Theorem holds.

Over about 40 years, he trained a steady stream of excellent research students, most of whom have academic positions in Britain and other countries, and he kept a keen interest in their careers. He knew how to motivate people to do mathematics, when to cajole and when to criticise, and he had an infectious enthusiasm for beautiful mathematical constructions and theories.

He was appointed Professor at Warwick in 1970 and elected FRS in 1984. He published over 80 research papers and four books. After his retirement in 1999, he continued to teach an advanced course for a further three years and he attended seminars until a few weeks before his death.

Bill Parry's father and brothers were active trade unionists, and some members of his family were members of the Communist Party, which he joined while a student at University College. When in Liverpool he came into contact with the Socialist Labour League which, to his later regret, he joined. On the Aldermaston March in 1958 he met the love of his life, Benita, who had just arrived from South Africa, and they married later that year, urged on by Gerry Healy, who frowned on cohabiting as Bohemian. Their daughter, Rachel, was born in 1967.

Through Benita, who works in the field of postcolonial studies and whose academic career began as Bill was nearing retirement, Bill enlarged his circle of friends, participating in discussions on history, politics, philosophy, literature and art. It was his habit to work at home in his study, with Benita working in hers a short distance away. But their lives were not all earnest talk, and he and Benita always said they experienced the Sixties in the Seventies and Eighties, having spent the Sixties extricating themselves from the austerities of their previous political commitments, despite which they remained strongly and uncompromisingly socialist.

Both in Sussex and Warwick they lived in the countryside, and it was Bill's great pleasure to visit his daughter and granddaughters in North Wales. Before and after retirement he immersed himself in poetry and latterly wrote poems himself, some of which have been published.

Peter Walters