Professor **Barry Johnson**, FRS, mathematician, was born on August 1, 1937. He died of cancer on May 5, 2002, aged 64.

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.

Born in Woolwich in 1937, Barry Edward Johnson was the son of an engineer, and the eldest of two brothers and an adopted sister. In 1951 the family moved to Tasmania, but when they planned to return to England the following February the headmaster of Hobart High School, noting Johnson's "exceptional high all-round intelligence", persuaded his father that Johnson should remain to go to university.

He gained an entrance scholarship to the University of Tasmania in March 1954 at the age of 16 1/2. The student was left in the care of a kind family, but with little spare cash for clothing or luxuries.

His major subject was mathematics, but he also studied physics and chemistry, and was awarded a prize by the Royal Australian Chemical Institute. He graduated with a first, and was encouraged to return to England to read pure mathematics at Cambridge.

Accepted by Gonville and Caius College, he started his research at the age of 21, and it was at this point that he chose the subject that was to become his life's work: functional analysis, an abstract form of classical analysis which studies spaces of functions, rather than individual ones, and infinite-dimensional generalisations of algebras of matrices, the latter being the natural setting in which to express our understanding of modern mathematical physics.

After gaining his doctorate in 1961, Johnson spent two years in America where he came into contact with leading functional analysts, who introduced him to the uniqueness-of-norm prob-lem for semisimple Banach algebras. A Banach algebra is an abstract mathematical object that has both algebraic and topological aspects. By definition, these aspects are loosely connected, and the problem is to prove they are tightly connected.

In 1962 Johnson married Jennifer Munday, whom he had met in Cambridge, and they returned to Britain in 1963, where he taught at Exeter University and then, from 1965, at Newcastle upon Tyne, where he remained until his retirement last year.

His work surged forward in Newcastle. First he found a solution to the uniqueness-of-norm problem, which became the seed for the growth of the now extensive automatic continuity theory. Johnson also quickly resolved several other important problems, some with his first, brilliant research student, Allan Sinclair, who is now a professor at Edinburgh.

Rapidly promoted, Johnson became a professor at the age of only 32. He was head of pure mathematics, 1976-84, head of the school of mathematics, 1983-86, and Dean of the Faculty of Sciences, 1986-89. In the 1970s he produced ground-breaking work on the cohomology of Banach algebras, a deep theory that classifies both general and specific classes of algebras. The concept of an "amenable" Banach algebra, which he introduced, was probably his single most influential innovation.

One manifestation of his influence was seen in a sequence of international conferences on Banach algebras held all over the world, at which his latest theorems were studied with excitement.

Johnson was elected a Fellow of the Royal Society in 1978, served as president of the London Mathematical Society 1980-82, and acted as chairman of the Pure Mathematics Panel for the research assessment exercise of 1996.

His marriage to Jennifer Munday was dissolved in 1979. In 1990 he married Margaret Jones (nee Brown). She survives him, along with two sons and a daughter from his first marriage, and by a stepdaughter and two stepsons.

Copyright © The Times, 2002

Peter Sprent, Emeritus Professor of Mathematics at the University of Dundee, writes: Few students have ever inspired their lecturers as did Barry Johnson (obituary, July 31) 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.

Copyright © The Times, 2002