The modern theory of the origin of the universe dates from a decade and a half after Einstein's completion of his theory of relativity. Using controversial arguments, Alexander Friedmann predicted what is now called the big bang solution to Einstein's equations, declaring that the universe emerged violently from a state of infinite compression, and is currently in the expanding aftermath of the primeval explosion.

Geoffrey Walker and his colleague H. P. Robertson then put Friedmann's arguments on a sound foundation, and the Robertson-Walker metrics, dating from the late 1930s, still form the basis of modern cosmology.

From Watford Grammar School Arthur Geoffrey Walker won a mathematics scholarship to Balliol College, Oxford, and in 1931 he took a first with distinction in differential geometry. He held the Harmsworth scholarship at Merton College from 1932 to 1934, and the university's senior mathematics scholarship in 1933. He took his doctorate in Edinburgh, where his external examiner was Sir Arthur Eddington. He also worked closely with Professor E. A. Milne during his later years at Oxford, and had great respect for Milne's ability to manipulate complicated mathematical expressions.

He was a lecturer at Imperial College, London in 1935-36 and at Liverpool, 1936-47. He was then appointed professor at Sheffield University, but returned to the Liverpool Chair of Pure Mathematics, which he held from 1952 to his retirement in 1974. He won the Junior Berwick Prize of the London Mathematical Society in 1947, and was elected president of the society for 1963-65. He was elected a Fellow of the Royal Society in 1955.

Had he been on Desert Island Discs, his one book would undoubtedly have been L. P. Eisenhart's Riemannian Geometry, which he said was the turning point of his career.

He was a very able administrator and had the happy gift of "reading down the diagonal", as he termed it. This meant that when presented with a massive document he could extract the essential features in a very short time. His colleagues had great respect for his integrity, and as a result he found himself on numerous committees which diminished his time and energy for research. In the 1950s he began a book with his pupil T. J. Willmore, and wrote the first chapter, but other duties intervened, and he persuaded Willmore to complete the book alone.

Walker was a genius at manipulation of complicated tensorial equations with a proliferation of suffixes. In his final published paper he presented his results in the modern suffix-free form to show that he could use modern notation, but it is probable that he obtained the results first by classical tensor calculus and then recast in modern notation. He was such a genius at classical tensor calculus that he felt he had no real need to master the more powerful methods of differential forms and exterior calculus which less able mathematicians are obliged to use.

A popular head of department, he will be remembered as one of the most powerful of British differential geometers, but he was also outstanding as a table-tennis player, and some proficiency at the game was sometimes said to be a necessary qualification for employment as a lecturer in Liverpool.

Unknown to most of his colleagues, he and his wife Phyllis were accomplished ballroom dancers, and he once surprised a friend by saying that he had won more prizes for dancing than he had for mathematics.

He is survived by his wife.

© The Times, 2001