by G. H. Hardy, rev. John Bosnell

© Oxford University Press 2004 All rights reserved

**Mercer, James** (1883-1932), mathematician, was born at Bootle, Liverpool, on 15 January 1883, the son of Thomas Mercer, an accountant, and his wife, Sarah Alice Mercer. He was educated at University College, Liverpool, and at Trinity College, Cambridge, where he obtained a scholarship in 1902. He was bracketed senior wrangler with John Edensor Littlewood in 1905, was a Smith's prizeman in 1908, and was elected a fellow of Trinity in 1909. He married, in 1911, Annie, fourth daughter of William Barnes, of Walton, near Liverpool; a son survived him. After a short period of service as an assistant lecturer in Liverpool University, Mercer was recalled to Cambridge as a fellow and mathematical lecturer of Christ's College in 1912, and, up to the outbreak of war in 1914, was active in both teaching and research. During the First World War he was a naval instructor, and saw action at the battle of Jutland.

Mercer, although he wrote comparatively little, and almost all of it before he was thirty, was a mathematician of high originality and great skill, who made important advances in more than one branch of analysis. He was one of the first English mathematicians to occupy himself with the then novel theory of integral equations, to which, and to the closely related theory of orthogonal series, he contributed a number of striking theorems. One theorem in particular, concerning 'kernels' with positive eigenvalues, has become famous, and appears under his name in every treatise on the subject. A second Mercer's theorem, published in 1909, plays an important part in the modern theory of divergent series.

After the war the high hopes raised by Mercer's early mathematical work were never fully realized. He resumed his activity on his return to Cambridge, and was elected FRS in 1922, but his health, which had always been uncertain, began to fail, and led to resignation of his lecturership in 1926. He never recovered his powers, and died in St Paul's Hospital, Endell Street, London WC2, on 21 February 1932.

G. H. HARDY, *rev.* JOHN BOSNELL

**Sources **

E. W. Hobson, *Obits. FRS,* 1 (1932-5), 164-5

E. W. Hobson, *Journal of the London Mathematical Society,* 8 (1933), 79-80

private information (1949)

personal knowledge (1949)

d. cert.

*CGPLA Eng. & Wales* (1932)

**Likenesses **

W. Stoneman?, photograph, RS

photograph, repro. in Hobson, *Obits. FRS,* facing p. 164

**Wealth at death **

£8181 18s. *9d.:* resworn probate, 5 April 1932, *CGPLA Eng. & Wales*

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