by M. F. Atiyah, rev.

© Oxford University Press 2004 All rights reserved

**Hodge, Sir William Vallance Douglas** (1903-1975), mathematician, was born in Edinburgh on 17 June 1903, the younger son and second of three children of Archibald James Hodge, a searcher of property records, and his wife, Janet, daughter of William Vallance, proprietor of an Edinburgh confectionary business. He was educated from the age of six at George Watson's School, Edinburgh, proceeding in 1920 on a mathematical bursary to Edinburgh University where he graduated with first-class honours in mathematics in 1923. With a van Dunlop scholarship from Edinburgh and an exhibition from St John's College he then went to Cambridge and took part two of the mathematical tripos, as a wrangler with distinction, in 1925. He spent a further year in Cambridge supported by a Ferguson scholarship.

In 1926 Hodge went as an assistant lecturer to Bristol, where, with a helpful head of department in Professor H. R. Hasse and a stimulating and learned colleague in Peter Fraser, the next few years were very profitable. In 1929 he married Kathleen Anne, daughter of Robert Stevenson Cameron, publishing manager of the Edinburgh branch of the Oxford University Press. They had a son and a daughter.

By 1930 Hodge had taken the first steps in the direction which would rapidly establish his international reputation. In November of that year he was elected to a research fellowship at St John's College, and the following year he was awarded an 1851 Exhibition studentship. Supported in this way he was able to take up an invitation from Solomon Lefschetz, the foremost geometer and topologist of that time, to spend a year at Princeton University, accompanied by his wife. Hodge was already a firm follower of Lefschetz's mathematics and his stay at Princeton, under the influence of Lefschetz's dominant personality, propelled him further along his already chosen path. While in America Hodge also spent a couple of months at the Johns Hopkins University, Baltimore, where Oscar Zariski was the leading light in algebraic geometry.

Hodge returned to Cambridge in 1932 and was appointed to a university lectureship (1933) and fellowship (1935) at Pembroke College. In 1936, by a stroke of good fortune, H. F. Baker retired from the Lowndean chair of astronomy and geometry and Hodge, although only thirty-two, was elected as his successor.

Hodge's major achievement in mathematics was his development of the theory of harmonic integrals. This work, for which he was awarded the Adams prize in 1937, was published in definitive form in 1941. It was described by Hermann Weyl as 'one of the great landmarks in the history of science in the present century'. Essentially Hodge's work extended to higher dimensions the basic relation between the topology and analysis of algebraic functions of one variable which had been established in the nineteenth century. The passage of time has served to justify Weyl's assessment, and the theory of harmonic integrals has continued to occupy a central place in mathematics.

During the Second World War the shortage of staff in Cambridge led to Hodge's taking on the additional post of steward (or bursar) of Pembroke. This further involvement in college affairs no doubt played its part in his appointment in 1958 as master of the college, a post he held until his simultaneous retirement from the Lowndean chair in 1970.

On the national scene Hodge was, for several decades, one of the dominating mathematical figures. He was one of the founders of the British Mathematical Colloquium and was chairman of the International Congress of Mathematicians in Edinburgh in 1958. He also played an important part in the International Mathematical Union, helping to revive it after the war. Elected FRS in 1938, Hodge was the Royal Society's physical secretary from 1957 to 1965 and was involved in the move from Burlington House to Carlton House Terrace. He was awarded the royal medal of the Royal Society in 1957 and the Copley medal in 1974. He was knighted in 1959.

Hodge's standing in mathematics is indicated by the many honours he received. He held honorary degrees from the universities of Bristol (1957), Edinburgh (1958), Leicester (1959), Sheffield (1960), Exeter (1961), Wales (1961), and Liverpool (1961). He was an honorary member of several foreign academies including the USA National Academy of Sciences, and was an honorary fellow of both St John's (1964) and Pembroke (1970) colleges in Cambridge.

Despite his high offices and honours Hodge was modest and unassuming. Genial in manner and temperament, endowed with sturdy Scottish common sense, he got on well with colleagues and students. He thrived on hard work and responsibility. Hodge died on 7 July 1975 in Cambridge.

M. F. ATIYAH, *rev.*

**Sources **

M. F. Atiyah, *Memoirs FRS,* 22 (1976), 169-92

personal knowledge (1986)

*The Times* (9 July 1975), 16g

*The Times* (2 Aug 1975), 14h

*CGPLA Eng. & Wales* (1975)

**Likenesses **

Elliott & Fry, photograph, 1959, NPG *[see illus.]*

photographs, RS

**Wealth at death **

£52,320: probate, 28 Sept 1975, *CGPLA Eng. & Wales*

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