The early volumes of the Proceedings were slim and were issued annually as single parts after the close of each session. Until 1907 the communications were printed, in full or by title, in the order in which they were delivered at the successive meetings of the Society. Gradually the number of contributions made at each meeting decreased. At an intermediate stage, for example, there might be one full hour's lecture accompanied by two or three papers read by title. Ultimately the current practice obtained whereby, at the majority of meetings, there is a single lecture, which need not necessarily be embodied in a paper submitted to the Society for publication.
By the middle 1920s it was felt that the size of page used was too small and a second series of the Proceedings was begun in 1927. Each volume of the new series generally consisted of four parts, published over a period of two years. The wrappers of the parts were originally brown, but were changed to green in 1958; in that year also short book reviews were published for the first time. The number of parts appearing annually was increased from two to three in 1979 and from that date volumes have appeared annually. Although it is not mentioned in the minutes, an important reason for embarking on a second series must have been the wish to raise the level of the papers published, which, although it had risen considerably over the years, remained somewhat uneven. In this connection it may be noted that the new Constitution of the Society adopted on 15 January 1932 contains for the first time the provision that every paper published must first have been submitted by the Editors to at least one referee of recognised authority, and reported upon favourably by him.
An interesting item from the Minutes of the Committee held on 7 November 1942 (but not referred to subsequently) records that, in response to an appeal that appeared the previous month in Nature, it was agreed that the Society's publications should be sent for perusal by mathematicians held as prisoners of war in prison camps in Great Britain.
The original annual subscription, which included the cost of the publications, was five shillings (£0.25). This rose to seven shillings and sixpence in 1885 and remained at that rate until 1919 when it became ten shillings. In 1954 it was raised to fifteen shillings and since 1958 there have been further more frequent increases as a result of inflation. The current annual subscription is £11.
4. Colloquia
When Whittaker came to the Edinburgh chair in 1912 after Chrystal's death he soon began to inject fresh vitality into his department. He instituted a mathematical laboratory, where various branches of numerical analysis were taught that had previously been offered systematically in no British university. From its inception the laboratory clearly supplied a very definite need and requests were received for a vacation course from persons unable to attend during the normal academic teaching terms. This demand resulted in the running of the first mathematical colloquium sponsored by the Society. It was held from 4-8 August 1913 in Edinburgh University. Three courses of five lectures each were given. A W Conway, who was Professor of Mathematical Physics at University College, Dublin, spoke on 'The Theory of Relativity and the new Physical Ideas of Space and Time', Dr D M Y Sommerville, who was then Lecturer in Mathematics at St Andrews, spoke on 'Non-Euclidean Geometry and the Foundations of Geometry', while Whittaker himself lectured on 'Practical harmonic analysis; an illustration of Mathematical Laboratory practice.' The colloquium was a striking success, being attended by 77 participants from all over Great Britain. For their entertainment golf matches were arranged in the evenings and there were visits to the Zoological Gardens, the Census Office, and new laboratories at the University and in George Heriot's School.
A second short colloquium was held in Edinburgh in July 1914 immediately after the Napier Tercentenary Celebration organized by the Royal Society of Edinburgh. No details are recorded in the minutes, possibly because of the outbreak of war immediately thereafter. After the war, largely through the enthusiasm and drive of Herbert Westren Turnbull (1885-1961), who had been appointed to the Regius Chair of Mathematics in St Andrews in 1921, the Society's colloquia were resumed. The first meeting in St Andrews in 1926 set the pattern for future colloquia, which have been held there at regular intervals since then. Meetings usually occupy ten days during which a number of short courses are given on a wide spread of topics in pure and applied mathematics. Ample time is allowed for recreational activities and the colloquium usually includes a musical entertainment given by some of the participants. The weather, fortunately, has nearly always been fine. Early colloquia were attended by many school-teachers as well as by those working in universities, but the increasing specialization of mathematics has resulted in a sharp drop in the number of those in the former category and the introduction of more specialized lectures supplementing the general courses. Since 1926 colloquia have been held in 1930, 1934, 1938, 1951, 1955, 1959, 1964 and at four year intervals thereafter. The fifteenth colloquium will doubtless be held in 1984.
The Society has always had an interest in pedagogical matters. Before the 1914-19 war in May of three successive years 1911, 1912 and 1913 one-day Secondary Education Congresses were held in Glasgow, Edinburgh and Dundee, respectively, for those interested in the teaching of mathematics. At intervals since then Ordinary Meetings have been devoted to pedagogical subjects.
5. Some notable personalities in the history of the Society
As has been mentioned, Alexander Yule Fraser and Andrew Jeffrey Gunion Barclay were mathematical masters at George Watson's College at the time of the foundation of the Society. They became Presidents in 1889 and 1884, respectively. They both moved later to Glasgow, Fraser becoming headmaster of Allan Glen's School and Barclay chief mathematical master of Glasgow High School. Other Watsonians prominent in the Society's affairs were Jock Alison (1861-1952), a distinguished headmaster, who was President in 1892, and Donald Cameron McIntosh, who was Secretary for many years and President in 1905.
The Society's first two honorary members were most interesting and able men. Peter Guthrie Tait (1831-1901), who was a school-fellow of James Clerk Maxwell at Edinburgh Academy, was a distinguished Professor of Natural Philosophy with very wide interests. I suspect that today he is better known for his work on combinatorial topics, such as map colourings, and as a founder of the mathematical theory of knots, than for his work on physics. During his life-time he achieved considerable fame as the first person to study scientifically the flight of a golf ball. He demonstrated that the Magnus effect of underspin could greatly increase the range and time of flight of a driven ball. A story was told as a joke against the Professor that his son Freddie, who was a brilliant amateur golfer, had gone out and driven a ball 250 yards, which was further than the maximum range "proved" possible by his father. There were, however, no grounds for this, since Tait stated no maximum ranges for spinning golf balls. Tait was junior author with Sir William Thomson of the famous Mathematical Treatise on Natural Philosophy affectionately known as T and T'.
Until I read his obituary I had always imagined that Tait's colleague George Chrystal (1851-1911) was a pure mathematician with a main interest in algebra. In fact his chief interest was in electricity and magnetism, from an experimental as well as from a theoretical point of view. Like other Scottish professors at that time he acted as an inspector of schools and he was the originator of the Scottish Leaving Certificate examinations, Moreover, it is due to him that, over a long period of years until the recent establishment of sixth year studies, Mathematics was the one subject in which school pupils could be examined at a level beyond that of the Higher Grade. His experience in teaching mathematics in the University convinced him that 'algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules whose object is the solution of examination problems.' This led him to write his monumental treatise of nearly 1200 pages on Algebra, which appeared in two parts in 1886 and 1889, and had a powerful effect on the teaching of algebra in Great Britain and abroad. His aim was to develop the subject as a logical science. A shorter version, entitled Introduction to Algebra for the use of Secondary Schools and Technical Colleges, appeared in 1902. This was the textbook my father used when he was in Chrystal's first year class at Edinburgh University. I recall that, when I was a boy of fourteen, he offered me ten shillings (a considerable sum of money fifty years ago) if I would read the whole of it, but my stamina was not sufficient to enable me to do so.
Of the original members of the Society few can have given it greater service than its first Secretary, Cargill Gilston Knott (1856-1922), who served twice as President. When the Society began he was Assistant to Professor Tait, but at the end of the first session he left to become Professor of Physics at the Imperial University of Japan, where he remained for eight years. On his return in 1891 he was appointed to one of the first Lectureships in Edinburgh University and later become a Reader. He was an authority on magnetism and seismology and was responsible for conducting the magnetic survey of Japan. Later on he became General Secretary of the Royal Society of Edinburgh and was the editor of the Napier tercentenary volume and of the collected papers of P G Tait. In addition to his books and papers on physics he published a booklet of four-figure mathematical tables which is still widely used; I recently came across a copy in the University of Alberta bookstore in Edmonton. In the years 1892-93 there raged a controversy between the advocates of quaternions and the supporters of vectors. Knott was a leading figure on the quaternion side in these arguments. As Sir Edmund Whittaker wrote in his obituary of Knott, Tait 'had succeeded to the generalship of the quaternionites on the death of Hamilton and bequeathed it in turn to Knott.'
One of the most faithful early members of the Society was George Alexander Gibson (1853-1931). He was elected a member in 1884, while he was Assistant to the Professor of Mathematics in Glasgow University, and became in 1895 Professor of Mathematics at the Glasgow and West of Scotland Technical College. He returned to Glasgow University as Professor in 1909, retiring in 1927. He was the author of books on calculus which were notable for their rigour at a time when this was the exception rather than the rule, but his main interest was the history of mathematics. The Proceedings contain numerous papers by him on these two subjects. He also took an active part in meetings devoted to the teaching of mathematics.
No account of the Society would be complete without considerable mention being made of Sir Edmund Taylor Whittaker, who has already been referred to in this article more than once. After ten years as a Fellow of Trinity College, Cambridge, he moved to Dublin in 1906 to take up the post of Royal Astronomer of Ireland. In 1912 he came to Edinburgh to succeed George Chrystal as Professor of Mathematics. He was a man of extremely wide interests in mathematics and mathematical physics and was the author of several influential books as well as of numerous research papers.
Whittaker's institution of a Mathematical Laboratory at Edinburgh University has already been mentioned. Perhaps an even more important innovation made by him after his appointment there was the institution of 'research lectures' for staff, post-graduate students and visitors. In this respect he was far ahead of his colleagues in other British universities. I quote from Dr Martin's excellent obituary notice, published as part of a Whittaker Memorial Number in Volume 11 of our Proceedings:
These were given twice weekly, usually at three o'clock in the afternoon, and their principal aim was to bring into prominence topics suitable for original investigation. Their subject matter was related either to Whittaker's own researches at the time or to some important matter of contemporary interest. For instance, when Einstein first produced a unified field theory the lectures dealt with that theory while a course on spinors followed the publication by Cartan of his important book on the subject. Whittaker's ability to absorb and digest so much fresh mathematical work and to lecture on it term after term was truly remarkable. For it must be emphasized that his lecture notes were not just verbatim copies of the essential parts of the published papers on the subject, but contained what was almost a redevelopment of the subject by himself. His notes, incidentally, were written out in great detail and he wrote on the blackboard practically everything that he said. He wrote extremely fast but his writing was always legible. At the end of a lecture he may have been physically tired but he was certainly mentally exhilarated. The research room in the Mathematical Institute is a small homely lecture room with a fire-place at the back, and a few minutes before the end of Whittaker's lecture someone in the back row would put the kettle on the fire so that by four o'clock tea would be ready. Whittaker would then relax in his armchair by the fire, serenely happy with his colleagues and visitors around him, while the animated discussion which arose would cover anything from the lecture just given to academic affairs or religion. In this atmosphere Whittaker was in a most exhilarating form and the inspiration seemed to flow from him. Indeed, as far as research work is concerned, it is rather for his power of inspiring others than for his own work that he will long be remembered.
Whittaker took up the affairs of the Society with enthusiasm and as President and, for many years, a member of the Committee, exerted a strong influence. His efforts were always directed to the enhancement of the reputation of the Society as an organization for the promotion of mathematical research, as is evident from what has already been written regarding the Society's publications and colloquia.
The Society also owes a great debt to H W Turnbull, who has already been mentioned in connection with the colloquia held in St Andrews. His main interest as a young man was the theory of invariants, on which he gave a course of lectures to the 1926 meeting held there; this formed the basis of his well-known book The Theory of Determinants, Matrices, and Invariants, which appeared in 1928. It was under Turnbull's editorship that the second series of the Proceedings was begun in 1927 and it was largely due to his efforts that the second series became a mathematical journal of repute. Turnbull was a fine musician and an experienced mountaineer; he had served as President of the Scottish Mountaineering Club, in whose handbooks many of his climbs are recorded. In later life he became an authority on the history of mathematics and, after his retirement in 1950, he edited the correspondence of Isaac Newton on behalf of the Royal Society. He, his older colleague Professor J E A Steggall of Dundee and Dr Robin Schlapp of Edinburgh are the only members of our Society who have served three times as President.
I conclude this section by mentioning a man who was a fine mathematician but less successful in a worldly sense than those referred to above.
Robert Franklin Muirhead (1861-1941) was a graduate of Glasgow and Cambridge Universities and spent some time at the University of Göttingen. He took a great interest in the Society and was twice President, in 1899 and again in 1909. He was elected an Honorary Member in 1912. He held lectureships in Glasgow and Birmingham for brief periods and tutorships in London, Edinburgh and Glasgow, but never held any permanent position worthy of his talents. It is possible that this may have been because of his outspoken views on home rule and socialism. In his latter years he was head of a coaching establishment, the Glasgow Tutorial College. I first heard of Muirhead forty years ago from my supervisor, the late Professor G H Hardy, who had a high opinion of Muirhead's abilities, and some of his work on convexity which is of interest to statisticians has recently come into greater prominence. Men like Muirhead, or his younger colleague John Dougall (1867-1960), who was President in 1925, would easily have obtained university posts in the golden 25 years following the last war, but they lived in times, rather like those we have moved into recently, when appropriate positions were not available to everyone of ability.
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