Crispin Nash-Williams
   HOME

TheInfoList



OR:

Crispin St John Alvah Nash-Williams
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 letters, judged to be "eminently distinguished in their subject". This soci ...
(19 December 1932 – 20 January 2001) was a British mathematician. His research interest was in the field of
discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...
, especially
graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...
.


Biography

Nash-Williams was born on 19 December 1932 in
Cardiff, Wales Cardiff (; cy, Caerdydd ) is the capital and largest city of Wales. It forms a principal area, officially known as the City and County of Cardiff ( cy, Dinas a Sir Caerdydd, links=no), and the city is the eleventh-largest in the United Kingd ...
. His father,
Victor Erle Nash-Williams Victor Erle Nash-Williams (21 August 1897 – 15 December 1955) was a noted Welsh archaeologist. On the death of his father, Albert Henry Williams, his mother, Maude Rosetta (née Nash) Williams, formally adopted the surname "Nash-Williams". ...
( Williams), was an archaeologist at
University College Cardiff , latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1 ...
, and his mother had studied classics at
Oxford Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...
. As a small boy, Nash-Williams attended
Christ Church Cathedral School Christ Church Cathedral School is an independent preparatory school for boys in Oxford, England. It is one of three choral foundation schools in the city and educates choristers of Christ Church Cathedral, and the Chapels of Worcester College ...
in
Oxford Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...
, which was then headed by
Wilfrid Oldaker Wilfrid Horace Oldaker (13 June 1901 – 28 September 1978) was a clergyman of the Church of England, classical scholar, author, schoolmaster, Chaplain at Clifton College, Precentor of Christ Church Cathedral, Oxford, headmaster of Christ Church ...
. A biographer has said that Oldaker was a formative influence on Nash-Williams.D. J. A. Welsh
"Crispin St J. A. Nash-Williams (1932–2001)"
in ''Bulletin of the London Mathematical Society'', Vol. 35, Issue 6, November 2003, Pages 829–844
After studying mathematics at the
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
, earning the title of
Senior Wrangler The Senior Frog Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain." Specifically, it is the person who a ...
in 1953, he remained at Cambridge for his graduate studies, under the supervision of
Shaun Wylie Shaun Wylie (17 January 1913 – 2 October 2009David Rees David or Dai Rees may refer to: Entertainment * David Rees (author) (1936–1993), British children's author * Dave Rees (born 1969), American drummer for SNFU and Wheat Chiefs * David Rees (cartoonist) (born 1972), American cartoonist and televis ...
. He then continued his education for a year at
Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
, with
Norman Steenrod Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of ...
; all three of Wylie, Rees, and Steenrod are listed as the supervisors of his Ph.D. dissertation. He finished his dissertation in 1958, but before doing so he returned to Britain as an assistant lecturer at the
University of Aberdeen The University of Aberdeen ( sco, University o' 'Aiberdeen; abbreviated as ''Aberd.'' in List of post-nominal letters (United Kingdom), post-nominals; gd, Oilthigh Obar Dheathain) is a public university, public research university in Aberdeen, Sc ...
. He remained in Aberdeen for ten years, during which time he was twice promoted. In 1967 he moved to the
University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario Waterloo is a city in the Canadian province of Ontario. It is one of three cities in the Regional Municipality ...
and became one of the three faculty members in the newly formed Department of Combinatorics there. In 1972, he returned to Aberdeen University as Professor of Pure Mathematics, but stayed only briefly, moving to the
University of Reading The University of Reading is a public university in Reading, Berkshire, England. It was founded in 1892 as University College, Reading, a University of Oxford extension college. The institution received the power to grant its own degrees in 192 ...
in 1975, where succeeded Prof
Richard Rado Richard Rado FRS (28 April 1906 – 23 December 1989) was a German-born British mathematician whose research concerned combinatorics and graph theory. He was Jewish and left Germany to escape Nazi persecution. He earned two PhDs: in 1933 from th ...
, who had earlier been one of his dissertation examiners. He retired in 1996 and died on 20 January 2001, aged 68, in
Ascot, Berkshire Ascot () is a town in the Royal Borough of Windsor and Maidenhead in Berkshire, England. It is south of Windsor, east of Bracknell and west of London. It is most notable as the location of Ascot Racecourse, home of the Royal Ascot meeting, ...
, where his brother was rector.Nash-Williams biography
from the MacTutor history of mathematics archive.


Awards and honours

He was elected to the
Royal Society of Edinburgh The Royal Society of Edinburgh 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 established i ...
in 1969. In 1994, the University of Waterloo gave him an honorary doctorate for his contributions to
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...
. A conference in his honor was held on his retirement in 1996, the proceedings of which were published as a
festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the h ...
. The 18th British Combinatorial Conference, held in Sussex in July 2001, was dedicated to his memory.


Contributions

He is known for the
Nash-Williams theorem In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests) a graph can have:A graph ''G'' has ''t'' edge-disjoint spanning trees iff for every partition V ...
. Hilton. writes that "Themes running through his papers are
Hamiltonian cycle In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex ...
s, Eulerian graphs,
spanning tree In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is not ...
s, the marriage problem, detachments,
reconstruction Reconstruction may refer to: Politics, history, and sociology *Reconstruction (law), the transfer of a company's (or several companies') business to a new company *'' Perestroika'' (Russian for "reconstruction"), a late 20th century Soviet Unio ...
, and infinite graphs." In his first papers Nash-Williams considered the
knight's tour A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again im ...
and
random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
problems on infinite graphs; the latter paper included an important recurrence criterion for general
Markov chain A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...
s, and was also the first to apply electrical network techniques of Rayleigh to random walks. His dissertation, which he finished in 1958, concerned generalizations of
Euler tour In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends ...
s to infinite graphs. Welsh writes that his subsequent work defining and characterizing the
arboricity The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of spanning forests needed to cover all the edges of the graph. The Nash-Williams theorem provi ...
of graphs (discovered in parallel and independently by
W. T. Tutte William Thomas Tutte OC FRS FRSC (; 14 May 1917 – 2 May 2002) was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a majo ...
) has "had a huge impact," in part because of its implications in
matroid In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being ...
theory. Nash-Williams also studied
k-edge-connected graph In graph theory, a connected graph is -edge-connected if it remains connected whenever fewer than edges are removed. The edge-connectivity of a graph is the largest for which the graph is -edge-connected. Edge connectivity and the enumeration ...
s, Hamiltonian cycles in
dense graph In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction ...
s, versions of the
reconstruction conjecture Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to KellyKelly, P. J.A congruence theorem for trees ''Pacific J. Math.'' 7 (1957), 961–968. and Ulam.Ulam, S. M. ...
for infinite graphs, and the theory of quasi-orders. He also gave a short elegant proof of
Kruskal's tree theorem In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. History The theorem was conjectured by Andrew Vázsonyi and proved by ...
.


See also

*
List of University of Waterloo people The University of Waterloo, located in Waterloo, Ontario, Canada, is a comprehensive public university that was founded in 1957 by Drs. Gerry Hagey and Ira G. Needles. It has grown into an institution of more than 42,000 students, faculty, and ...


References


External links

* {{DEFAULTSORT:Nash-Williams, Crispin 1932 births 2001 deaths Graph theorists 20th-century British mathematicians Academics of the University of Aberdeen Academics of the University of Reading Alumni of Trinity Hall, Cambridge People educated at Rugby School Scientists from Cardiff University of Waterloo faculty Princeton University alumni