Whittaker, Sir Edmund Taylor

(1873-1956), mathematician and astronomer

by G. Temple, rev. I. Grattan-Guinness

© Oxford University Press 2004 All rights reserved

Whittaker, Sir Edmund Taylor (1873-1956), mathematician and astronomer, was born at 7 Virginia Street, Southport, on 24 October 1873, the only son of John Whittaker, gentleman, and his wife, Selina Septima, daughter of Edmund Taylor, who practised as a physician at Middleton, near Manchester. Whittaker was taught by his mother up to the age of eleven, when he entered Manchester grammar school on the classical side, but on promotion to the upper school he gladly escaped to specialize in mathematics. In 1892 a scholarship took him to Trinity College, Cambridge, where in 1895 he was bracketed second wrangler; he obtained a first class in part two of the tripos, and the Tyson medal, was elected a fellow of Trinity (1896), and was awarded the first Smith's prize (1897). In 1901 he married Mary Ferguson McNaghten, daughter of the Revd Thomas Boyd, of Cambridge, Scottish secretary of the Religious Tract Society; and granddaughter of Sir Thomas Jamieson Boyd. They had three sons and two daughters. Their second son, John McNaghten Whittaker (Jack), was professor of pure mathematics at Liverpool (1933-52) and vice-chancellor of the University of Sheffield (1952-65).

Astronomy professorships
In 1906 Whittaker was appointed professor of astronomy in the University of Dublin, with the title of royal astronomer of Ireland. The observatory at Dunsink was poorly equipped, and it was tacitly understood that the chief function of the professor was to strengthen the school of mathematical physics in the university, where Whittaker gave courses of advanced lectures. Some of his pupils were members of other academic foundations, among them éamon de Valera, later prime minister and president of Ireland.

In 1912 Whittaker was elected to the professorship of mathematics at Edinburgh where he taught until his retirement in 1946. His personal achievements included the institution in 1914 of what was probably the first university mathematical laboratory in Britain, the establishment of a flourishing research school, and the development of the Edinburgh Mathematical Society.

Whittaker made numerous and important contributions to mathematics and theoretical physics which had a profound effect by reason of their great range, depth, and fertility; but these were rivalled, if not surpassed, in interest, importance, and influence by his scientific books and monographs. In addition he wrote numerous philosophical and historical papers and books, which all bear the marks of his learning, literary powers, and critical judgement.

Whittaker's contributions to pure mathematics were mainly to the theories of interpolation, of automorphic functions, of potential theory, and of special functions. His interest in the theory of interpolation arose from his association with the actuaries engaged in life assurance in Edinburgh, especially G. J. Lidstone. He succeeded in solving two fundamental questions and thus provided a logical basis for the Newton-Gauss formula and for the method of the graduation or adjustment of observations. In the theory of automorphic functions he solved the problem of the uniformization of algebraic functions of any genus by considering a special discontinuous subgroup of elliptic transformations each of period 2.

Contributions to mathematical physics
The most significant section of Whittaker's researches, however, relates to the special functions of mathematical physics regarded as constituents of potential functions. He obtained a general solution of Laplace's equation which brought a new unity into potential theory by exhibiting all the usual special functions in the form of a 'Whittaker' integral, and he also introduced the important confluent hypergeometric functions. In theoretical physics he made substantial contributions to dynamics, to relativity and electromagnetic theory, and to quantum theory. In dynamics his discovery of the 'adelphic' integral provided the solution of the difficulties indicated by Poincaré's celebrated theorem relative to the convergence of the series solutions of celestial mechanics. In electromagnetic theory he gave a general solution of Maxwell's equations in terms of two real scalar wave functions, and gave a relativistic generalization of Faraday's theory of tubes of force. In general relativity he investigated the problem of giving an invariant definition of distance which should correspond to the actual procedure adopted by astronomers, and he obtained a generalization of Gauss's theorem on the Newtonian potential. In his researches on quantum theory he generalized Hamilton's 'principal functions', expressing them in terms of non-commutating variables, and thus obtained a new foundation for Schrödinger's wave equation.

In 1905 Whittaker co-founded the series of Cambridge Tracts in Mathematics and Mathematical Physics, an influential series of short volumes designed to introduce the principal elements of specific modern developments. His own contribution was The Theory of Optical Instruments (1907), which was later translated into German. Three of Whittaker's scientific books have had a great influence. A Course of Modern Analysis, published in 1902, and in many subsequent editions with the collaboration of G. N. Watson, remained in print throughout the century. It was the first, and for many years almost the only, book in English to provide students with an account of methods in mathematical analysis and mathematical physics. The Treatise on the Analytical Dynamics of Particles and Rigid Bodies (1904) remains the standard work on this subject. The Calculus of Observations (1924, with G. Robinson; 4th edn, 1944) brought together many techniques in numerical analytical analysis, together with the practical work effected in his laboratory.

Whittaker's monumental History of the Theories of Aether and Electricity was first published in one volume in 1910 and subsequently in a greatly enlarged edition of which Whittaker lived to complete only two volumes (1951-3). The History provides a systematic and critical account of the development of the physical theories of electromagnetism, atomic structure, and of the quantum theory from the seventeenth century to 1926. It will remain an outstanding achievement by reason of its clarity, comprehensiveness, and penetration, which give it the force and authority of an original investigation, although Whittaker was criticized for attributing special relativity theory to Henri Poincaré and Hendrik Lorentz rather than to Albert Einstein.

Whittaker also wrote historical articles of various kinds--for example, several fine obituaries for the Royal Society, and uncommonly good centenary articles on the appropriate occasion for major figures of the past such as W. R. Hamilton and Laplace. In 1899 he brought the British Association for the Advancement of Science nicely up to date on the three-body problem in celestial mechanics, and in 1912 he wrote the article on the theory of planetary perturbations for the great German Enzyklopädie der mathematischen Wissenschaften.

Scientific honours
Whittaker, who was knighted in 1945, was elected FRS in 1905, served on the council in 1911-12 and 1933-5 (vice-president 1934-5), and was awarded the Sylvester medal in 1931 and the Copley medal in 1954. With the Royal Society of Edinburgh he had continuous contact, being Gunning prizeman in 1929 and president in 1939-44. He was president of the Mathematical Association (1920-21), of the mathematical and physical section of the British Association (1927), and of the London Mathematical Society (1928-9), being awarded its De Morgan medal in 1935. An honorary member of a number of foreign learned societies, he received honorary degrees from several universities, and was an honorary fellow of Trinity College, Cambridge (1949).

At Cambridge in his Tarner lectures (1947) Whittaker lucidly traced the development of natural philosophy from Euclid to Eddington, and in 1951 he gave the Eddington memorial lecture, 'Eddington's principle in the philosophy of science'. At Oxford he gave the Herbert Spencer lecture (1948), 'The modern approach to Descartes's problem'. He figured as a natural theologian in his Riddell memorial lectures (Durham, 1942) on 'The beginning and end of the world' and in the Donnellan lectures (Dublin, 1946) on 'Space and spirit' in which he restated the classical scholastic arguments for the existence of God in the light of current theories of scientific cosmogony.

Whittaker was received into the Roman Catholic church in 1930. He served as honorary president of the Newman Association (1943-5), was awarded the cross Pro Ecclesia et Pontifice in 1935, and was appointed a member of the Pontifical Academy of Sciences in 1936. He died at his home, 48 George Square, Edinburgh, on 24 March 1956.

Whittaker's death marked the end of an epoch, for he was conversant with a range of mathematics which no other Briton has encompassed. His pervasive influence in mathematics is seen in his peculiar facility for coining names for analytical concepts and entities, many of which have obtained a wide currency in the language of mathematics. That influence was mainly the effect of his amazing intellectual powers but it was reinforced by his never-failing kindness to his students, the hospitality offered in his Edinburgh home, his slightly mischievous humour, and the devotion and support of his wife.

G. TEMPLE, rev. I. GRATTAN-GUINNESS

Sources  
G. Temple, Memoirs FRS, 2 (1956), 299-325
W. H. McCrea, Journal of the London Mathematical Society, 32 (1957), 234-56
'Memorial issue', Proceedings of the Edinburgh Mathematical Society, 11 (1958-9), 1-70
The Times (26 March 1956), 14c
Biographical register of old Mancunians (1965), 80
b. cert.
CGPLA Eng. & Wales (1956)
personal knowledge (1971)
private information (1971)

Archives  
RS, corresp. and papers |  ICL, corresp. with Herbert Dingle
L. Cong., corresp. with O. Veblen
NRA, priv. coll., corresp. with J. M. Whittaker
Nuffield Oxf., corresp. with Viscount Cherwell
RAS, letters to Royal Astronomical Society

Likenesses  
T. Haddon, oils, 1933, NPG [see illus.]
W. Stoneman, photograph, 1933, NPG
B. Schotz, bronze head, c.1944, Royal Society of Edinburgh
photograph, repro. in The Times

Wealth at death  
£20,023 6s. 11d.: probate, 2 July 1956, CGPLA Eng. & Wales


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