The Edinburgh Mathematical Society 1883-1933
|Mathematics in Scotland||History Topics Index|
1. The beginnings of the Society
It is about 7.45 pm on Monday 12 March 1883 and we are passing the Mathematics Class Room of the University of Edinburgh. A lecture is taking place and we peep through the door to see why there is one at this unusual hour. Professor George Chrystal, The Mathematics Professor, is addressing around 60 men. We have stumbled across the first ordinary meeting of the newly formed Edinburgh Mathematical Society. Chrystal, who had his 32nd birthday four day earlier, was a graduate of Aberdeen and Cambridge. After being an assistant to James Clerk Maxwell at the Cavendish Laboratory he was Regius Professor of Mathematics at St Andrews 1877-1879, then Professor at Edinburgh.
The men Chrystal is addressing are mainly mathematics masters from Edinburgh schools. Among them we recognise Andrew Barclay and Alexander Fraser, both Mathematical Masters at George Watson's College, Edinburgh, and Thomas Muir, Mathematical Master at the High School, Glasgow. We recognise a few university men: Robert Allardice, Chrystal's assistant; Peter Guthrie Tait the Professor of Natural Philosophy at the University of Edinburgh; and Cargill Knott, Tait's assistant, who is carefully taking notes and is clearly the Secretary.
Let us listen for a moment to what Chrystal is saying:
The time can scarcely be better chosen for founding a mathematical society in Scotland. The Mathematical tide is certainly beginning to flow in England largely due to the influence of such men as Stokes, Cayley, Sir William Thomson, and Professor Tait. At present in England a large number of able men are devoting themselves to purely mathematical work. You must also have noticed that mathematics is coming fast to the front in America. The starting of the great new mathematical journal there has tended greatly to stimulate mathematical activity; and the founding of a new college specially devoted to the highest branches of research is already producing remarkable effects.We stay around until the meeting ends and hear James Blyth, the Professor of Mathematics and Natural Philosophy at the Andersonian College, Glasgow, move a vote of thanks to Professor Chrystal. Blyth spoke of the benefit the Society would be to schoolmasters. Then Thomas Muir, a Mathematical Master at the High School, Glasgow, seconded the motion, and touched on the difficulties of teaching algebra in schools. He said that there is pressing need for an elementary text-book on algebra, thoroughly scientific in its treatment of the subject. Chrystal would write perhaps the finest such text and publish it three years later - Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges published in 1886.
In Scotland we are unquestionably on the eve of a revolution of our system of secondary education. If we are not, we ought to be. In the meantime, I am not concerned with the raising of the average standards in our schools. I am thinking more of the raising of the maximum. As to the question of the maximum standard, there can be no question whatever that it lays under a reproach - that reproach, in fact, Dr Johnson levelled at it when he said that every man in Scotland could get a mouthful of learning, but no man a bellyful. The reasons for that are not far to seek. They mainly result from the lack of that great stimulator of arts and sciences - money. The effect of this revolution must be to raise the demand for highly-trained schoolmasters. So pressing does this appear to me to be that for several winters back - more particularly this winter - I have been thinking of trying to start something in Edinburgh in the nature of a mathematical seminary. But now, in my opinion, the establishment of a Mathematical Society is a better means of obtaining the object I had in view.
There is a wide range of mathematical science at the present day, and it is difficult to keep abreast of the literature on the subject. There are great advantages to be secured by the members of the subdividing that work and communicating at the meetings the latest views in the different departments. I want to speak now of the great development of geometry, for which we are indebted to Monge who is the real originator of all that is best in modern geometry.
We speak to some members of the new Society after the meeting. We are told of a circular issued by Cargill Knott, Andrew Barclay and Alexander Fraser, addressed 'to gentlemen in Edinburgh, in Cambridge and throughout Scotland generally whom deem likely to take an interest in such a Society'.
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.The meeting on Friday 2 February 1883 had been a great success. Fifty-six founder members had either been present or had applied to join the new Society on that day. About 25 were Mathematics masters, a couple were Rectors such as George Thom at the Dollar Institution, then there was James Bolam, a self-taught mathematician from the Government Navigation School in Leith, Robert Omond who headed at The Observatory, Ben Nevis, a number of Edinburgh undergraduates, a few Ministers of religion, and a few university teachers of mathematics and natural philosophy.
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.
John Mackay had been elected President while Cargill Knott agreed to act as both secretary and treasurer. Later in 1883 Thomas Muir was elected to be the second president and he gave his presidential address on The Promotion of Research with Special Reference to the Present State of the Scottish Universities and Secondary Schools on 8 February 1884. Given the title of the address it might come as a bit of a surprise to learn that Muir was mathematics and science master at Glasgow High School. He had been in this post for ten years and he would continue for another eight years. He had already published Treatise on the theory of determinants (1880) and was working on the first volume (five were eventually published) of History of determinants (1890). We will eavesdrop on Muir in a moment, but to make sense of what he is saying we need to understand about the state of mathematical education at the time.
2. The Scottish degree in 1883
Up to 1860 an undergraduate in a Scottish university (St Andrews (founded 1411), Glasgow (1450), Aberdeen (1494), and Edinburgh (1582)) studied for an M.A., essentially a set course consisting of English, Latin, Greek, Mental Philosophy, Mathematics and Natural Philosophy. After 1860 Honours degrees were introduced, built on top of the fixed M.A. course. The whole university timetable fitted on a single sheet of paper.
Women were not admitted to the M.A. course. Mathematics was taught by a professor and one assistant . Natural Philosophy, which was part of the Mathematics Department, was similar.
|Natural Philosophy |
Peter Guthrie Tait
Let us note some consequences of this situation:
- A mathematical society aimed primarily at university staff would make no sense - only 8 university based mathematicians in 4 Scottish universities and travel from St Andrews and Aberdeen to Edinburgh was hard.
- There was no opportunity for mathematical research (or even to learn about up-to-date mathematical results) at universities except for these 8 men.
- With 2 staff to cover all mathematical teaching (to every M.A. student) there was little chance for research or even reading about the latest results.
- There was a good number of schoolmasters with a passion for mathematics who, had the opportunity existed, would have studied considerably more mathematics than was in the Honours Mathematics and Natural Philosophy course.
- The Edinburgh Mathematical Society was founded to fill this gap - to provide the means for further study of mathematics.
Muir understood precisely what was wrong with the Scottish system, and how the Edinburgh Mathematical Society might help.
3. Muir on mathematics in Scotland
Let us eavesdrop on Muir talking about mathematical education in the Scottish universities:
We recognise two of the functions of a University - instruction and research; we ignore, so far as mathematics is concerned, a third and equally important function, - instruction in research. 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.So students are not well set up to do research. What about research by the professors:
But next the questions may be asked - What careers are there open for such men after they have completed their post-graduate course? Is there anything like the same possibilities for them as are within the reach of Cambridge wranglers? The answer to the first question is, that there are home and colonial professorships, and masterships in the secondary schools.
First and foremost is the extraordinary anachronism of a single professorship for the wide domain of Mathematics. Who that thinks for a moment of the vast additions that have been made to mathematical knowledge, even within the present century, but sees the flagrant inadequacy of this provision? .... the very best professors will be the first to confess that half-a-dozen men will not fully represent it..... can it be too often brought to notice that a single German University is able to show as many professors of the subject as all the Universities of Scotland put together?The force of Muir's argument is that research can be done in the secondary schools:
Besides this overburdening of the Scotch [sic] Professor, by throwing on his shoulders the full weight of an overgrown subject, there is the aggravation of wasting his energy in teaching the most elementary portions of it. Nothing in connection with our Universities is more astounding to a foreigner than the fact that there are large numbers of students enrolled every year to begin the first proposition of Euclid, and that, of all the mathematical students within the walls, by far the greater portion have confined their studies to elementary Algebra, Geometry and Trigonometry. Fortunately this condition of things is beginning to astound others besides foreigners.
Let us glance now at the secondary schools, and examine what possibilities there are in connection with them for the furtherance of research. In these institutions we have, on a small scale, exactly the same machinery in action, as in the Arts Faculty of a University. ... Gentlemen, we must remember that there is an immensity of work to be done for which giants are wholly unnecessary, and that no work is more useful than preparing the way for the giants of the future. There is room and need for the exertions of every one, down to hewers of wood and drawers of water. I assert with confidence - for I believe that those with more experience than myself will endorse what I say - that there is not a single member of the Edinburgh Mathematical Society but might do useful work in the cause of mathematical research.We should record that Muir was elected a Fellow of the Royal Society (1890) while a schoolteacher in Glasgow. Two years later he went to the Cape, South Africa, as Superintendent General of Education. His scholarly five volumes on the History of Determinants are a mine of information still worth dipping into today.
4. The Society develops in 1883-86
The fourth president of the Society was Robert McNair Ferguson, the Headmaster of the Institution, Edinburgh. He served during session 1885-86. On Friday 12 November 1886 the Edinburgh Mathematical Society began its fifth session. Dr Ferguson delivered an address in which he congratulated the Society on its vigorous growth and encouraging prospects. He expressed a hope for the further improvement of the universities by an increased staff of extra and infra-mural lecturers. Regarding the position of mathematical masters in secondary schools, he thought that they should more frequently be entrusted with the highest authority. After a few remarks on the methods of mathematical tuition, he pointed out the desirability of continuing to widen the work of the Society in the interests of such professions as those of the engineer and the actuary.
Let us look at the meetings of the Society over this period. From 1883 to 1886 the Society held 31 meetings at which talks were given (the first meeting only dealt with the setting up of the Society). During these 31 meetings, 27 people (all members of the Society except 2) read 83 papers.
|Of these 27 there were:|
8 university staff
2 ministers of religion
1 Kew scientist
1 medical doctor
|The 83 papers were read by:|
31 university staff
|Those who delivered the greatest number of papers were:|
Muir - schoolmaster - 12 papers
Mackay - schoolmaster - 10 papers
Chrystal - professor - 8 papers
Fraser - schoolmaster - 6 papers
Allardice - assistant - 6 papers
5. John S Mackay: a schoolmaster scholar
We have already spoken of Muir. Let us look briefly now at the second most prolific member, another schoolteacher John S Mackay. He was brought up in Perth were he attended Perth Academy. He entered the University of St Andrews in 1859 and he graduated with an M.A., completing the course in 1863. He had taken the fixed course (all that was available when he entered) but now he wanted to carry on to take the new honours mathematics course which had just been introduced. He somehow didn't meet the regulations had to graduate with the M.A. he earned in 1863 two years later.
Mackay was appointed as a Mathematics Master at Perth Academy in 1863, spending three years in this post while he attended the Theological Hall with the intention of entering the United Presbyterian Church. However, he decided that he would make teaching his career and in 1866 he was appointed as a Mathematics Master at the Edinburgh Academy; he held this post until he retired in 1904. The University of St Andrews honoured him with the award an honorary LL.D. in 1884. Mackay was unmarried, lived at 69 Northumberland Street, Edinburgh, where he died at the age of 70. An obituary contains the following sad story of Mackay's research career:
Of all the great Alexandrine geometers, the works of one only, Pappus, remained to be edited. The Oxford scholars of the eighteenth century had neglected him, and a sixteenth-century Latin translation, together with a bare reprint of a small part of his text by a French editor, was all that was extant. For years, Mackay had given his holidays to the collation of manuscripts, and his nights to the patient interpretation of the old mathematician; and at last his work was done, and the whole book lay complete in his desk, in his beautiful handwriting, with a wealth of drawings. He went in one day to Williams and Norgate's foreign bookshop in Frederick Street, then managed by Mr Wheatley, an excellent scholar; and Mr Wheatley said, 'I've something today, Mr Mackay, that will interest you,' and he produced the first volume of Hultsch's edition of Pappus, a work that has held the field to this day, and is the Magnum Opus of its distinguished author. Mackay took the book home. He found that Hultsch and he had collated the same MSS., had arrived at the same interpretations, had noted the same difficulties, down to the smallest - a wrong letter, an omitted - the German had noted them all. Some men, in Mackay's place, would have made haste to send their own book to the printer, hoping to gain, by all but contemporaneous publication, some part of the scholar's reward. But Mackay had a sterner code of duty and of honour. The work was done, and well done; the needs of his fellow-students of Greek mathematics were sufficiently met; and what was lost was a matter for him alone. A few years later, in a less direct and poignant way, Mackay found himself forestalled by the publication of Allman's "Greek Geometry". This was a book that Mackay could have written to perfection, and perhaps with even greater learning than the Irish scholar displayed.
6. Edmund Whittaker's influence - colloquia of 1913 and 1914
One of the major influences on the Society was Edmund Whittaker. He was appointed Professor of Mathematics at Edinburgh in 1912 following the death of George Chrystal in November of the previous year. Whittaker had studied at Cambridge (1892-95) where he was elected a fellow of Trinity (1896) and continued as a lecturer, making revolutionary changes to the Cambridge courses based on his famous book A Course of Modern Analysis (1902). After six years as Royal Astronomer of Ireland (1906-12), he was appointed to the chair at Edinburgh. Whittaker was a broad mathematician, an excellent analyst familiar with the latest research developments but also deeply interested in the physical applications of mathematics. Soon after he arrived in Edinburgh, Whittaker set up the Edinburgh Mathematical Laboratory to give a practical side to his interest in numerical analysis. His influence on the Edinburgh Mathematical Society was rapid, for in 1913 they ran the first mathematical colloquium to he held in the UK. At first Whittaker was able to bring the schoolmasters to an understanding of the latest mathematical developments. Knott wrote:
The Mathematical colloquium organised by the Edinburgh Mathematical Society this year for the first time, began its meetings yesterday in the rooms of the Mathematical Department of Edinburgh University. The success of the movement is strikingly shown by the fact that the number of members is 76, of whom no fewer than 20 are professors or lecturers in Universities or University Colleges, nearly 50 are engaged in Mathematical teaching in secondary schools throughout England and Scotland, and the rest are occupied with the practical application of mathematics, as in the Census, Ordnance Survey, and Meteorology Departments of the Government. Special interest attaches to this course, as it is the first of its kind to be held in Great Britain, and also because of the fact that the newly-equipped Mathematical laboratory of the University is to be used by Professor Whittaker in his demonstrations on some of the more important applications of mathematics.Knott explained Whittaker's role in the Colloquium:
The idea of holding such a colloquium was an outcome of Professor Whittaker's announcement that he purposed organising, as part of the Mathematical Honours curriculum in the University of Edinburgh, a mathematical laboratory for systematic numerical discussion of functions and methods of calculation. Several correspondents had expressed the hope that vacation courses in this line of study might be established; and it was decided to make a first experiment. It was resolved, however, not to limit the colloquium to a discussion of one branch of mathematics, but to enlarge its scope by the inclusion of two other domains of mathematical thought. The broad features of the programme we owe to Professor Whittaker; and its variety was such as to appeal to all types of mathematical mind.The following courses were arranged:
- A Course of Five Lectures by A W Conway, Esq., M.A., D.Sc., Professor of Mathematical Physics, University College, Dublin, on The Theory of Relativity and the New Physical Ideas of Space and Time.
- A Course of Five Lectures by D M Y Sommerville, Esq., M.A., D.Sc., Lecturer in Mathematics in the University of St Andrews, on Non-Euclidean Geometry and the Foundations of Geometry.
- A Course of Five Lectures and Demonstrations by E T Whittaker, Esq., Sc.D., F.R.S., Professor of Mathematics in the University of Edinburgh, on Practical Harmonic Analysis and Periodogram Analysis; an Illustration of Mathematical Laboratory Practice.
Again in the following year a Colloquium was organised. It too had a large attendance by schoolteachers wanting to understand cutting edge developments in mathematics. The following short courses of lectures were arranged:
- Two lectures by M d'Ocagne (Professor at the École Polytechnique and the École Nationale des Ponts et Chaussées, Paris, and Past President of the Société Mathématique de France), on Nomography.
It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired.
- Four lectures by H W Richmond, M.A., F.R.S. (Fellow and Lecturer of King's College, Cambridge, and University Lecturer in Mathematics), on Infinity in Geometry.
The "line at infinity," the "cyclic points," and the "circle at infinity" are familiar conceptions, and may serve to indicate the class of questions to be discussed in these lectures.
- Four lectures by E Cunningham, M.A. (Fellow and Lecturer of St John's College, Cambridge), on Critical Studies of the Modern Electric Theories.
Of recent years most things in Physics have been explained in terms of electrons: and electric theories of the constitution of matter, gravitation, spectroscopy, etc., have been freely produced. Some of these theories will be described, and the points at which they are theoretically incomplete will be indicated.
- Two lectures by E T Whittaker, Sc.D., F.R.S. (Professor of Mathematics in the University of Edinburgh), on The Solution of Algebraic and Transcendental Equations in the Mathematical Laboratory.
The methods described will be chiefly arithmetical, and the lectures will therefore be supplementary to the lectures of Professor d'Ocagne on nomographic methods.
The list of members shows that nearly one hundred enrolled, an increase of twenty on the previous year. Members came from various parts of the British Isles, as well as from several European countries, America, South Africa, and India. Over thirty were professors or lecturers in Universities, but the majority were teachers in secondary schools and colleges. Astronomy, engineering, actuarial and statistical sciences, were also represented.
7. Scottish education in 1928
Changes took place in the Scottish universities which had a major impact on the Society. For example lecturers were employed from 1892 and the size of the university departments increased substantially. Other changes took place due to World War I - large numbers of young men had been killed with a major impact on the teaching profession. Universities were expanding and taking on those with research potential who no longer needed to find employment in secondary schools. The Scottish universities began to award Ph.D. degrees for an original research thesis from 1919.
|Natural Philosophy |
Charles Barkla *
Charles G Darwin *
Robin Schlapp *
* indicates EMS member
8. Whittaker and MacRobert - personality clash
Tensions began to come to the fore as Whittaker continued to drive the Society towards research - not the type to low level research advocated by Muir, but rather he wanted the Society to be world leading in research. Schoolteachers continued to join the Society, even graduates with poor honours degrees would join immediately after graduating. The mathematical talks at the meetings, however, reached a level where fewer schoolteachers were attending. There was no attempt to put on courses to bring members up to the current research level, the level of most of the talks. The colloquia, which had filled that role, had stopped due to World War I. They had started up again in 1926 due to Turnbull's enthusiasm and were held in St Andrews.
The schoolteachers, who continued to join the Edinburgh Mathematical Society, had a vigorous supporter within the Society. Thomas MacRobert was, like Whittaker, educated at Cambridge (1907-10). He spent his whole career in Glasgow, being appointed an assistant to George Gibson, the professor, in 1910 without having undertaken any research. It was six years before his first publication appeared (the important book Functions of a complex variable) and by this time he had been a lecturer at Glasgow for three years. He became professor when Gibson retired in 1927.
MacRobert and Whittaker were opposites in many respects. MacRobert was the left wing Labour supporter, a devout Protestant, and although an excellent mathematician, was rather old-fashioned in his approach. Whittaker was right wing, an Anglican who converted to become a Roman Catholic in 1927, and had a remarkable ability to keep pace with the latest mathematical developments to which he made substantial contributions. MacRobert and Whittaker joined the Society at around the same time (1911, 1912 respectively). MacRobert firmly believed that the Society should continue to provide a means for schoolteachers to continue their mathematical development.
Matters came to a head over the Society's publications. The Proceedings had contained articles by schoolteachers from its beginning, some of high quality but in the Muir spirit of research. The Mathematical Notes had been added to provide a means for publishing new proofs of existing results, short research notes etc. In 1927 MacRobert proposed expanding this into the Journal of the Edinburgh Mathematical Society which would publish articles of pedagogic interest, historical articles, etc. After battles in the Committee over a period of four years, MacRobert basically won the day except it must have been clear to him that he would not win over the title of the Journal. Fed up with the tensions in the committee he resigned.
An EMS Committee meeting took place on 6 March 1931 in Glasgow. It first decided on the title of the new Journal - The Scottish Mathematical Journal - then recorded MacRobert's resignation. A long discussion on the future of the Society followed. The following is recorded in the committee minutes:
Professor Whittaker expressed the view that we should in future become a research society, and leave the Glasgow Association to provide for school teachers [minutes were later changed and "school teachers" was replaced by "those whose main interest is pedagogic."] In that way, he stated, we should probably get grants from the research fund of the Royal Society. Experience had shown that it is impossible in the same Society to cater both for researchers and school teachers [again changed later as above]. In particular, he proposed that the publication of the new Scottish Mathematical Journal be held up for a time, while an approach was made to the Glasgow Association to see whether they would be responsible for the Journal. Professor Whittaker also suggested that the Society should give some initial financial assistance to the Association [added: in the event of their undertaking the publication of the Journal.]The next EMS Committee meeting took place on 1 May 1931 in Edinburgh. It first recorded William Arthur's resignation [He was the editor of the Mathematical Notes which was to raise its profile as the Scottish Mathematical Journal. He was a colleague of MacRobert at Glasgow] The future of the Society was again discussed:
Professor Whittaker repeated the main points of what he had said at the previous meeting. He outlined the growth of the Society; and urged that the time had come when two Societies were required. He urged that the publications of our own Society should be devoted solely to research, while a second Society should be responsible for the publication of papers of pedagogic interest and of the type of research which is of interest to those engaged [added: primarily] in the teaching of mathematics. He considered that such a division would be also a financial benefit to both kinds of work. He insisted that the friendliest relations should be maintained between the two Societies, and that this Society should help to finance the other at its start.An indication of the strength of feelings is shown by the fact that MacRobert prevented the Society holding meetings in Glasgow from 1931 until he retired in 1957. Glasgow meetings restarted following his retiral.
From 1931 onwards the number of schoolteachers in the Society became less, and it moved towards its position today of being essentially a research Society for university staff. However this did not happen quickly. The immediate reaction of the Society was not to follow Whittaker's wish, but it put on a full programme for the schoolteachers, mostly involving talks on mathematical education. However, schoolteachers did not return in numbers to the meetings and research talks soon became the norm.
9. Schoolteacher problem continues
At the first meeting of the session 1937-8, Alex Inglis (Bell Baxter School, Cupar, Fife) objected to the planned programme for the session, asking why there's nothing of interest to schoolteachers. Inglis did not attend the December meeting, so Etherington (the Secretary and a Lecturer at Edinburgh) wrote to him, informing him that the President, Mr Lawson, has arranged that Dr Mackie of Leith Academy would open a discussion on the teaching of mathematics in February. Etherington also commented on the possibility of catering for the schoolteachers at the mathematical colloquium, another request by Inglis, and mentioned that Whittaker has approached Inglis, explaining his own views on the matter. Etherington explained that he is "very sympathetic" to Inglis's point of view and that he thinks the responsibility for the "forgetfulness of teacher's interests" lies with the teachers on the Committee, who didn't object to the proposed syllabus.
Inglis replied approving of the planned discussion of teaching:
But there I am afraid is the snag! There is no doubt that Prof. Whittaker is right when he pointed out to me that very few school teachers attend meetings of the Society. Whether that is due to the type of programme offered or to the laziness (or indifference) of teachers to attend, I am unable to say. Probably is it a combination of both.
Concerning the Colloquium, I suppose that the same thing applies also, but nevertheless if at least I have "planted the seed" which may possibly bear fruit sometimes in the future, then maybe I shall have done something. As you say discussions may be arranged on the spot, as it were.
Speaking generally of my own views is that it is time that there was some such organisation in Scotland as the Mathematical Association in England. There is no provision at all for the teachers of Mathematics in Scotland who wish to know something of the progress made by others in his own craft. For this I blame primarily the teachers themselves, who are too indifferent to organise such an Association, and secondly I blame the Training Colleges. The latter seem to be staffed for the most part by those who do not have first hand knowledge of the teaching problems that confront us in the modern schools. This was made quite evident by the paper Mr Taylor gave last January.
The Training Colleges provide Summer Courses for teachers in Infant and Junior Schools, and give courses in Rural Gardening, Country Dancing and - possibly - Elocution, but as for a course say on the best way of teaching logarithms to those who know no algebra, or the best way of teaching the convergence and divergence of series to those who have merely reached the standard of the leaving certificate, these problems are never attempted; perhaps because there is no one in the Training Colleges competent to deal with them, or perhaps because if someone did attempt to deal with them then he would have no audience. Through the Central Mathematics Committee of the Educational Institute I have put forward this point of view, but I doubt is if will come to anything.
As far as I can see at present the only hope of such matters being systematically dealt with is the EMS, and hence my remarks at the meeting of 5th November.
I am very grateful to you for the trouble you have taken over this matter, trouble which may be of no avail as I have tried to explain, and I am sorry that you have had this extra work. However, perhaps in about a hundred year's time the name of Etherington will be regarded as that of the prime mover in the foundations of a Scottish Mathematical Association!
Article by: J J O'Connor and E F Robertson