## William Edge

©Professor W. L. Edge, mathematician, died on September 27 aged 92. He was born on November 8, 1904.William Edge was one of the last survivors of the great Cambridge school of geometry founded by H. F. Baker in the earlier part of this century. It reached its high point in the 1920s, and included P. du Val, W. V. D. Hodge, T. G. Room, J. G. Semple, J. A. Todd and H. S. M. Coxeter (who still thrives).

William Leonard Edge was educated at Stockport Grammar School and Trinity College, Cambridge, from which he went to Edinburgh University in 1932. He was to remain there for the rest of his academic career, retiring in 1975.

Travelling did not appeal to him, although he did attend the conference in Toronto in 1979 celebrating Coxeter's 75th birthday. He also regularly returned to Trinity, and was even persuaded to travel to the University of Sussex on two occasions.

He published 91 research articles and one book, Ruled Surfaces , between 1932 and 1994. His writing style was always polished and the argument in every paper is traced with absolute clarity. Unusually among mathematicians, every work is his alone. He would perhaps have been surprised to know that his later works are referred to in other mathematical works more than his earlier ones.

His early work was entirely in algebraic geometry, and especially algebraic surfaces in "ordinary" space. He devoted many papers to careful exegesis of families of quadrics, that is, surfaces of degree two. In 1953 he published his first paper in finite geometry, bringing all his experience of complex geometry to bear on the elucidation of finite spaces. Such geometries now have many applications in such areas as the theory of error-correcting codes.

He was fond of maintaining that, had he ever married, his output would have been far less. He expressed a certain admiration for the monastic culture that had once prevailed among academics. In fact, he was something of a misogynist and always voted against the admission of women to Trinity.

He looked back with enormous pleasure to Baker's "tea parties", and was a fund of anecdotes concerning Cambridge men, and about Edin burgh colleagues such as Sir Edmund Whittaker and Alec Aitken.

Apart from mathematics his great loves were walking and music, and his lodgings had always to accommodate a grand piano. Together with Aitken (violin), Walter Ledermann (viola) and Robin Schlapp (violin), he formed the "mathematical quartet".

They performed in particular on the first Friday of each month that the Edinburgh Mathematical Society met. There was always a dinner for the speaker at Whittaker's house, and Whittaker, who hated small-talk, would say after dinner, "Edge, would you care to perform?"

The quartet alternated between Mozart's G minor and his E flat (his only two piano quartets), and played nothing else on these occasions. Edge was also a capable singer, and performed the solo in a Bach cantata for participants at one of the St Andrews colloquia that still take place every four years.

It was said that he was not available for university work in the early afternoon, because every day after lunch he took a bus to the Pentland Hills to walk from Pennicuik to Balerno. At some time during the Second World War, however, universities were asked to restrict their activities to daytime to avoid the blackout in the evening. At a faculty seminar, Whittaker proposed that lectures be put forward to 2pm, and asked if all agreed. "No, sir," said an indignant Edge, "a gentleman does not work in the afternoon." In later years, he did not much like it when this remark was quoted.

He was devoted to his undergraduate students, but none ever did any research with him. It was so much the custom to send any high-flyer to Cambridge for further study that Edge only ever had one research student, in 43 years.

In conversation, Edge was a Johnsonian figure. He spoke in a deep Lancashire baritone, with a very particular rhythm that did not permit interruption. His letters are a wonderful mixture of pessimism about the state of universities, analysis of other people's research articles (with reprimands for details omitted or lack of historical perspective) and warm personal affection.

Edge had a deep knowledge of classical algebraic geometry, and although he published a considerable number of works in group theory and finite geometry, it was to this that he returned. The last time that his research student paid him a visit, in March 1996, Edge upbraided him for not having solved several classical problems, which more modern algebraic geometry had also left undone. Although his hearing and sight were now weak, his mind was as sharp as ever.

© The Times, 1997