Wall had already been awarded a fellowship at Trinity College in 1959 before the award of his doctorate and he held this fellowship until 1964. He did not remain in Cambridge for all of this period, for instance he was awarded a Harkness Fellowship which allowed him to spend the academic year 1960-61 at the Institute for Advanced Study at Princeton. In addition to his fellowship, Wall was appointed a College Lecturer at Cambridge when he returned from the United States in 1961.
In 1964 Wall moved from Cambridge to Oxford where he was appointed Reader in Mathematics and a fellow of St Catherine's College. After a year he was appointed to the chair of Pure Mathematics at the University of Liverpool, taking up the professorship in Liverpool in 1965. During 1967 was a Royal Society Leverhulme visiting professor in Mexico. A SERC senior research fellowship from 1983 to 1988 enabled him to concentrate on research over this period.
Wall's research is mostly in the area of geometric topology and related algebra. In particular he has made substantial contributions to the study of singularities, especially isolated singularities, of differentiable maps and algebraic varieties. He has written a number of highly influential books including Surgery on compact manifolds (1970) and A geometric introduction to topology (1972). This latter work is an introduction to algebraic topology for a reader without background in general topology. The book builds up to a proof of the Alexander duality theorem in the plane; a result which generalises the Jordan curve theorem.
In 1995 Wall published The geometry of topological stability written jointly with A A du Plessis. His current research continues the studies of applications of techniques developed in this book which is having spin-offs to results about hypersurfaces in projective space. To date he has published over 160 research articles on mathematical topics.
Wall's work has led to him receiving many awards. He was elected a fellow of the Royal Society in 1969 and the Royal Society has honoured him further with the award of its Sylvester Medal in 1988. He was a member of the Council of the Royal Society from 1974 to 1976.
He has served the London Mathematical Society in many ways over a large number of years being on the Council from 1972 to 1980 and then for a second spell from 1992 to 1996. He served as the 59th President of the London Mathematical Society from 1978-80. The Society has made him a number of awards to mark his fine mathematical achievements, including the award of their Junior Berwick Prize, their Whitehead Prize in 1976 and their Pólya Prize in 1988. The Whitehead Prize and the Pólya Prize were awarded for his work on surgery on manifolds and L-theory. In 1990 Wall was elected a foreign member of the Royal Danish Academy of Sciences.
In 2000 he was elected an honorary member of the Irish Mathematical Society.
Wall retired in 1999 and was made Emeritus Professor at the University of Liverpool. At the same time he was appointed Senior Fellow at the University of Liverpool, a position he held until 2003. Retirement certainly did not mean that Wall was less in demand as a plenary speaker at international conferences. He was a main speaker at the conference 'Singularity theory' held in Sao Carlos, Brazil in 1994 and was then asked again to be a main speaker at this 'Singularity theory' conference in 2000, 2002, 2006, and 2008. He was also a main speaker at the 'Singularity theory' conference held in Sapporo, Japan in 2003. Wall continues to publish important research articles, and an outstanding book Singular points of plane curves in 2004. Cícero Fernandes de Carvalho writes in a review:-
Although important results about singularities of algebraic curves may be traced back to Newton, this field's more steady development only gained momentum in the late nineteenth century, with the results of Max Noether on the resolution of singularities. A short time after that, another important contribution appeared in the work of Karl Brauner on the fundamental group of the complement of a link in the 3-sphere, in the beginning of the twentieth century. From then on, a growing interplay between the fields of topology and algebra contributed to a deeper understanding of singularities. This interaction, and many of its results, are fully exposed and explained in the book under review. ... In this reviewer's belief this is an excellent textbook for a graduate course on singularities of plane curves, and certainly is another most valuable contribution from the author.Outside mathematics Wall has many interests including home wine making, reading, gardening, walking and an interest in politics which has seen him as treasurer of the Wirral Area SDP from 1985 to 1988. He then became a member of the Wirral West Liberal Democrat Party. From 1987 he has been a Governor of West Kirby Grammar School for girls, and from 2000 he has been Treasurer of Hoylake Chamber Concert Society.
Article by: J J O'Connor and E F Robertson