:''This English mathematician is sometimes confused with the Irish mathematician
William S. Burnside (1839–1920).''
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William Burnside (2 July 1852 – 21 August 1927) was an English
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. He is known mostly as an early researcher in the theory of
finite group
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 marked ...
s.
Burnside was born in
London
London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a majo ...
in 1852. He went to school at
Christ's Hospital
Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553. ...
until 1871 and attended
St. John's and
Pembroke Colleges 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 ...
, where he was the
Second Wrangler
At the University of Cambridge in England, a "Wrangler" is a student who gains first-class honours in the final year of the university's degree in mathematics. The highest-scoring student is the Senior Wrangler, the second highest is the Secon ...
(bracketed with
George Chrystal
George Chrystal FRSE FRS (8 March 1851 – 3 November 1911) was a Scottish mathematician. He is primarily know for his books on algebra and his studies of seiches (wave patterns in large inland bodies of water) which earned him a Gold Meda ...
) in 1875. He lectured at Cambridge for the following ten years, before being appointed professor of mathematics at the
Royal Naval College in
Greenwich
Greenwich ( , ,) is a town in south-east London, England, within the ceremonial county of Greater London. It is situated east-southeast of Charing Cross.
Greenwich is notable for its maritime history and for giving its name to the Greenwich ...
. While this was a little outside the main centres of British mathematical research, Burnside remained a very active researcher, publishing more than 150 papers in his career.
Burnside's early research was in
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
. This work was of sufficient distinction to merit his election as a fellow of the
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
in 1893, though it is little remembered today. Around the same time as his election his interests turned to the study of
finite group
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 marked ...
s. This was not a widely studied subject in
Britain
Britain most often refers to:
* The United Kingdom, a sovereign state in Europe comprising the island of Great Britain, the north-eastern part of the island of Ireland and many smaller islands
* Great Britain, the largest island in the United King ...
in the late 19th century, and it took some years for his research in this area to gain widespread recognition.
The central part of Burnside's group theory work was in the area of
group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to ...
s, where he helped to develop some of the foundational theory, complementing, and sometimes competing with, the work of
Ferdinand Georg Frobenius, who began his research in the subject during the 1890s. One of Burnside's best known contributions to group theory is his
''paqb'' theorem, which shows that every finite group whose order is divisible by fewer than three distinct primes is
solvable.
In 1897 Burnside's classic work ''Theory of Groups of Finite Order'' was published.
[ The second edition (pub. 1911) was for many decades the standard work in the field. A major difference between the editions was the inclusion of ]character theory
In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about ...
in the second.
Burnside is also remembered for the formulation of Burnside's problem
The Burnside problem asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. It was posed by William Burnside in 1902, making it one of the oldest questions in group theory and was infl ...
that concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it, and also for Burnside's lemma
Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, the orbit-counting theorem, or the Lemma that is not Burnside's, is a result in group theory that is often useful in taking account of symmetry when ...
(a formula relating the number of orbits
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
of a permutation group
In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to it ...
acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Augustin Cauchy
Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He w ...
.
He received an honorary doctorate
An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hon ...
(D.Sc.
Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...
) from the University of Dublin
The University of Dublin ( ga, Ollscoil Átha Cliath), corporately designated the Chancellor, Doctors and Masters of the University of Dublin, is a university located in Dublin, Ireland. It is the degree-awarding body for Trinity College Dubl ...
in June 1901.
In addition to his mathematical work, Burnside was a noted rower. While he was a lecturer at Cambridge, he also coached the rowing crew team. In fact, his obituary in ''The Times
''The Times'' is a British daily national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its current name on 1 January 1788. ''The Times'' and its sister paper ''The Sunday Times'' (fou ...
'' took more interest in his athletic career, calling him "one of the best known Cambridge athletes of his day".
He is buried at the West Wickham
West Wickham is an area of South East London, England, mainly within the London Borough of Bromley with some parts lying in the London Borough of Croydon. It lies south of Park Langley and Eden Park, west of Hayes and Coney Hall, north of ...
Parish Church in South London.
Books
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Notes
References
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External links
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{{DEFAULTSORT:Burnside, William
1852 births
1927 deaths
19th-century English mathematicians
20th-century English mathematicians
Group theorists
People educated at Christ's Hospital
Alumni of St John's College, Cambridge
Alumni of Pembroke College, Cambridge
Academics of the Royal Naval College, Greenwich
Royal Medal winners
Second Wranglers
Fellows of the Royal Society
De Morgan Medallists