Emeritus Professor Herbert Westren Turnbull, M.A., LL.D., F.R.S.

by A C Aitken

The death of Emeritus Professor H W Turnbull at Grasmere on May 4, 1961, was felt as a personal loss not merely by mathematicians in Scotland, with which he had had associations for forty years, but by many British, American and foreign mathematicians whom he numbered among his friends.

Herbert Westren Turnbull, second son and second of the seven children of William Peveril Turnbull, H.M. Inspector of Schools at Wolverhampton and later at Sheffield, was born at Tettenhall, Wolverhampton on August 31, 1885. Educated at Sheffield Grammar School, he went up in 1903 to Trinity College Cambridge, with an Entrance Scholarship. In the Tripos of 1907 he was Second Wrangler, in 1908 he was in the First Class of Part 2 (1st division), in 1909 he was a Smith's Prizeman. These distinctions were in keeping with a remarkable family tradition; for his father (four of whose sons went to Cambridge) had likewise before him been Second Wrangler and a Smith's Prizeman, being later a Fellow of Trinity, an uncle had been Third Wrangler, a cousin, R W H T Hudson, was Senior Wrangler, his elder brother and a cousin were Wranglers, while three lady cousins, one of whom was Dr Hilda P Hudson, the distinguished author of Cremona Transformations in Plane and Space, gained First Class in Mathematics at Cambridge or Oxford, and yet another cousin was Tutor in Mechanical Science at Trinity Hall. Herbert Turnbull was a lecturer at St Catharine's College in 1909 and at the University of Liverpool in 1910. In July 1911 he married Ella Drummond, daughter of Canon H D Williamson, and went with her to Hongkong, where he was a lecturer at Hongkong University in 1912, Master at St Stephen's College from 1911-15, and Warden of the University Hostel from 1913-15. He had indeed intended, following the example of his elder brother Arthur, to settle abroad from 1911 in educational missionary work. The climate, however, proved detrimental to his health and he was forced to abandon this course. He returned to England, but during the First World War could find no university post open to him; at the same time, attested for military service, he was found unfit, and so he taught at Repton from 1916-19. From 1919-26 he was Fereday Fellow of St John's College, Oxford; this fellowship had a special association with Staffordshire, where he was born.

In 1919 he was appointed an H.M. Inspector of Schools, and for a period of two years it seemed that after those earlier vicissitudes his future career would be the same as that of his father. However, in 1921 the Chair of Mathematics at the United College, St Andrews, fell vacant; and Turnbull was appointed, being still only thirty-six years old. This was the central and decisive step in his career. He filled the chair with great distinction, influence and acceptance until 1950, when he retired at the age of sixty-five, choosing as his home the Lake country, always congenial to him for its mountains and its early associations of holiday with his father and brothers, and there he worked on the great task allotted to his retirement, namely the editing, under the auspices of the Royal Society of London, of the scientific correspondence of Newton. He lived to see the publication, by the Cambridge University Press, of the first two handsome volumes, which appeared in 1959 and 1960. With the help of Dr J F Scott, who continues the work, the third volume was complete in manuscript, except for the Index, and the fourth begun.

In Scotland his name will be associated with St Andrews. Though the first of his papers, on ternary quadratic types, was published as early as 1910, it was at St Andrews that he wrote the great majority of his sixty and more original memoirs and his books (except for the Newton volumes), it was there that he founded a school of algebraic research, for the most part in the symbolic invariant theory which he had learned from Alfred Young and J H Grace at Cambridge and of which he was himself the last great master, and there also that he carried out those historical studies, based on documents he had himself discovered or sought out from 1932 onwards, leading to the publication of the James Gregory Tercentenary Memorial Volume simultaneously with the International Congress of the Edinburgh Mathematical Society which in 1938 commemorated the tercentenary year of the birth of Gregory. It is of special interest that this Congress met in our own rooms at the invitation of our own Society on July 4, 1938, and in St Andrews on July 5 at the invitation of the University of St Andrews; many will still recall how the delegates, having attended in this way the Ordinary Meeting of the Society on that date and witnessed the unveiling of the portrait of the President, Sir D'Arcy Thompson, proceeded with Sir D'Arcy to St Andrews. The Royal Society of Edinburgh sponsored the publication of the Memorial volume, the Carnegie Trust for the Universities of Scotland made a generous grant towards its production.

At this celebration Herbert Turnbull, ably seconded by his wife, was the central figure, both host and participant, as he was also host for a quarter of a century and more to the Edinburgh Mathematical Society at their meeting each June at St Andrews and their four-yearly Colloquia there. He was President of the Edinburgh Mathematical Society in 1926-27, 1933-34 and 1950-51, and co-Editor of its Proceedings from 1924 to 1933.

In our own Society Turnbull's Fellowship dated from 1922. He served on the Council over the period 1928-31, was awarded the Keith Prize for original work of merit belonging to the period 1923-25, and the Gunning Victoria Jubilee Prize for the period 1940-44. He was elected a Fellow of the Royal Society in 1932, and awarded the Honorary LL.D. of the University of St Andrews in 1952.

A more extensive article in the Biographical Memoirs of the Royal Society of London will include a detailed appraisement of his mathematical work; brief evaluations are to be found in our own Proceedings (46) for 1925-26, page 396 and in the Year Book for 1945, pages 44-45, in the citations accompanying the awards of the Prizes mentioned above. It is as a man that he will be remembered, of the highest character and the utmost simplicity, generosity and true humility. Extra-academically he was versatile; as a cricketer, a golfer, a chess player, a mountaineer, expert in his day on the high Alps, very familiar with the mountains of the Scottish Highlands and the Lake country, a member of the Alpine Club, President from 1948 to 1950 of the Scottish Mountaineering Club. His biography of his father, Some Memories of William Peveril Turnbull (Bell, 1919), is of the utmost interest as a picture of Cambridge, of education, of social life and of a distinguished family during the Victorian and Edwardian eras. He was an excellent musician, a pianist of professional competency, as was also his wife, who survives him. Their son, Derwent Greville Turnbull, is an Instructor-Commander in mathematics in the Royal Navy.

Herbert Westren Turnbull's RSE obituary by A C Aitken appeared in Royal Society of Edinburgh Year Book 1962, 47-49.

[See also Biographical Memoirs of Fellows of the Royal Society, 8, 1962.]