Young, Alfred

(1873-1940), mathematician

by N. H. Bingham

© Oxford University Press 2004 All rights reserved

Young, Alfred (1873-1940), mathematician, was born at Birchfield, near Widnes, on 16 April 1873, the son of Edward Young, a Liverpool wine merchant, and his wife, Betsey, née Glynn. He was educated at Monkton Combe School, near Bath, from where he gained a scholarship to study mathematics at Clare College, Cambridge. He matriculated in 1892, graduated as tenth wrangler in 1895, and took part two of the mathematics tripos in 1896. After lecturing at Selwyn College, Cambridge, from 1901 to 1905 he was fellow, and later bursar, at Clare, and received the degree of ScD at Cambridge in 1908. In that year he was ordained, and he served as curate in Hastings from 1908 to 1910, when he was presented by Clare to the living at Birdbrook, Halstead, Essex. He married on 20 November 1907 Edith Clara Wilson, who survived him; they had no children.

Young published twenty-seven scientific papers, the first in 1899, and the last posthumously in 1952. All but one (on electromagnetism) were on algebra. His original interest lay in the algebraic theory of invariants, an important area of nineteenth-century mathematics aiming to study properties of geometric figures which remain unchanged by projection. His first paper was on the invariant theory of quartic curves, and this led him to write his only book (with J. H. Grace), Algebra of Invariants of 1903. This book synthesized the English work on invariants stemming from Arthur Cayley (1821-1895) with continental work by Paul Gordan and others; Young was the algebraist and Grace the geometer of the collaboration, and the book proved to be influential in its field.

In 1901 Young began the long series of papers on quantitative substitutional analysis which became his great mathematical achievement. He published nine papers in this series (the last appeared in 1952). In modern algebraic terminology, quantitative substitutional analysis relates the theory of groups (perhaps the most important area of algebra in both the nineteenth and twentieth centuries) and their representations, a subject then undergoing intense development at the hands of William Burnside (1852-1927), Frobenius, and Schur. Young's theory forms part of the representation theory of the symmetric groups Sn (the group of permutations of n objects), where his name is commemorated in the 'Young tableaux' of which the theory makes systematic use. The significance of his work was realized after the publication in 1928 of the third paper in the series, which provided the algebraic machinery needed for important parts of the new subject of quantum mechanics. In Hermann Weyl's classic book Theory of Groups and Quantum Mechanics (2nd edn, 1930) Young's work is used to study quantum numbers and the Clebsch-Gordan series, important in spectroscopy and elsewhere. His ideas have also been used in pure algebra, most notably in the work by G. James and A. Kerber, The Representation Theory of the Symmetric Group (1981), in combinatorial theory, probability, and statistics. The Collected Papers of Alfred Young, 1873-1940, edited by his pupil G. de B. Robinson, was published in 1977 by the University of Toronto Press.

Young was elected fellow of the Royal Society in 1934. Unusually for a twentieth-century mathematician, he did not make mathematics his profession. He was rector of Birdbrook from 1910 to 1940. He died on 15 December 1940 at Saffron Walden General Hospital, Essex, and was buried in the churchyard at Birdbrook, where his widow was later interred.

N. H. BINGHAM

Sources  
H. W. Turnbull, 'Alfred Young, 1873-1940', Journal of the London Mathematical Society, 16 (1941), 194-208; repr. in The Collected papers of Alfred Young, 1873-1940, ed. G. de B. Robinson (1977)
G. de B. Robinson, The representation theory of the symmetric group (1981)
G. E. Andrews, Bulletin of the American Mathematical Society, 1 (1979), 989-97
CGPLA Eng. & Wales (1941)
b. cert.
m. cert.
d. cert.

Archives  
Clare College, Cambridge, papers
University of Toronto, Thomas Fisher Rare Book Library, mathematical papers

Wealth at death  
£27,262 19s. 7d.: probate, 24 March 1941, CGPLA Eng. & Wales


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