Instructor, University of California, Berkeley 1961-62; Visiting Lecturer, Yale University 1962-63; Lecturer, Exeter University 1963-65; Lecturer, Newcastle University 1965-68, Reader 1968-69, Professor of Pure Mathematics 1969-2002, Head of Department 1976-83, Head, School of Mathematics 1983-86, Dean, Faculty of Science 1986-89; FRS 1978; President, London Mathematical Society 1980-82; married 1962 Jennifer Munday (two sons, one daughter; marriage dissolved 1979), 1990 Margaret Jones (née Brown; two stepsons, one stepdaughter); died Newcastle upon Tyne 5 May 2002.

Barry Johnson, Professor of Pure Mathematics at Newcastle University from 1969, was a creative mathematician of great power whose discoveries exerted an influence around the globe. In his late twenties he made his name by solving a problem of several decades' standing which many distinguished mathematicians had attempted without success, and over the next 35 years his deep and original researches made him a world leader in the field of mathematical analysis. He also played an important part in British scientific life.

He was born in 1937 in Woolwich, south-east London, moving soon afterwards to Surrey where he was educated at Epsom County Grammar School. When he was about 14 his parents moved to Tasmania and sent him to Hobart State High School, but after only two years they decided to move back to Britain. They did so, however, without their gifted son: the Headmaster in Hobart was so impressed with his pupil that he prevailed upon them to allow Barry to remain in Hobart and took it upon himself to secure Barry's entry to the University of Tasmania at an unusually early age (when he was not yet 16). Thanks to this quick start he was able to begin postgraduate study towards a doctorate in Cambridge having only just turned 21 and with his National Service behind him.

After getting his doctorate Barry Johnson spent two years at leading US universities (Berkeley and Yale), returning to a lectureship at Exeter University in 1963. In 1965 he joined a flourishing group of mathematical analysts at Newcastle University, where he remained for the rest of his career, apart from sabbatical visits overseas. He became a professor in 1969 at the age of 32.

While in America he married Jennifer Munday, whom he had met in Cambridge. The marriage took place in Reno, Nevada, in 1962. In the course of the next four years the couple had two sons and a daughter, born variously in Connecticut, Exeter and Newcastle. To his children he was a devoted father whose dedication to the life of the mind in no way prevented him taking them for bicycle rides, enjoying music or constructing elaborate wooden toys.

Johnson brought to his research an incisive mind, technical virtuosity and a great love of mathematics. Soon after his arrival in Newcastle he solved a crucial open problem in a field of analysis which was a focus of international interest at the time: he proved the uniqueness of the norm topology on a semi-simple Banach algebra.

This amounts to proving that the algebra and the geometry in a certain type of abstract mathematical structure are related in a subtle and surprising way. This was perhaps his most spectacular single achievement, but it was his profound work in the years following this early success which has had a deeper and longer-lasting influence. He was the prime mover in the development of a theory known as the cohomology of Banach algebras, which remains an essential component of present-day research in analysis.

Johnson's sharp mind, directness, force of personality and high principles could daunt even very good scientists, but these qualities were accompanied by such modesty and humanity that he inspired as much affection as respect. He threw himself heart and soul into any task he took on, whether it was Head of Department, Dean of Science or governor of the Royal Grammar School in the city. In teaching foundation-year students, of whatever aptitude, he could descend from his Olympian heights and empathise with their struggles. He never exploited his status to avoid academic chores, carrying them out with exemplary efficiency.

He was an individualist, and he respected the individuality of others to the extent that he did not attempt to build up a scientific school in Britain in the way that his talents would have permitted. To some this is a matter for regret. Early in his career, before the long squeeze on the universities, there were ample opportunities, but it was not in his nature. His researches did, however, attract a world-wide following.

Johnson was elected a Fellow of the Royal Society in 1978, and as a Fellow was involved in numerous public duties. One of these was the presidency of the London Mathematical Society (1980-82), the national learned society for mathematics. During this period there was controversy over the society's position on the holding of the quadrennial International Congress of Mathematicians in Warsaw while martial law was in force in Poland and several well-known mathematicians were political prisoners. Johnson held firmly to the view that the society was obliged to be non-political, and that protest was a matter for the individual.

Other public contributions included service on various national committees of the Royal Society and research councils. He was a member (1992) and chairman (1996) of the panel set up by the Higher Education Funding Council to assess the quality of research in pure mathematics throughout the British universities, and thereby determine the level of public funding each research unit would receive. Johnson's stature as a scientist and his absolute rectitude gave the outcome a degree of credibility and general acceptance that not all subject areas enjoyed.

His first marriage ended in separation in 1977. Some time later he met Margaret Jones and enjoyed a very happy partnership with her for the rest of his life. They married in Santa Barbara in 1990, and Margaret's three children also became very close to him.

One often meets the belief that mathematicians achieve little after they have passed 40. Barry Johnson is a refutation of this view. He continued to make significant discoveries throughout his career, even when his talents were directed more towards service to his university and the wider scientific community. In his last few years his work enjoyed another flowering. In particular, in the penultimate year of his life he published the solution of "the derivation problem for the group algebras of connected groups", a problem which had exercised him and other specialists for the preceding 35 years.

Barry Johnson's career illustrates the international character of mathematics. While based at Newcastle he had spells as a visiting professor at Yale, Los Angeles, Berkeley and Newcastle, New South Wales, and he had close scientific links with mathematicians in several other countries. His retirement conference last year drew 80 mathematicians from 15 different countries.

Nicholas Young, 17 May 2002 © Independent Digital (UK) Ltd