John Edward Campbell

John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, 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, graduating in 1884. He then won a scholarship to study at the Oxford University, at Hertford College. 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 made his most notable contribution to mathematics in 1897 by introducing a formula for multiplication of exponentials in Lie algebras. This formula was later elaborated by Henri Poincaré (1899) and Henry Frederick Baker (1902). It was later systematised geometrically by Felix Hausdorff (1906) 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. He was elected a Fellow of the Royal Society in 1905, and served as president of the London Mathematical Society 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 to examine the Cambridge Mathematical Tripos. He was the uncle of Air Chief Marshal Sir Donald Hardman.

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