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 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 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.