William Leonard Edge

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to be "eminently distinguished in their subject". ...

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

finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...

. Students knew him as WLE.

Life

Born in

Stockport Stockport is a town in Greater Manchester, England, south-east of Manchester, south-west of Ashton-under-Lyne and north of Macclesfield. The River Goyt, Rivers Goyt and River Tame, Greater Manchester, Tame merge to create the River Mersey he ...

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 Colleges of the University of Cambridge, 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 ...

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 a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

student of

H. F. Baker Henry Frederick Baker Royal Society, FRS Royal Society of Edinburgh, 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 ...

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 alg ...

’s 1868 delineation of the

quadric In mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids. More generally, a quadric hype ...

ruled surface In geometry, a Differential geometry of surfaces, surface in 3-dimensional Euclidean space is ruled (also called a scroll) if through every Point (geometry), point of , there is a straight line that lies on . Examples include the plane (mathemat ...

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 mathemat ...

invited Edge to lecture at

University of Edinburgh The University of Edinburgh (, ; abbreviated as ''Edin.'' in Post-nominal letters, post-nominals) is a Public university, public research university based in Edinburgh, Scotland. Founded by the City of Edinburgh Council, town council under th ...

. 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 (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called sc ...

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 (''p ...

arise as lines and planes in these spaces, and the projectivities of these spaces provide representation of some

finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...

s. 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 (mathematics), 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 ...

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 associa ...

PSL(4,2). The next year he parametrized the lines of the space S over GF(3) in analogy to the

Klein quadric In mathematics, the lines of a 3-dimensional projective space, ''S'', can be viewed as points of a 5-dimensional projective space, ''T''. In that 5-space, the points that represent each line in ''S'' lie on a quadric, ''Q'' known as the Klein qua ...

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 The Royal Society of Edinburgh (RSE) is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was establis ...

. His proposers were Sir Edmund Taylor Whittaker,

Herbert Westren Turnbull Herbert Westren Turnbull (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, on the outskirts of ...

, 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 House in

Bonnyrigg Bonnyrigg is a town in Midlothian, Scotland, which is southeast of Edinburgh city centre, between the Rivers North and South Esk. The town had a population of 14,663 in the 2001 census which rose to 15,677 in the 2011 census, both figures b ...

, 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