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Old Tripos Days at Cambridge V
Part of a version of an address to the South-West Wales Branch of the Mathematical Association, Swansea, on 2 March, 1935, by Andrew R Forsyth. It was published in The Mathematical Gazette 19 (234) (1935), 162-179.
The Tripos examination.
What of the examination itself, the goal of all the work ? The examining body, five in number, had no relation to the teaching. Each year two persons were nominated by the two colleges who belonged to the pair in a rota: each nominee might happen to be a lecturer in his college, but equally he might be a non-resident. The two nominated were the moderators for that year; they served for a second year with the title of examiners. The fifth member of the body (called the additional examiner) served for only a single year: always a man of distinction, but usually unrelated to the teaching, a sort of superior external examiner whose main duty centred in the latest advanced applied subjects included in the Tripos in the early 'seventies, the last straw on that camel's back.
All the papers were set for all the candidates alike in sheer ignoration of any preferences or preparation: there were no optional subjects; no picking or choosing among sets of questions, lettered and starred and numbered: no instruction limiting the number of questions to be answered. Nothing was said about full marks: they could be obtained only by full performance (which, let me say, would have been beyond the power of any examiner to achieve in the time, even with a full knowledge of the answers desired). There were two sections of the papers: the first extended for four days: the second, following after an interval of a little more than a week, lasted for five days.
During the first three days of the earlier section there was a limitation surviving from a past age: while subjects such statics, dynamics, astronomy, optics, hydrostatics, were included, the use of the differential and integral calculus was forbidden. There were questions in Euclid, to be written with the verbal rigour of an ancient style unknown to a modern generation. There was one question in arithmetic, a lonely poser: I have been told that, in some limited betting, long odds were always given against the Senior Wrangler obtaining any marks for that question. In preparing the list of successful candidates on this section, the examiners took account solely of the first three days' answers: the list was declared as qualifying the included candidates for honours. No standard for inclusion was fixed by the University: the unframed convention, transmitted from year to year, dared not exact a high percentage; and the competition, near the proverbial line that is never drawn beforehand, was keen indeed.
The qualifying list appeared on a Saturday; on the following Monday the second section began its five days' run. There were eight papers, of the bookwork plus rider type: there were two papers of problems, one by each of the two moderators. Some of these might be "do-able": most of them were not. They represented the inventive possibilities of the utmost range of the setter's fancy, without regard to teaching, or books, or suitability, perhaps fairly described in Pope's words
Tricks to shew the stretch of human brain,
Mere curious pleasure or ingenious pain.
In the "Five Days", the papers nominally covered all the subjects in the schedule: and the schedule was framed so as to include nominally all mathematics, there being no Part II or Part III or anything but simply the Tripos. Thus each subject perforce was scantily represented; all the questions ever set by an examiner, who had acted before, were eagerly scrutinised as though they were clues in a crossword puzzle. The papers were very long though there was a rubric requiring them not to contain more questions than a well-prepared candidate could answer in the time - with an inevitable inference that, in my day, there were no well-prepared candidates. In this section of the examination - the division into separated Parts came into operation only in 1882 - the stage was set for the grand competition in which all the interest and the excitement centred. All the training had prepared for a struggle which was an academic Grand National or Derby. Many of the questions were set at the ablest type of candidate alone, all other types being then ignored; indeed, towards the end, the very vocabulary of the questions belonged to an esoteric language strange to not a few of these successful candidates for honours. Of course, there was outside gossip as to the probable result: the dinner waiters in my college certainly ran a sweepstake in my own year: throughout the colleges there was eager speculation about the coming Senior Wrangler; and such speculation was not ill-informed, because usually the favourite won, down to 1882. I have said, down to 1882; for in those days there was only a single Tripos list, and the Senior Wrangler had his pride of place for the complete range of the study. It is true that only the men near the top of the list had answered a modest selection of the questions, but all questions were propounded unreservedly for all candidates. It often happened that two highly-placed men would be bracketed whose performances had little in common: lower down, the answers had become scattered fragments, often deserving no more than charity marks: in the humblest positions the differences became minute, and the ordered list ended in a dense ruck. But never in all the years had there been a bracket at the top of the old Mathematical Tripos.
The last paper was set on a Friday afternoon. On the succeeding Friday morning in the academic centre of the University, the Senate-House, as soon as the great bell of St Mary's in a tense silence had tolled the nine strokes for the hour, the Senior Moderator read the list to an assembled mob of alert undergraduates, who had come to the academic Senate-House in every conceivable costume that was not academic. It is the moment for yet another Senior Wrangler, an ephemeral embodiment of success and fame: it was the moment also for yet another Wooden Spoon, an equally ephemeral embodiment of the economy of labour endowed with a picturesque name. And, almost as in a day, they faded into the past, making way for another presentation of the old story, as unchanging as a nursery tale.
At this distance of time the Tripos seems interesting. As an institution it was well established; it bore high repute inside Cambridge; and it had a fascination for the sporting sense of a non-mathematical world outside. There was nothing in any university in the world that, for a student, was deemed comparable with the achievement of a Senior Wrangler. That outside world, even a large part of the small world resident in Cambridge, only saw a result in the form of an ordered list, never pausing to consider its significance and its influence.
But let me say a little about the whole course, as an insider. We students acquired good manipulative skill, possibly more expert for its purpose than is acquired today; but we became skilful mechanics rather than engineers. We were schooled indeed, even the ablest; but our education was imperfect. We were drilled in the gymnastic that led to swift answer according to rule and pattern. In the examination there was no leisure to think: even during our training there had been little leisure for thinking, because we always were being taught; and independence in reading was almost a misdemeanour in the eyes of some coaches. Further - and this is a grave charge against the style of competitive examination nominally intended for general qualification - most of the candidates had only the scantiest of tests after their long training. There would be a hundred or more candidates in any one year: many of the questions (including all that carried the highest marks) were utterly beyond the powers of all but a few of the hundred men; the vast majority had to scramble in mark-scraping. Yet all alike were the academic offspring of the one Alma Mater: all were sent out to the world with the same badge of graduation in honours. As an instance, avowedly extreme, let me state the mere fact that, in my year, the Senior Wrangler had fully sixty-five times as many marks as the Wooden Spoon. One of the two men may have been tested adequately; the other, certainly after the very earliest stages, could not have been tested at all; and he was not the only individual, out of more than a hundred men, neglected at the close of the long training of an undergraduate career. Any school inspector, with only a scrap of experience, would have denounced the examination: and no one, not even the Recording Angel himself, could induce me to believe that, except for the purpose of piling up marks in answer to a horde of questions, any Senior Wrangler was ever worth sixty-five Wooden Spoons.
With the production of the Tripos list the association of coach and pupil ended. They passed out of one another's lives; and the coach returned to the same round of drill with the pupils who were to go through the final mill. The ablest of the men who had achieved an adequate measure of academic success had to begin life all over again, endowed with an examination facility that soon became atrophied in most instances in the absence of any practice. Here there is a temptation to embark on a discussion of the aims, the subjects, and the spirit, of a university education. There can, of course, be no single universal aim; but to my mind, the production of experts, whether mathematicians or specialists of any type, ready for research, almost driven thither by enthusiastic mentors, should not be the dominating aim of any great school of thought in a university. Such a discussion would, however, be long-drawn-out; and it would involve issues different from those which I have tried to describe.
But I must not conclude this sketch of a past era without a final remark. Do not imagine that the old system was nothing but a merciless grind. Undoubtedly, it was stern in its demands. But it earned, and it has received, tributes of gratitude for its efficiency. Among its products (in so far as they have been its products) have been men of high distinction in State and Church and University, in public life, in learned professions, in the pursuit of science, in the advancement of learning. In my own time at Cambridge there had begun (though it was hardly so recognised) a ferment of opinion against the unmitigated domination of written examinations as the sole trustworthy test of ability and powers. For many years success in one or other of the Triposes had been the only avenue to office, whether professorial inside or outside Cambridge or administrative within the several colleges. But other qualities began to be exacted. My own college had taken the initiative by requiring, from a candidate for fellowship, a thesis or a dissertation as evidence of constructive ability; and the spirit of that example spread. Nowadays there seems a tendency to rush to an opposite extreme in proceeding to the selection of individuals for responsible positions. Research (often spelt with a capital R) is made the prominent requisite; and some original production, perhaps with little enquiry as to its significance and seldom with any enquiry as to the inspiring share of a professor, becomes a dominant testimonial, occasionally to the comparative neglect of the indispensable qualities of human personality. Again I must warn myself off disputable ground beyond the boundaries of my theme; so let me end by commending to your consideration my sketch of one chapter in the mathematical history of a vanished age.
The Introduction is at THIS LINK
Last Updated April 2020