1. The early years
This account of our Society is based to some extent on my Presidential address, which was given on 19 October 1977 and was devoted to the first fifty years.
In the latter half of the nineteenth century there was an upsurge of interest in mathematics that resulted in the foundation of a number of mathematical societies in different countries. The London Mathematical Society (1865), the Moscow Mathematical Society (1867), the Société Mathématique de France (1873), the Edinburgh Mathematical Society (1883) and the New York Mathematical Society (later American Mathematical Society) (1888) were all founded in this period. There had, of course, been earlier more local societies, such as the Spittalfields Mathematical Society, which flourished over a long period before becoming defunct, as well as one or two much older bodies, for example the Mathematische Gesellschaft in Hamburg (1690), which still survive.
In Great Britain top-ranking mathematicians and mathematical physicists, such as Cayley and Clerk Maxwell, could compare with any to be found outside these islands; however, at a lower level, the schools and universities were not producing comparable numbers of mathematicians able to advance their subject. Our sister society in London was founded at the suggestion of two students at University College, George Campbell De Morgan and Arthur Cooper Ranyard, with the blessing of the former's father, Professor Augustus De Morgan, who become its first president. It rapidly became a society of professional mathematicians. By contrast, the stimulus for the foundation of the Edinburgh Mathematical Society came from school teachers, and, in particular, from two mathematical masters at George Watson's College in Edinburgh, Alexander Yule Fraser (an M.A. of Aberdeen) and Andrew Jeffrey Gunion Barclay (an M.A. of Edinburgh). In conjunction with Dr Cargill Gilston Knott (1856-1922), who was then Assistant to the Professor of Natural Philosophy in Edinburgh University, they issued the following circular 'to gentlemen in Edinburgh, in Cambridge and throughout Scotland generally whom they deemed likely to take an interest in such a Society'.
EDINBURGH UNIVERSITY,
JANUARY 23, 1883.Dear Sir,
We, the undersigned, beg to call your attention to the following proposal, in the hope that you will find it in your power to give it your support:-
It is proposed to establish, primarily in connection with the University, a Society for the mutual improvement of its members in the Mathematical Sciences, pure and applied.
Amongst the methods by which this object might be attained may be mentioned: Reviews of works both British and Foreign, historical notes, discussion of new problems or new solutions, and comparison of the various systems of teaching in different countries, or any other means tending to the promotion of mathematical Education.
It is suggested that the Society be formed, in the first instance, of all those who shall give in their names on or before February 2, 1883, and who are (1) present or former students in either of the Advanced Mathematical Classes of Edinburgh University, (2) Honours Graduates in any of the British Universities, or (3) recognised Teachers of Mathematics; and that, after the above mentioned date, members be nominated and elected by ballot in the usual manner.
It may be added that Professors Tait and Chrystal have expressed themselves as highly favourable to the project, as one that may lead to important results.
If there are any of your friends who might take an interest in the Society, kindly inform them of its objects, and invite them to attend the Preliminary Meeting, to be held in the MATHEMATICAL CLASS ROOM here, on Friday, February 2,1883, at Eight p.m., at which meeting your presence is respectively requested.
We are,Yours faithfully,
CARGILL G. KNOTT, D.Sc.(Edin.), F.R.S.E.
A. J. G. BARCLAY, M.A.(Edin.).
A. Y. FRASER, M.A.(Aberdeen).
As indicated in the letter, the preliminary meeting was held in the Mathematics Class Room, Edinburgh University, on Friday, 2nd February 1883, at 8 p.m. with Dr Knott in the chair. To quote from the minutes: 'The Chairman, in his introductory remarks, mentioned that Professor P G Tait (Professor of Natural Philosophy at Edinburgh University) had suggested that the Society regard itself as the resuscitation of the Physico-Mathematical Society, which had led a vigorous existence during the years 1836-39, had revived at subsequent intervals, but finally collapsed in 1850, leaving behind it, however, a library, some fragmentary apparatus, and a ballot-box'. It would be interesting to have further information about this former society.
This suggestion, however, was not taken up and those present at the meeting turned their attention to a series of eight motions setting up the Edinburgh Mathematical Society, its aim being the mutual improvement of its members in the mathematical sciences, pure and applied.
The first officers of the Society were elected, Mr (later Dr) John Sturgeon Mackay (1843-1914) being the first President. He was chief mathematical master at The Edinburgh Academy and was an able mathematician with a scholarly interest in the early Greek geometers. It was agreed that the Society should consist of Ordinary and Honorary Members, the only restriction on the former being that they should be proposed and seconded at one ordinary meeting and balloted for at the next.
One motion that was carried unanimously was that Professor Tait and Professor Chrystal (his colleague in the chair of mathematics at Edinburgh University) be elected Honorary Members. These two distinguished gentlemen (see Section 5) were, accordingly, our first Honorary Members. The next motion, which was merely agreed to, rather than carried unanimously, was that the professors of pure and applied mathematics in the other Scottish universities be invited to become Honorary Members. However, this motion was not pursued, since its proposers were not officers of the Society and the rules agreed at the second meeting of the Society restricted the proposers of such motions, as they do today, to members of the Committee. Nevertheless, at subsequent meetings Sir William Thomson (later Lord Kelvin) and Professor Charles Niven, Professor of Natural Philosophy at Aberdeen University, were elected Honorary Members.
It is interesting that school teachers rather than university staff took the leading part in the foundation of the Society. As Honorary Members, Professors Tait and Chrystal were not, of course, eligible as officers and the first professor to become President was James Edward Aloysius Steggall (1855-1935), who was Professor at University College, Dundee. Of the ten first Presidents seven were school teachers, while three were members of staff of universities; in contrast, the ten most recent Presidents have all been University Lecturers or Professors. Moreover, during the last thirty years only one President has not held a University appointment, and he joined the staff of a University immediately afterwards. The total number of Ordinary Members admitted at the first ordinary meeting of the Society in March 1883 was 51. By the end of the first session 58 persons had become members of the Society. Of these 15 had a university connection, including five from Cambridge, but about 40 were teachers, of whom five came from George Watson's, and one (R T Omand) was the director of the observatory on the summit of Ben Nevis. Over the years the percentage of university members has, of course, increased; however, as late as 1926, just before the second series of the Proceedings was instituted, their percentage had only risen from 26% to 36%. The present (1982) membership of the Society is about 300.
At the first meeting Professor Chrystal gave an address on 'Present Fields of Mathematical Research'. It may be of interest to list the titles of other talks given during the first session:
The triangle and its six inscribed circles (J S Mackay).
The nine-point circle (D Munn).
New proof of Professor Tait's problem of arrangement (T Muir).
Fundamental notions of the differential calculus (A Y Fraser).
Plücker's first equation concerning the singularities of curves (C G Knott).
Some notes on quaternions (C G Knott).
Some theorems relating to the radical axes of circles (D Munn).
These illustrate the preponderance of geometrical subjects during the early years of the Society. The early volumes of the Proceedings usually contained extensive appendices displaying geometrical figures, which would nowadays be very expensive to print.
The state of mathematics in Scotland at the time of the Society's foundation can be judged from the admirable and hard-hitting address given on 8 February 1884 by our second president Thomas Muir (1844-1934), who was at that time mathematical master at Glasgow High School. A graduate of Glasgow he had previously served as an Assistant to Professor Blackburn there and had also spent some time in continental universities. In 1892 he went out to Cape Town as Superintendent-General of Education, and spent the rest of his life there. From 1878 until his death he concerned himself with determinants and their history, a subject on which his books and papers, of which he published 307, are still the leading authority. He was elected a member of the Royal Society in 1900 and knighted in 1915.
Muir's presidential address, entitled 'The Promotion of Research; with Special Reference to the Present State of the Scottish Universities and Secondary Schools', was privately printed by Alexander Gardiner of Paisley and is to be found in some libraries bound up with Volume 2 of the Proceedings. Great changes have taken place in universities and schools during the last hundred years, but even up till the Second World War much of what he wrote in 1884 was still to some extent relevant. As an example, I quote:
A Scotch University student who has a special taste for mathematics, and has come to the University to develop that taste, has usually something like the following career: Of the two or three mathematical classes taught in the University, he very probably enters the highest. There he obtains a knowledge of Synthetic and Analytical Conics, the elements of the Differential Calculus, and, it may be, of the Integral Calculus as well. He knows there is no hope for him if he does not take his Master of Arts degree, and he gives his attention to Classics and Mental Philosophy with this end in view, continuing by himself his reading in Mathematics as far as it may be possible to do so. In time he graduates: this entitles him to compete for a scholarship: he competes, and is successful, leaves for Cambridge, and his University knows him no more. Probably in the newspapers we observe that Mr Donald Scott of a certain northern university has gained an open scholarship at Johnshouse, and the competition having been between him and a number of young men fresh from the English public schools, we are gratified accordingly with his startling success. Gentlemen, I put it to you, if this is a thing for us as Scotsmen to be altogether proud of. When in these cases a young Scotch student competing with English students of the same age gains a scholarship, there may be cause for gratulation: but the Scotsman who glories in the part his Universities play in the matter glories in his own shame. Is it really past hoping for that all this may yet be changed?
Muir was, of course, well aware of the deficiencies of the Cambridge coaching and examination system; after all these had been referred to by Augustus De Morgan in his presidential address in 1865 to the London Mathematical Society, of which Muir was a member. That was not the point at issue. What was relevant was that the 'three years' course of mathematical drill at Cambridge', whether 'well planned or ill planned,' was to be 'got nowhere else, certainly not in Scotland.'
In 1884 University Lecturers scarcely existed. In Mathematics the sole professor might be aided by one or two Assistants with whose help he could only hope to cover a fraction of the subject. Time for research would take a low place in face of the more urgent demands of teaching and administration. Muir contrasted this unfavourably with the situation in Germany, where one university might have more professors of mathematics than existed in all the Scottish universities.
2. Meeting places and times
The Society now meets regularly in all eight Scottish Universities and joint meetings with the London Mathematical Society have been held in Edinburgh and Newcastle.
During its first two sessions the Society met in Edinburgh University, but moved in the autumn of 1884 to the Edinburgh Institution in Queen Street. This I take to be the precursor of the present Melville College, known affectionately during my school days as "Stution". This was the ordinary venue of meetings until June 1913, when the Society returned to Edinburgh University. The first meeting outside Edinburgh was held in March 1900 in the Glasgow Philosophical Society's rooms, during the presidency of R F Muirhead, who was a Glasgow man. Annual meetings in May or March of each year were held thereafter from 1901 to 1905 in the United Free Church College in Glasgow, later known as Trinity College. From 1906 till 1912 the annual Glasgow meeting was held in the Glasgow and West of Scotland Technical College (which evolved into the present University of Strathclyde). Thereafter from 1913 until 1931, once and latterly twice a year, meetings were held in the Mathematics Class Room of the University of Glasgow.
The move to Glasgow University was made shortly after Professor George A Gibson's translation from the chair in the College to the chair in the University. Gibson's connection with the Society goes back to its very early years (he was admitted in February 1884), but his predecessor in Glasgow, William Jack, although elected an Honorary Member in 1902, seems to have taken little interest in the Society. The billets advertising the Glasgow meetings are of interest, since from 1912 at the last meeting in the Royal Technical College until the last meeting in the University of Glasgow in 1931 they bear the invitation: Professor and Mrs Gibson (later Professor and Mrs MacRobert) "At Home", 10 The University. This pleasant custom was revived briefly at the time of the Glasgow meeting on 30 May 1980. I shall explain later why these Glasgow meetings ended abruptly in 1931 and did not resume until 1957.
The Society first began to meet annually in St Andrews in 1922. Its first meeting in Dundee took place in 1930 during Professor Steggall's last year of office as President. The first meeting in Aberdeen was in 1937.
Except for meetings in St Andrews (and until recently in Aberdeen), which are held on a Saturday, ordinary meetings have, since the foundation of the Society, been normally held on Friday evenings. Initially meetings began at 8 p.m. but over the years there has been a gradual movement to earlier times and the main lecture is now generally given in the late afternoon.
During the 1939-1945 war, meetings were usually held on Saturday mornings in Edinburgh. In both world wars there was, naturally, some curtailment of the Society's activities and for this reason, during the sessions beginning in 1917, 1939 and 1943, no changes were made in the offices of President and Vice-President.
3. Publications
When the Society was founded, it was the general practice for mathematical societies to print papers read at meetings. During its first session the Edinburgh Mathematical Society had not enough money to do this, and so copies of papers read were deposited with the Secretary. During the second session the Society resolved to print its proceedings in whole or in abstract, so that Volume 2 of the Proceedings was the first to be published and appeared in 1884. It was not until 1894 that Volume 1, covering the first session, appeared. It contains J S Mackay's paper on the six scribed circles of the triangle. This paper (uncut until I examined it in the Glasgow Departmental Library copy) occupies 124 pages and contains 72 figures printed on 24 pull-out sheets. Even so, it forms only part of the author's work on the subject.
The early volumes published by the Society are, accordingly, Proceedings of the Society in the strict sense of that word. The papers presented were in nearly all cases written by members of the Society, although occasionally the work of some other mathematician might be read. For example, P G Tait was interested in determining the form of a certain curve arising in the motion of a device described by De Morgan and known as Milner's Lamp. For this purpose he consulted Cayley, whose paper On a differential equation and the construction of Milner's Lamp appeared in Volume 5.
The subjects discussed in these early papers cover a wide range, but with a preponderance of Euclidean geometry. There are several articles on historical and pedagogical points, including collections of mnemonics.
By 1909 it was felt that the more elementary and pedagogic articles should not appear in the Proceedings and, at Professor G A Gibson's suggestion, it was agreed "to issue at stated intervals a supplement to the Proceedings dealing with the teaching of Mathematics and Science, the supplement to be called 'Mathematical Notes, a review of Elementary Mathematics and Science, published by the Edinburgh Mathematical Society' ". The first number appeared in April 1909. Succeeding parts have been issued at irregular intervals, some being published together with the Proceedings and some separately. The last number (No. 44) appeared in 1961.
In this connection it is, I think, of interest to mention a controversy that took place between 1927 and 1931 concerning the Society's publications. Perhaps controversy is too strong a word, since the disagreements occurred within the Committee and, so far as I can discover from the minutes, did not surface in the meetings of the Society. Nevertheless, strong feelings were aroused that had not entirely subsided when I first came to Glasgow 29 years ago. As one might guess, the main protagonists were both very strong characters with very different personalities. Perhaps the only things they had in common were that they had been undergraduates at Trinity College, Cambridge, had been classed as Wranglers in the Mathematical Tripos and had an interest in the theory of special functions. It is possible that this last bond may have exacerbated their different points of view. The older of the two was, of course, the late Sir Edmund Whittaker (1873-1956), who was Professor of Mathematics at Edinburgh from 1912 to 1946. During a period of nearly 40 years Whittaker exerted a powerful influence on the affairs of the Society; see Section 5. The younger of the two was the late Professor Thomas M MacRobert (1884-1962), who was Professor of Mathematics at Glasgow University from 1927 to 1954.
To set the scene I mention that, whereas in the early years of its existence the Society's membership consisted predominantly of school teachers, the number of teacher members had slowly declined as the level of research papers and lectures rose. The Mathematical Notes had, of course, been set up to cater especially for teachers and to print expository and historical articles, but, by the late 1920s, it was felt by some that this was not enough.
In December 1927, Professor MacRobert outlined to the Committee a scheme he proposed to bring forward in greater detail at the next meeting. In essence his scheme was that the Proceedings should be retained for research papers, but that the Society should publish in place of the Mathematical Notes a new periodical, to be called the Journal of the Edinburgh Mathematical Society, which would contain articles on History, Methods of Teaching, Notes, Discussions on Elementary Mathematics, etc. At the following meeting these proposals were discussed and agreed, although the proposed method of financing them was not accepted. At a subsequent meeting in May 1928, the Committee went further and agreed to start printing a first part of the Journal in its new form.
What happened after that is unrecorded since the matter is not referred to in either the minutes of the Society or those of the Committee until over two years later when, in July 1930, the Committee formed a subcommittee to update the Society's rules and make mention in them of the Society's publications. It was then agreed to expand the Mathematical Notes, and a change of name to the Journal of the Edinburgh Mathematical Society was again suggested.
From this point onwards the Committee appears to have divided into a pro-Journal and an anti-Journal party. Some members objected to the title Journal of the Edinburgh Mathematical Society on the grounds that it would clash with the recently founded Journal of the London Mathematical Society and other names were suggested such as Bulletin of the Edinburgh Mathematical Society and Scottish Mathematical Journal. The latter found most favour and appeared in a draft set of rules that later went before the Society, although those rules that concerned publications were never discussed by the Society at ordinary meetings but were always deferred.
On the anti-Journal side the view was expressed that the Society should in future become a research society and that the Glasgow Mathematical Association should be left to provide for those whose main interest was in pedagogic matters. It was claimed that in this way the Society was more likely to receive grants from the Royal Society. However, by this time the Secretary had received a letter from Professor MacRobert, who stated that he felt so much out of sympathy with the policy of the rest of the Committee that he felt impelled to resign from the Committee. He remained a member of the Society, but no further meetings of the Society were held in Glasgow for more than twenty years.
The anti-journalists had won. To complete their victory they needed to dispose of the Mathematical Notes and the proposed Journal, but this proved to be more difficult. The editor of the Notes, Mr William Arthur - a much respected member of the Glasgow staff - was asked to approach the Glasgow Mathematical Association to see whether they could assume responsibility, and he agreed to do so. However at their next meeting the Committee was informed that the Association had declined and that Mr Arthur had resigned both from the Committee and from the editorship of the Notes. As a last resort approaches were made to the Educational Institute of Scotland suggesting that they might make themselves responsible for publishing the Notes, but these were unsuccessful. Accordingly, the final outcome was that, after four years of discussion, no change was made in the Society's publications and the Proceedings and the Notes continued to appear as before. It may be of interest to observe that five years later in 1936 the Glasgow Mathematical Association did commence publication of a periodical devoted to historical and pedagogical matters, called the Journal of the Glasgow Mathematical Association. This survived until 1953.
After a lapse of over fifty years, when one looks back at this small ripple in the even tenor of the affairs of the Society, one cannot help feeling that the proposal to establish a journal for historical and pedagogical matters was a useful and imaginative idea, which would have enhanced the reputation of the Society without detracting from the research pretensions of the Proceedings. With hindsight one suspects that the most cogent argument against the Journal was one, which, if it was made at the time, is not recorded in the minutes, namely the shortage of suitable high quality material, which ultimately caused the demise of the Mathematical Notes as well as of the Glasgow Journal.
It may be of interest to mention that the possibility of an amalgamation of the Edinburgh Proceedings with the Proceedings of the Glasgow Mathematical Association (now the Glasgow Mathematical Journal to form a new Scottish Mathematical Journal was discussed in 1965, the view being that such a journal would carry greater prestige than either of its constituents since it would be of greater size and might appear more frequently. For a variety of reasons this proposal was not taken up, largely because it would have cut by about half the mathematical journals received under exchange agreements by the Glasgow and Edinburgh University Libraries.
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