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 ...

, Ireland – 1 October 1924,

Oxford, Oxfordshire 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 Un ...

, 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 , mottoeng = For so much, what shall we give back? , top_free_label = , top_free = , top_free_label1 = , top_free1 = , top_free_label2 = , top_free2 = , established = , closed = , type = Public research university , parent = ...

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

Oxford University 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 ...

, 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 colleg ...

. 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 Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s. This formula was later elaborated by

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

(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 who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, and ...

(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. Life and career Marius Sophu ...

. 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 societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

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 , 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 ...

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. It is the oldest Tripos examined at the University. Origin In its classical nineteenth-century form, the tripos was a ...

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 John Maurice Hardman Campbell (1891–1973) was a British physician, cardiologist, and medical journal editor. Biography After education at Winchester College, J. Maurice Campbell studied at New College, Oxford, where he graduated with a fir ...

(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. The r ...

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