William Leonard Edge FRSE (8 November 1904 – 27 September 1997) was a British mathematician most known for his work in

finite geometry Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...

. Students knew him as WLE.

Life

Born in Stockport to schoolteacher parents (his father William Henry Edge being a headmaster), Edge attended Stockport Grammar School before winning a place at

Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...

in 1923 with an entrance scholarship, later graduating MA DSc. In 1928 Trinity College made him a Research Fellow and he was also an Allen Scholar. William Edge was a

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

student of

H. F. Baker Henry Frederick Baker FRS FRSE (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as ...

at Cambridge. Edge's dissertation extended

Luigi Cremona Antonio Luigi Gaudenzio Giuseppe Cremona (7 December 1830 – 10 June 1903) was an Italian mathematician. His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. He worked on algebraic curves and alge ...

’s 1868 delineation of the

quadric In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension ''D'') in a -dimensional space, and it is de ...

ruled surface In geometry, a surface is ruled (also called a scroll) if through every point of there is a straight line that lies on . Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, t ...

s in projective 3-space RP³. Edge made a "systematic classification of the quintic and sextic ruled surfaces of three-dimensional projective space." In 1932

E. T. Whittaker Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th-century who contributed widely to applied mathema ...

invited Edge to lecture at

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

. An anachronism, Edge never drove a motor car and disdained the mass-media of radio and television; he was distressed by the decline of school geometry. In 1949 he became Reader, and professor in 1969. In the 1950s Edge began to explore

vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...

s over

Galois field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

s as an entry to

. Points and lines of finite

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, ...

arise as lines and planes in these spaces, and the projectivities of these spaces provide representation of some finite groups. For example, in 1954 he described the space ''S'' over GF(3): 40 points, 13 in each plane and 4 on each line. In ''S'' he described a 16-point quadric with two reguli of four lines each. He also extended work of Moore, Jordan and Dickson on the

alternating group In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted by or Basic pr ...

A₈ as represented by the

projective special linear group In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space ''V'' on the associat ...

PSL(4,2). The next year he parametrized the lines of the space S over GF(3) in analogy to the Klein quadric description of lines in RP³. Edge's student James Hirschfeld has advanced the science of finite geometry also. In 1934 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir

Edmund Taylor Whittaker Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th-century who contributed widely to applied mathema ...

Herbert Westren Turnbull Prof Herbert Westren Turnbull FRS FRSE LLD (31 August 1885 – 4 May 1961) was an English mathematician. From 1921 to 1950 he was Regius Professor of Mathematics at the University of St Andrews. Life He was born in the Tettenhall district, o ...

, Edward Thomas Copson and David Gibb. He won the Society's Keith Prize for 1943–45. Edge retired in 1975. A lifelong bachelor and devout Roman Catholic, Edge spent his final years in the care of the

Sisters of Nazareth The Congregation of the Sisters of Nazareth, until recently known as the Poor Sisters of Nazareth, are a Roman Catholic apostolic congregation of religious sisters of pontifical right, based in London, England. Members live in "Nazareth Houses" i ...

House in Bonnyrigg, just south of Edinburgh, and died there on 27 September 1997. Since 2013, every year the School of Mathematics of the University of Edinburgh celebrates the EDGE Days, an annual one-week workshop in algebraic geometry named after Edge.Edge Days 2020
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References

* {{DEFAULTSORT:Edge, William 1904 births 1997 deaths 20th-century British mathematicians British geometers Alumni of Trinity College, Cambridge Academics of the University of Edinburgh People from Stockport Fellows of the Royal Society of Edinburgh