Barry Johnson's father was an engineer whose first jobs used his skill as a toolmaker then later he became a planning engineer. Barry's mother was a secretary at Warner Brothers. Barry was the oldest of his parents three children, having one younger brother and a younger adopted sister. He was educated at Epsom County Grammar School in Surrey, England, and then at Hobart State High School in Tasmania after the family moved there in 1951. After his family returned to England, Johnson remained at Hobart High School since the headmaster had told them of his :-
... exceptional high all-round intelligence
persuading him to remain there to study for a place at university.
Although only 16 years of age, he won an entrance scholarship to the University of Tasmania in March 1954. He entered the University of Tasmania, living with a :-
... kind family, but with little spare cash for clothing or luxuries.
Johnson studied mathematics as his main subject but he was also extremely successful in his subsidiary subjects of physics and chemistry, winning a prize from the Royal Australian Chemical Institute. During the university vacations he undertook National Service so that he was exempted from the otherwise compulsory military service when he returned to England. He was awarded a B.Sc. with First Class Honours from the University of Tasmania in 1956. Peter Sprent, who taught him during his undergraduate years, writes :-
Few students have ever inspired their lecturers as did Barry Johnson at the University of Tasmania in the 1950s. It was then the practice in the mathematics department to encourage honours students to give seminars for fellow students and lecturers. Johnson's contribution to these, as well as his penetrating and challenging (but never aggressive) questioning of views expressed in lectures left no doubt among his teachers that we were contributing in a modest way to the training of a mathematical giant. A small incident that epitomises this remains fresh in my memory. Berated by colleagues for having set too hard an examination paper, my defences crumbled when a senior colleague's response to my request to justify the charge was: "Of course, it was. Barry Johnson only got 98 per cent." I pleaded guilty.
In order to undertake research in pure mathematics Johnson returned to England but he first taught at a grammar school in Tamworth before he began research in functional analysis at Gonville and Caius College of the University of Cambridge in October 1958. He held a Rhondda Memorial Scolarship at Cambridge where his postgraduate studies were supervised by John Williamson. Johnson later wrote:-
This was probably the luckiest thing that happened to me because I was supervised by Professor J H Williamson who had a remarkable record as a supervisor. I met a number of research students who now have university teaching positions and also gained a lot of experience of life to transform me from a very dull bookish type to a more socially acceptable individual.
Johnson completed his doctorate in 1961 with a thesis Centralisers in topological algebras. The work studies, in particular, algebras whose left and right structures are very different. He was then appointed as an instructor in mathematics at the University of California at Berkeley spending the year 1961-62 at Berkeley. He remained in the United States in the following year, spending 1962-63 as a visiting lecturer at Yale University. While in the United States Johnson married Jennifer Munday in Reno. The couple had met in Cambridge and they had one daughter and two sons. The newly married couple returned to England in 1963 when Johnson was appointed as a lecturer in mathematics at the University of Exeter. After two years at Exeter, he was appointed as a lecturer in mathematics at the University of Newcastle-upon-Tyne. Promoted to Reader at Newcastle in 1968, he became Professor of Pure Mathematics in the following year :-
Barry enjoyed lecturing at all levels from service teaching, even first year agriculture students, to postgraduate students and would initially describe himself to total outsiders as a 'teacher'.
Johnson spent the year 1970-71 as a visiting professor at Yale University. In 1976 he became Head of the Department of Pure Mathematics at Newcastle and in the following year he was separated from his wife. Soon after this he met Margaret Jones who had three children from a previous marriage; they married in Santa Barbara in 1991. This was during a year in which Johnson was visiting professor at the University of California at Los Angelos, at Santa Barbara, and at Berkeley.
In 1978 Johnson was honoured by being elected a fellow of the Royal Society of London. He served as Head of the School of Mathematics at Newcastle from 1983 to 1986 and then he became Dean of the Faculty of Science, holding this office from 1986 until 1989. He visited the United States again in the academic year 1990-91 as we mentioned above.
Johnson served the London Mathematical Society as a member of the Council during 1975-78, then as the 60th president of the Society in 1980-82. This was a particularly difficult period to hold the presidency since the International Congress of Mathematicians was held in Warsaw during a time of great political tension. Johnson firmly believed, however, that the London Mathematical Society must remain totally non-political and that members of the Society could express their political views only as individuals. He also served the London Mathematical Society as editor of their Newsletter for four years. In 1993 he was appointed as auditor for the Higher Education Quality Control Council in the Division of Quality Audit. This Council rates the teaching quality of the universities in England. Johnson was a governor of the Royal Grammar School in Newcastle from 1987. He was a member of the Pure Mathematics Research Assessment Exercise panel in 1992 and was chair of the panel in the next exercise which took place four years later.
Johnson is well known for his work on Banach algebras and operator algebras, in particular, studying cohomology in these algebras. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. In these he examined the theory of centralizers and the continuity of transformations. In 1964 he wrote a joint paper with Ringrose Derivations of operator algebras and discrete group algebras and his next papers continued to examine the continuity of homomorphisms, derivations and linear operators.
In 1972 Johnson wrote a joint paper with Ringrose and Kadison on cohomology of operator algebras and in the same year his book Cohomology in Banach algebras (1972) appeared. We mentioned above that Johnson was President of the London Mathematical Society during 1980-82. His presidential address to the Society was on Noncommutative generalisations in mathematics which reported on progress in using ideas from commutative operator theory and applying them to the noncommutative case. Particularly, he reported on applications to noncommutative algebraic topology, noncommutative integration and noncommutative dynamical systems.
In later work on group algebras both for semisimple Lie groups and more general groups, he showed that every derivation is inner.
His way of doing mathematics is described in  as follows:-
Barry Johnson was a highly influential pure mathematician. He liked to work alone, often sitting at home in an armchair with pencil and clipboard, but the theorems he brought to life sometimes had worldwide influence.
His interests are described in :-
Barry was a voracious reader, reading anything and everything: histories, biographies, novels, and travel books. The other important thing in his life was walking regularly. He walked through many of his mathematical problems, and in any crisis would go off alone and walk. Barry also liked listening to music and doing his own repairs and alterations to their house and their cottage on the Scottish borders.
He developed cancer on February 2000 and fought the disease bravely. Despite his deteriorating physical condition, he continued to undertake cutting edge mathematical research. He died of cancer in St Oswald's Hospital in Newcastle upon Tyne aged 64.
Article by: J J O'Connor and E F Robertson