John Edward Campbell (27 May 1862,

Lisburn Lisburn ( ; ) is a city in Northern Ireland. It is southwest of Belfast city centre, on the River Lagan, which forms the boundary between County Antrim and County Down. First laid out in the 17th century by English and Welsh settlers, with t ...

, Ireland – 1 October 1924,

Oxford, Oxfordshire Oxford () is a cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the oldest university in the English-speaking world; it has buildings in every ...

, England) was a mathematician, best known for his contribution to the Baker-Campbell-Hausdorff formula.

Biography

Campbell was born in a family of a doctor, also named John Campbell. He studied first at the Methodist College in Belfast and then at

Queen's University Belfast The Queen's University of Belfast, commonly known as Queen's University Belfast (; abbreviated Queen's or QUB), is a public research university in Belfast, Northern Ireland, United Kingdom. The university received its charter in 1845 as part of ...

, graduating in 1884. He then won a scholarship to study at the

Oxford University The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...

, at

Hertford College Hertford College ( ), previously known as Magdalen Hall, is a constituent college of the University of Oxford in England. It is located on Catte Street in the centre of Oxford, directly opposite the main gate to the Bodleian Library. The colle ...

. There he won the Junior Mathematical University Scholarship in 1885, became a College Fellow in 1887, obtained a Senior Scholarship in 1888, and eventually became a tutor. Campbell was noted as a charming and highly devoted teacher and a proponent of women's education.John Edward Campbell
www-history.mcs.st-and.ac.uk Campbell made his most notable contribution to mathematics in 1897 by introducing a formula for multiplication of exponentials in

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...

s. This formula was later elaborated by

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

(1899) and Henry Frederick Baker (1902). It was later systematised geometrically by

Felix Hausdorff Felix Hausdorff ( , ; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré (''à mogré' (Fr.) = "according to my taste"), who is considered to be one of the founders of modern topology and who contributed sig ...

(1906) F. Hausdorff, "Die symbolische Exponentialformel in der Gruppentheorie", ''Ber Verh Saechs Akad Wiss Leipzig'' 58 (1906) 19–48. and became known as Baker-Campbell-Hausdorff formula. In 1903, Campbell published a book on ''Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups'' where he popularised the ideas of

Sophus Lie Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial cont ...

. He was elected 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 1905, and served as president of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

from 1918 to 1920. He was tutor to the future literary scholar C. S. Lewis in 1917, assisting Lewis with Responsions in mathematics as part of the entrance requirements for Oxford University. Campbell was the first mathematician from Oxford who was invited, shortly before his death, by the

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

to examine the

Cambridge Mathematical Tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. Origin In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate s ...

. A memorial plaque for Campbell can be seen in

St Ebbe's, Oxford St Ebbe's is a Church of England parish church in central Oxford, named after the seventh-century abbess Æbbe of Coldingham. The church is within the conservative evangelical tradition and participates in the Anglican Reform movement. It has memb ...

Personal life

Campbell married Sarah Hardman (born in Oldham ca. 1862) in the Ashton Registration District in the late 1889. They had three sons and one daughter, all born in Oxford: * John Maurice Hardman Campbell (1891–1973) *William Percy Campbell (2 May 1894 – 24 October 1914) *Patrick James Campbell (22 December 1897 – ) *Dorothea Mary Hardman Campbell (28 December 1902 – ?). William enrolled into the Oxford College in October 1913 but went to the World War I fronts the next year. He fought with the

Wiltshire Regiment The Wiltshire Regiment was a line infantry regiment of the British Army, formed in 1881 under the Childers Reforms by the amalgamation of the 62nd (Wiltshire) Regiment of Foot and the 99th Duke of Edinburgh's (Lanarkshire) Regiment of Foot. T ...

as a Second Lieutenant in the 3rd Battalion (attached 2nd Battalion) starting from October 1914 and was killed in action only a few weeks later.William Percy CAMPBELL (1894–1914)
. St Margaret's War Memorial He was the uncle of Air Chief Marshal Sir Donald Hardman.

Books

* *

References

{{DEFAULTSORT:Campbell, John Edward 1862 births 1924 deaths Fellows of Hertford College, Oxford Fellows of the Royal Society Alumni of Queen's University Belfast People educated at Methodist College Belfast 19th-century Irish mathematicians 20th-century Irish mathematicians Scientists from Belfast