by E. T. Whittaker, rev. J. J. Gray

© Oxford University Press 2004 All rights reserved

**Forsyth, Andrew Russell** (1858-1942), mathematician, was born in Glasgow on 18 June 1858, the only child of John Forsyth, whose family had come from Campbeltown, and his wife, Christina Glen, of Paisley. When Forsyth was in his sixth year his mother died and in January 1868 his father, who was then engaged as a marine engineer in a Liverpool boat trading with the Mediterranean, entered him at Liverpool Collegiate Institution where he remained for eight years. In March 1875 his father died, and it was only by overcoming great financial difficulties that Forsyth was able in April 1877 to compete for the entrance scholarships at Trinity College, Cambridge, which he entered the following October. Although the Cambridge professors at the time were of unsurpassed eminence--Arthur Cayley in pure mathematics, G. G. Stokes and James Clerk Maxwell in mathematical physics, and J. C. Adams (the discoverer of Neptune) in celestial mechanics--they did not teach undergraduates, and Forsyth obtained most of his instruction from his coach, E. J. Routh. However, he had the audacity to attend a course by Cayley, where he was the only auditor under the standing of MA.

Forsyth graduated as senior wrangler and first Smith's prizeman in 1881, and in October of the same year won a Trinity fellowship with a dissertation on the theory of the double theta functions. This subject is almost incredibly rich in identities of all kinds, great numbers of which were already known: what Forsyth did was to show that practically all of them can be obtained by specialization from a single theorem of immense generality, which includes 4096 particular cases. On the basis of this theorem he developed the whole subject systematically. In October 1882 he left Cambridge to become the first professor of mathematics in the newly established University College at Liverpool; in January 1884 Trinity called him back as a college lecturer and at the end of 1885 appeared his well-known *Treatise on Differential Equations.* A number of original papers followed and in 1886, at the age of twenty-seven, he was elected a fellow of the Royal Society. By 1890 he had come to be recognized generally as the most brilliant pure mathematician in the British empire.

Forsyth had for some time realized, as no one else did, the most serious deficiency in the Cambridge school, namely its ignorance of what had been and was being done on the continent of Europe. He determined to reform this state of things, and with this aim published in 1893 his *Theory of Functions,* a book which exercised considerable influence on British mathematics. From the day of its publication, the face of Cambridge was changed: most of the pure mathematicians who took their degrees in the next twenty years became function-theorists. The subject of this book was complex function theory as it had been developed by Cauchy, Riemann, and Weierstrass. Forsyth was praised internationally for being one of the first to try to bring these three approaches together, but his way of doing this was also subject to criticism. His book was marred by numerous failures to establish analytic sense: here as later in his life Forsyth's formal skill blinded him to deeper questions. Not long after publication of his *Theory of Functions,* which despite the criticisms levelled at it secured for Forsyth a place of outstanding honour in the record of British university studies, his own reputation as a mathematician began to decline. The fact was that, although he was the initiator of the new developments, he himself belonged essentially to the old order. His special gift was a wonderful dexterity and generalship in operations involving a great number of symbols. In discovering formulae expressive of relations and identities, or structural forms invariant under transformations, he was supreme, but he arrived at his results by a combination of manipulative skill and intuition rather than by conscious logical processes, and he was not fitted by nature to excel in the types of problem which then came into fashion, such as those concerning the range of validity of equalities involving limit-processes.

In 1895 Forsyth was elected to succeed Cayley in the Sadleirian chair of pure mathematics. As head of the Cambridge school he was conspicuously successful, and many of the wranglers of the period 1894-1910 became original workers of distinction. British mathematicians were already indebted to him for the first introduction of many theories which had originated on the continent, and the importation of novelties continued to occupy his attention. A great traveller and a good linguist, he loved to meet eminent foreigners and invite them to enjoy Trinity hospitality.

In 1910 Forsyth married Marion Amelia *(d.* 1920), daughter of Henry Pollock, master of the supreme court of justice, and the recently divorced wife of C. V. Boys. He then resigned his chair and his fellowship (although this was his for life) and left Cambridge for ever. In April 1913 he was appointed to a chair in the Imperial College of Science and Technology, South Kensington, at that time an institution of comparatively recent origin, where his organizing ability did great service. His wife died in September 1920, and he retired, sooner than he needed to, in 1923. Forsyth died on 2 June 1942 at Bailey's Hotel, South Kensington, where he was living, after a long and unhappy retirement. He was cremated at Golders Green four days later.

E. T. WHITTAKER, *rev.* J. J. GRAY

**Sources **

E. T. Whittaker, *Obits. FRS,* 4 (1942-4), 209-27

personal knowledge (1959)

J. J. Gray, 'Mathematics in Cambridge and beyond', *Cambridge minds,* ed. R. Mason (1994), 86-99

*CGPLA Eng. & Wales* (1942)

**Archives **

CUL, corresp.

ICL, papers

RS, papers | BL, corresp. with Macmillans, Add. MS 55197

CUL, corresp. with Sir George Stokes, etc.

UCL, letters to Karl Pearson

**Likenesses **

Barraud, photograph, *c.1885,* RS

Maull & Fox, photograph, 1892, RS

W. Stoneman, photographs, 1917-31, NPG

Brown, Barnes & Bell, photograph, RS

photograph, repro. in Whittaker, *Obits. FRS,* facing p. 209

**Wealth at death **

£30,465 *4s. 6d.:* probate, 28 July 1942, *CGPLA Eng. & Wales*

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