Cambridge Papers

by W. W. Rouse Ball

The general effect of these changes was to destroy the homogeneity of the tripos. Objections to the new scheme were soon raised. Especially, it was said—whether rightly or wrongly—that part I contained too many technical subjects to serve as a general educational training for any save mathematicians; that the distinction of a high place in the historic list produced on its results tended to prevent the best men taking it in their second year, though by this time they had read enough to be able to do so; and that part II was so constructed as [306] ]to appeal only to professional mathematicians, and thus the higher branches of mathematics were neglected in the University by all save a few specialists.

Whatever value be attached to these opinions, the number of students studying mathematics fell rapidly under the scheme of 1886. In 1899 the board proposed^[79] further changes. These seemed to some members of the senate to be likely still further to decrease the number of men who took up the subject as one of general education; and the two main proposals were rejected, 15 February 1900 by votes of 151 to 130 and 161 to 129.

A few years later, in 1907^[80], the board brought forward another scheme, proposing changes so sweeping as almost to destroy the identity of the tripos. Under this the examination in part II was abolished—a change on which all parties were agreed. There was introduced an examination, called part I, confined to elementary mathematics, which could be taken as early as the second term of residence, and for which in certain cases of failure a student could present himself again, but this, although an examination for honours, did not qualify for a degree. [307] ]In the new part II, taken normally at the end of the third year of residence and qualifying for a degree, candidates were given some option in the subjects of their examination, and order of merit was abolished. The first examination under this scheme was held in 1908.

A remarkable feature in the history of the Cambridge mathematical school is the fact that for nearly two hundred years most students were accustomed to rely for preparation for it on work done with a private tutor or “Coach.” Towards the close of the seventeenth century we first read of these “pupil-mongers” (among whom Laughton of Clare was the most famous) who made it their business to prepare men for their “acts.”

With the rise of the senate-house examination the importance of this class of teachers increased, for success in that examination was regarded as the crown of the academic course, and brought with it, in the shape of a fellowship, an immediate competence with a reasonable prospect of an assured career. It was the business of private tutors to prepare their pupils for the examination, and among those who in this way came to the front shortly after the middle of the eighteenth century were Richard Watson, John Wilson whose name is still known by its association with a proposition in the theory of numbers, and Robert Thorp. The last named [308] ]teacher was described, about 1761, as being “of eminent use to young men in preparing them for the Senate-House Examinations and peculiarly successful”; and it was added that “one young man of no shining reputation with the assistance of Mr Thorp’s tuition had stood at the head of wranglers.”

In a grace of the senate, passed in 1781, it is stated that almost all sophs then resorted to private tuition, and for more than a century subsequently, the practice was well established. These were the men who really directed the reading of the students. Even non-residents, if reputed to be successful coaches, drew pupils. Thus John Dawson, a medical practitioner at Sedbergh, regularly prepared pupils in the vacations for the senate-house examination, and at least eleven of the senior wranglers between 1781 and 1800 are known to have studied under him.

During the nineteenth century the system developed under two remarkable teachers, William Hopkins, 1793–1866, and Edward John Routh, 1831–1907, to whom the vast majority of the better known Cambridge mathematicians of this century owed most of what they learnt in their undergraduate days. Hopkins in the twenty-two years from 1828–49, had among his pupils one hundred and seventy-five wranglers, of whom seventeen were [309] ]senior, forty-four in one of the first three places, and one hundred and eight in one of the first ten places. So too Routh, in the thirty-one years from 1858–88, had between six hundred and seven hundred pupils, most of whom became wranglers, twenty-seven being senior in the tripos and forty-one Smith’s prizemen. To organize teaching on this scale demanded rare gifts.

Perhaps it may be of interest to describe, by way of example, the general features of Routh’s system. He gave catechetical lectures three times a week to classes of eight or ten men of approximately equal knowledge and ability. The work to be done between two lectures was heavy, and included the solution of some eight or nine fairly hard examples on the subject of the lectures. Examination papers were also constantly set on tripos lines (bookwork and riders), while there was a weekly paper of problems set to all pupils alike. All papers sent up were marked in public, the comments on them in class were generally brief, and, to save time, solutions of the questions were circulated in manuscript. Teaching also was supplemented by manuscripts on the subjects. Finally to the more able students he was accustomed, shortly before their tripos, to give memoirs or books for analyses and commentaries. The course for the first three years and the two earlier long vacations covered all the subjects of the [310] ]examination—the last long vacation and the first term of the fourth year were devoted to a thorough revision.

Under Hopkins and Routh there was no trace of what is called cramming; they might say that a particular demonstration was so long that it could not be required in the tripos, but none the less they expected their pupils to master it. The system had faults, but it had the merit of providing a systematic grounding in a wide field of subjects. The effectiveness of teaching of this kind was dependent on intimate constant personal intercourse, and the importance of this cannot be overrated. The scandal of the system consisted in the fact that a man was compelled to pay heavy fees to the University and his College for instruction, and yet found it advantageous at his own expense to go elsewhere to get it.

During the last quarter of the nineteenth century college lecturers began to share with the coaches the general direction of studies. Post-graduate work was also to some extent brought under the influence of professors and university lecturers—these not uncommonly suggesting subjects for dissertations for fellowships, Smith’s prizes, etc. But the students thus influenced were not numerous, and it still remains true that the majority of mathematical undergraduates are so out of touch [311] ]with the professors in the subject as to be unacquainted even with their personal appearance.