George Neville Watson, Sc.D. (Cantab.), Hon.LL.D. (Edin.), Hon.Sc.D. (Dub.), F.R.S., Hon.F.R.S.E.

by R A Rankin

George Neville Watson was born on January 3 1, 1886, at Westward Ho! in Devon, and died in Leamington Spa on February 2, 1965. He was educated at St Paul's School, London, and at Trinity College, Cambridge, where he held a Major Scholarship. In 1907 he was classed as Senior Wrangler in Part I of the Mathematical Tripos and he obtained First Class Honours in Part II of that Tripos the following year. In 1910 he became a Fellow of Trinity College and held his Fellowship until 1916. However, in 1914, he went to University College, London, as an Assistant Lecturer and was promoted to an Assistant Professorship the following year.

Professor R S Heath, who was the first Professor of Mathematics in Birmingham University, retired in 1918 and Watson was asked to succeed him. He remained in Birmingham from 1918 until his retirement at the age of sixty-five in 1951. In 1925 he married Elfrida (Freda) Gwenfil Lane, the daughter of the late Thomas Wright Lane.

For his outstanding contributions to mathematics Watson received awards from many societies and institutions. In 1912 the Royal Danish Academy presented him with their Gold Medal and in 1946 he received the Sylvester Medal of the Royal Society of London, of which he was elected a Fellow in 1919. In 1947 he was awarded the De Morgan Medal of the London Mathematical Society of which he had been successively Honorary Secretary, Honorary Editor and President.

He had a great admiration for his friend and co-author, the late Sir Edmund Whittaker, but, although he doubtless received several invitations, he only visited Scotland twice, once in June 1939 to receive his Honorary LL.D. from Edinburgh University, and in July 1914 to attend the Napier Tercentenary Congress. He used to say that he feared to make a third visit (and this no doubt explains why he was not admitted in person to his Honorary Fellowship of this Society in 1949), as each of his two previous visits had precipitated a major European catastrophe.

Watson's mathematical publications consist of over one hundred and fifty papers and three books. Of the latter the best known is the treatise entitled Modern analysis, which is extensively used both by students and research workers, and is known affectionately as W and W. The first edition of this work appeared in 1902, the sole author being the late Sir Edmund Whittaker; it rapidly made a name for itself. The first half contained an account of the methods and processes of analysis, and these were applied, in the second half, to obtain the principal properties of the special functions used in mathematics and its applications. Watson was a friend and former pupil of Whittaker, and he offered to share the work of preparation of a second edition. This appeared in 1915 and proved to be a considerably expanded version of the original work, but followed the same general plan. New chapters on Riemann integration, integral equations and the Riemann zeta-function were added by Watson, and the existing chapters were rewritten to a very considerable extent. The new edition was an improvement on the old both in the rigour of the treatment and the comprehensiveness of the results included, and has proved its value over the years. Nevertheless these superior merits were at, first not universally acknowledged, and some mathematicians continued to prefer the original edition with its less formal style and greater motivation of general results. Additional material was added in later editions of the treatise and it occupies a unique place among textbooks on analysis.

Much of Watson's early work was concerned with special functions and asymptotic expansions. What is known as Watson's Lemma appeared as a lemma in a paper on the parabolic cylinder functions. This result enables one to obtain the asymptotic expansion of a function that can be expressed as a Laplace integral. Results of this kind prepared the way for his monumental Treatise on the theory of Bessel functions, the first edition of which appeared in 1922. This work, which extends to more than 800 pages, superseded all earlier books on the subject, and, in a subject where many differing notations had been used, Watson's notations became standard. The book contains not only formulae and theoretical investigations, but also extensive tables, some of which Watson had himself calculated. During the 1939-45 War the book was in great demand in government scientific establishments, both in this country and abroad. It became difficult to acquire until a second edition appeared in 1944. By that time, however, Watson had lost interest in the subject and only minimal alterations were made. It is, of course, understandable that his interests should have changed, and a great amount of further work would have had to be done in order to incorporate new work published since the first edition. Nevertheless, as a textbook on Bessel functions the volume is still unsurpassed and is likely to remain so for many years.

During the years between 1928 and the beginning of the Second World War much of Watson's work was concerned with problems connected with the famous Indian mathematician Srinivasa Ramanujan, who died in 1920, and this was Watson's most prolific period. He wrote numerous papers on subjects such as singular moduli, mock theta functions and partition functions. His well-known work on general transforms also dates from this period. After the war his flow of original papers diminished but he was still writing interesting papers in 1962. Perhaps his major contribution in this more recent period was his work on periodic sigma functions.

In personal appearance Watson was tall and spare. He had a shy, courtly and slightly formal manner. To his friends, and other acquaintances whom he liked, he could be charming, but, if he disliked someone, he did not hide his feelings. Except in the last few years of his retirement, he kept remarkably fit although he took very little exercise. He was not a good correspondent, in the sense that, unless he was interested in the subject or writer of a letter, he rarely bothered to reply. When his interest was aroused, however, he would take great care in framing a reply and the letters he did write are minor works of art full of characteristic touches and unusual items of information. Mathematics was not his only interest and railways, their history, time-tables and locomotives had a lifelong fascination for him. He had a remarkably retentive and accurate memory for factual and numerical information of every kind. With his passing we have lost a most interesting personality and one of the great mathematicians of the classical school of analysis.

Fuller details of Professor Watson's life and publications can be found in the obituary notice in the journal of the London Mathematical Society, on which the present obituary is based.

George Neville Watson's RSE obituary by R A Rankin appeared in Royal Society of Edinburgh Year Book 1966, 37-39.

[See also Biographical Memoirs of Fellows of the Royal Society.]