T H E
PROMOTION OF RESEARCH;
Special Reference to the Present State
SCOTTISH UNIVERSITIES AND SECONDARY
THOMAS MUIR, M.A., F.R.S.E.,
PRESIDENT OF THE SOCIETY.
ALEXANDER GARDNER, PAISLEY.
LONDON: 12 PATERNOSTER Row.
This address, written hurriedly during the pressure of other work, was undertaken in order to discharge an obligation to the Mathematical Society, and was not meant for further publication. Immediately after it had been read, however, a strong desire was expressed by office-bearers and other members present to have it printed and published in the ordinary way. If I had from the first intended it so to appear, I should doubtless have adopted a somewhat different style, and have taken pains to make it a more substantial contribution to the discussion of so important a subject. As I cannot afford the time now to recast it, I print it with some hesitation exactly in the form in which it was read, hoping merely that it may find readers as indulgent as the Edinburgh audience for which it was prepared.
Mr Chairman and Gentlemen,
Immediately after you had done me the honour to elect me President of the Society, I somewhat unexpectedly learned that in the programme of the session there was included a President's address. In ordinary circumstances it would have been more pleasing to me to have the item entitled the President's Paper, or the President's Half-hour at the Black Board. As matters stand, however, the society being still young in years, and still engaged in feeling its way towards firm ground, it seems to me there are not a few things worthy of our consideration, which can be treated of without the use of chalk and symbols.
It is of importance to us, for example, to recall at intervals the ends we had in view in uniting ourselves together to have suggestions made of any new means whereby these ends may be the better furthered, and to take interest, as a body, by discussion and friendly criticism, in anything outside the society that either seeks the same ends as we do, or exercises an unfavourable influence on the advancement of them. Again, it is of value to us to hear, as we did last session, some one who has travelled in more realms than one of the mathematical universe, tell us in what districts labour and skill are urgently needed, what lands are lands of promise, and what kind of workmen this or that field is suitable for.
Of these two classes of subjects I select the former as being that with which I am the less unfitted to deal in the so-called address. I say 'so-called' because I have a lingering feeling against the use of the term. For the nonce I should wish separated from it the ideas of authoritative wisdom and paternal advice which it sometimes connotes. In what I have got to say I have no counsel to give the members of the society: my wish is rather to take counsel with them on a subject in which, as their membership implies, they evince a cordial interest - the Promotion of Mathematical Research.
I assert at the outset as an established fact that we do not, as a nation, take that part in research which, considering the amount of our population, our advancement in civilization, and the acknowledged capabilities of our people, we ought to take. Writers of other nationalities tell us so, and many of our own most eminent men have thought it their duty to draw attention to the fact. And what is true of research generally is more manifestly true of research in pure Mathematics. Whatever means of publication we think of - books, journals, or the serials of learned societies, - we find they have all the same tale to tell of disproportionate unproductiveness. Books containing original work in pure Mathematics are now rare in almost any country; in Scotland, however, their number is practically nil: of journals, we have none: and our only society to be honourably mentioned as publishing memoirs and shorter communications on the subject of Mathematics is the Royal Society of Edinburgh. It is the Transactions and Proceedings of this Society alone, that have for a long period of years saved us from utter reproach. (We have good ground to hope that as it has been in the past with the Royal Society, so it will be even more abundantly in the future: and such, I am sure, is the sincere desire of every member of the Mathematical Society; not only so, but we should even consider that we had fulfilled part of our aims, if our Society were the means of encouraging and bringing to light young men of ability in research, who might honourably aspire to recruit the ranks of the Royal Society.) One is, of course, reminded in stating facts of this kind regarding the backwardness of Scotland, that the home of Scotsmen is abroad, and that, were we to take nationality as against nationality, the result might be different. No doubt there are crumbs of comfort to be got in this way. They do not, however, by any means make up the deficiency; and even if they did, the serious question would remain, whether it was good or bad policy for a country to export more than it could well spare. But let any one try to count up the number of Scotsmen resident in England or abroad who publish original work in pure mathematics, and the stern fact will meet him as before, that though we may produce many promising students of mathematics and our share of successful examinees, we do not turn out mathematicians able and willing to advance the boundaries of their subject.
Little need be said by way of pointing out that this is not as it should be. Workers in even the nonmathematical sciences would consider it a matter for regret, and students of general history would regard it as a fact of unpleasing import. The reason for it is not that Mathematics is despised or underrated in Scotland: we know, on the contrary, that it is as widely taught here, and valued at the very least as highly as in any other country. Nor can this so far gratifying fact be for a moment held as a palliation of the other: it rather only adds increased significance to it. It points to teachers and methods of teaching that are either devoid of vitality, or are alive with a depressing utilitarianism. I venture to say that the teacher, who never feels a desire to know more of his subject than what his text-books give him, takes a low view of his profession; and that the teaching, which never kindles in the hearer a spark of enthusiasm for his subject, or awakens in him a longing to know more and to explore for himself, is not the highest kind of teaching, but fails in a vital point. As for the historical significance of the decline of original research in a nation, so far as this regards Mathematics I cannot do better than quote the eloquent and impressive words of the late Professor Henry Smith of Oxford, who from his wide culture and general robustness of mind was one of the last men to take a one-sided or pessimistic view. "In these days," he says, "when so much is said of original research and of the advancement of scientific knowledge, I feel that it is our business to see, that so far as our country is concerned, mathematical science should still be in the vanguard of progress. I should not wish to use words which may seem to reach too far, but I often find the conviction forced upon me that the increase of mathematical knowledge is a necessary condition for the advancement of science, and, if so, a no less necessary condition for the advancement of mankind. ... Perhaps also," he continues, "it might not be impossible to show, and even from instances within our own time, that a decline in the mathematical productiveness of a people implies a decline in intellectual force along the whole line; and it might not be absurd to contend that on this ground the maintenance of a high standard of mathematical attainment among the scientific men of a country is an object of almost national concern."
When we begin to think of the agencies whereby mathematical research may be revived, the mind turns at once to the UNIVERSITIES, one of the great functions of which is the advancement of knowledge. Of recent years, it is true, doubts have been expressed as to the wisdom of combining instruction and research, and strong arguments have been given for the establishment of national institutions devoted to research alone. Colonel Strange's opinion on this point was very strong, and no man of his time did more than he to draw attention to the whole subject, and to rouse the country from the languor into which it had fallen. In his evidence before the Royal Commission on the Advancement of Science, he says:- "I consider education to be quite a different thing from national research, that they should be kept as distinct as possible, and that one great evil now existing is the mixing up of those two things." Although Colonel Strange was not alone in holding this view, the great bulk of opinion, now at least, is in favour of it only so far as certain special subjects are concerned, the line being drawn so as to include such departments of science as Astronomy, Meteorology, Solar Physics, etc., which more immediately affect the national welfare, and for the pursuit of which extensive collections of apparatus are required at particular spots of the earth's surface. At any rate, public opinion is not ripe for the separate endowment of Mathematical research;- and yet, had the Government stepped forward when it was necessary for Professor Sylvester to leave his country and go to America, and said, "We shall be proud to have you draw upon us for a sufficient income: do as you have been doing, and we shall ask no questions," - had the Government, I say, done this, there would have been many to applaud and few but the ignorant to condemn.
To the Universities, then, in the first place, we must look for aid. Leaving for the moment the question of the doing of original work by the professors themselves, let us look at the means employed for making original workers out of promising students. It is in this we in Scotland most fail. 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. 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? Is it altogether absurd to suggest that a graduate who gains a scholarship should remain during the tenure of his scholarship in his own university, there to grow in knowledge under his favourite professor's guidance, to learn to teach, to be initiated into independent research, and to be a cord of strength to his alma mater and to his country? Surely there are no vested interests with ogre eyes in the way here. There need be no additional lectures for the scholar's benefit:- if at the age he has reached he cannot pursue his own reading in the higher subjects, it may be safely affirmed that he never will. His experiments in teaching need be a loss to no one:- to many a student preparing for a degree examination, or desirous of knowing a special subject, they would undoubtedly prove a gain. His attempts at independent literary work need harm nobody:- his professors would be only too glad to put minor problems in his way, and if by chance he had the enthusiasm to carry him safely through a piece of the so much wanted bibliographical work, fellow-labourers the world over would rise and call him blessed.
It may be objected to this scheme, that the independent literary or scientific work of such an author would not be worth much. I reply that the scheme is not proposed with this intention. The work would be avowedly 'prentice-work, and the time to judge of its value would come when the author had reached the full maturity of his powers. But I go farther, and say, that although it is not a sine qua non that the work should be valuable, still it is absolutely certain that not a jot of it need be valueless, or unworthy of being put on record. The amount of useful skilled labour which is needed for the advancement of mathematics, or indeed of any science, is practically unlimited; and surely a graduate capable of gaining one of the few scholarships or fellowships of a poor but numerously-attended university, is capable of at least this skilled labour. And then, who doubts but that what has happened elsewhere would happen with us, that occasionally men of original power would arise whose very first-fruits would be all-important, and who would redeem in one year more years of mediocrity than their predecessors had left to be redeemed.
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. Of this there can be no reasonable doubt, because we know that under the present imperfect arrangements quite a number of positions such as these have recently been secured by graduates whose whole University education had been obtained in Edinburgh. The answer to the second question we may give in the national manner, by asking in return if Cambridge of recent years has done anything more than this for her ordinary wranglers. If she has, it is due to nothing else than the lamentable system in vogue which marks out Cambridge as a University, and the so-called Universities of Scotland as Schools.
We often hear it said that, other things being equal, the mathematician who hails from Cambridge has in competitions for professorships and masterships a marked advantage. Very probably this is true; and probably also it has been found to hold when other things were not equal. But in ordinary fairness we must bear in mind that, as matters are at present arranged, when the said other things are not equal, it amounts almost to certainty that the inequality is not due to the inferiority of the Cambridge-trained man. How could it be otherwise? There is a three years' course of mathematical drill at Cambridge not to be matched in any other country of the world. The course may be well planned or ill planned, the drill may be carried out on wise or unwise principles, but there it is, and its like is to be got nowhere else, certainly not in Scotland. So long as this is the case, we must be prepared to see repetitions of the appointments complained against, and must school ourselves to be moderately thankful when, as recently, other Universities get a chance.
This superiority of Cambridge, I have said, is quite independent of the question whether the system pursued there be in its details good or bad. There are many thoughtful mathematicians and other men of science, even among those who have enjoyed a Cambridge training, who are strongly of opinion that it is not by any means wholly good. They deprecate the breakneck pace, and the utilitarian spirit which sacrifices everything to what is known to 'pay' in examinations; and they deplore that almost unique and absolute power it possesses of quenching originality. The perfect man under the Cambridge system is too often, they say, the man who can merely acquire mathematical theorems and methods with rapidity, and reproduce them on demand with like speed. As for the student of high reflective powers or the student of genius, we are asked to believe that unless he is also endowed with great strength of mind and will, he will not come out of the ordeal unscathed. Now, it is mainly students of these two latter types that, for the purposes of research, a University ought to cherish and develop. And my contention - made with all deference - is, that the Scotch graduate who spends three additional years in his own University, following out the course I have indicated, partly and chiefly devoting himself to the study of the higher departments of his subject in continuation of his undergraduate course, partly busying himself with teaching and lecturing, partly engaged in literary work and mathematical investigations, and all this under the eyes of professors earnestly occupied themselves in similar ways - such a graduate, I say, has every chance to turn out a better man for his profession than the graduate of Cambridge under the present regime. We recognise, as has been said, two qualifications for a professorship - skill to instruct and ability for research: it is hard to see where there are now at Cambridge special facilities for obtaining either the one or the other.