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John Campbell was educated at University College Belfast and Oxford and became a fellow in 1887. His book Lie's Theory of Finite Continuous Groups (1903) introduced Lie's ideas to British mathematicians.
Campbell is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. His research turned later to differential geometry. After a son was killed in World War I, Campbell seemed to give up mathematical research.
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John E Campbell was elected to the Royal Society of London in 1905. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.
J E Campbell was the London Mathematical Society President in 1918 - 1920. You can see a history of the LMS and a list of the presidents.
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