William Leonard Edge

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Born: 8 Nov 1904 in Stockport, England
Died: 27 Sept 1997 in Bonnyrigg, Scotland

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William Edge's parents were both schoolteachers. He was educated at his local school, Stockport Grammar School, and from there he went to Cambridge where he studied mathematics at Trinity College. After graduating, he continued working for his doctorate at Trinity on projective geometry. Cambridge was at that time a centre for geometry research with Baker's school flourishing there. Edge's fellow students included P du Val and J G Semple but other famous geometers joined the group while Edge was at Cambridge including the slightly younger men H S M Coxeter and J A Todd.

After holding a fellowship at Trinity he was offered a lectureship at the University of Edinburgh by E T Whittaker which he accepted and took up the post in 1932. Edge was to spend the rest of his career at Edinburgh and David Monk, writing in [1], suggests that the reason that Edge never moved to a chair in another university was because:-

... the Scottish hills and mountains, which he loved, kept him in Edinburgh.

After studying classical geometry Edge moved towards the topic which is most associated with him, finite geometry. He had an amazing geometrical feel for complex situations as well as a skill at handling intricate combinatorial arguments which were characteristic of his work.

Edge wrote nearly 100 papers and his mastery of the area ranks him with Coxeter as one of the leading geometers of this century. His work was a continuation of work started by the great geometers of the late 19C and early 20C, in particular Castelnuovo, Cayley, Clebsch, Cremona, Fano, Fricke, Georges Humbert, Klein, Plücker and Schläfli.

Humbert discovered a plane sextic curve of genus 5 having five cusps for its singular points. These have interesting geometrical properties and Edge investigated them in a series of papers spanning 40 years. In 1890 Castelnuovo studied and classified algebraic surfaces with hyperelliptic prime sections. Edge continued and completed Castelnuovo's investigations. Castelnuovo proved that a non-ruled surface whose prime sections have genus 2 is the projection of a nonsingular rational surface of order 12 in projective 11-space. Edge explicitly examined one such projection in a paper on Castelnuovo's normal surface.

The equation of the scroll of tangents of the common curve of two quadrics is due to Cayley in 1850. Salmon, in his famous text, gave an equation in covariant form. Edge gave a procedure for finding this equation in 1979. Bring's curve was first studied in Klein's 1884 book in connection with the transformation to reduce the general quintic equation to the form x+ex+f=0. Some of Edge's work on Bring's curve extends work due to Clebsch.

Edge investigated a pencil of canonical curves of genus 6 on a del Pezzo quintic surface in a 5-dimensional projective space. He investigated the group of self-projectivities of the space, which is isomorphic to the symmetric group S. He also used geometrical configurations to investigate groups and, although his work was out of fashion at a time when group theorists were moving towards the classification of finite simple groups, his work did provide a deeper understanding of some of these groups, for example Conway's simple groups. Edge was not someone uninterested in modern techniques, however, and in a 1991 paper he included computer-drawn pictures.

Other topics Edge worked on, all of which exhibit his mastery of the subject, include nets of quadric surfaces, the geometry of the Veronese surface, Klein's quartic, Maschke's quartic surfaces, Kummer's quartic, the Kummer surface, Weddle surfaces, Fricke's octavic curve, the geometry of certain groups, finite planes and permutation representations of groups arising from geometry.

His papers are almost all written as single author papers but he did collaborate with his friends Coxeter and Du Val. In fact when he attended the celebrations for Coxeter in Toronto in 1979 it was the first time Edge had crossed the Atlantic and he said only his great friendship with Coxeter had made him overcome his reluctance to travel.

I [EFR] asked Edge a few years ago if he would come to St Andrews and give a talk on the history of mathematics. He said he knew nothing of the history of mathematics. I didn't give up that easily and asked him if he would not speak on Cayley's mathematics. 'Never met Cayley' replied Edge. He paused for a second before adding 'Knew his landlady though'.

A colleague now at St Andrews, C M Campbell, attended Edge's courses in the 1960s. He described them as difficult lectures which required a lot of work to appreciate their content but, once this work had been put in, the quality and insight in Edge's lectures became apparent. Edge taught the algebra courses at Edinburgh at this time but he taught algebra with a strong geometric flavour reflecting his deep knowledge, feel and love for geometry.

Edge had a deep concern for his students, both while they were studying at Edinburgh and after they had graduated. He kept in touch with these students in many different ways including sending his best wishes when he saw a notice of marriage in the press.

Monk [1] describes Edge's lifestyle and interests outside mathematics as follows:-

Edge never married. He lived in a succession of lodgings, carefully chosen for the quality of the cooking and space for a piano. Music was an abiding interest and he had a fine singing as well as a sonorous speaking voice.

Reference (One book/article)

References elsewhere in this archive:

William L Edge was elected an honorary member of the Edinburgh Mathematical Society in 1983. You can see a history of the EMS and a list of the honorary fellows.