I 



NA TURE 



49 



THURSDAY, NOVEMBER 21, 1878 



MATHEMATICS AT CAMBRIDGE. 



THE Cambridge Examination for Mathematical 

 Honours has for a long time enjoyed a high re- 

 putation, especially among Cambridge men, who have 

 been accustomed to point to it as the model of what 

 an examination should be. The credit thus claimed 

 has been in past times more or less deserved, but to 

 what extent it is so now is a question on which there 

 may be variety of opinion. Like every other institution, 

 the practical usefulness of which depends upon the ease 

 with which it can adjust itself to external conditions, the 

 Tripos examination must undergo changes to meet cor- 

 responding changes from the outside ; and there may 

 come a time when the external conditions operate so 

 powerfully that mere modifications are insufficient, and 

 when the changes made must be both radical and ex- 

 tensive. The old Tripos system has recently been put 

 to a severe strain, and it is admitted on all hands that 

 the result has proved unsatisfactory. We propose to 

 inquire into the causes which have brought this about, 

 and to discuss the measures by which it is hoped the 

 evil will be met. 



It may be laid down as a fundamental axiom that a 

 university honours examination should be in harmony 

 with the studies of the candidates, and that it should be 

 reasonable in its demands upon them. What the very 

 best students may be expected to answer after faithful 

 work during their undergraduate course should clearly 

 be taken as a guide in fixing a superior limit to the 

 number and difficulty of the questions. Nor should this 

 estimate be pitched too high, because there are other 

 subjects of interest and study besides mathematics, in 

 which it is desirable that even the best of young mathe- 

 maticians should engage, and an education based on 

 mathematics alone must necessarily be defective. 



If we accept these propositions we must admit that the 

 estimate of what is reasonable towards the candidates 

 was very different fifty years ago to what it is now. One 

 cannot help looking back with regretful eyes on the Tri- 

 pos questions of that time, so remarkable for their sim- 

 plicity and elegance, as well as for the happy appreciation 

 of the degree of difficulty such questions should possess. 

 The questions of more recent times, although they are 

 often to be admired from an aesthetic point of view, are 

 in many instances far beyond the reach of any but the 

 very best men, and may be described as being somewhat 

 too difficult and elaborate. 



There are obvious reasons why, as time goes on, the 

 questions should become more difficult ; stiU it would be 

 interesting to trace the changes over some considerable 

 period, so as to be able to explain how the Tripos ex- 

 amination has reached its present form. The changes 

 must have been of a gradual character, because the tra- 

 ditions and customs of the examination have been faith- 

 fully transmitted from one set of examiners to the next. 

 One can see, however, that if any particular person were 

 to examine often, as has occasionally happened, or if 

 several persons of like tastes were to examine together, 

 *e should find the questions displaying a particular bia?. 

 Vol, XIX. — No. 473 



When this should occur, the studies of the candidates 

 would receive the same bias, and particular^branches of 

 mathematics would thus be pushed for a time into undue 

 importance. So much was this the case about the year 

 1864 that Sir G. Airy, when delivering the Rede lecture 

 in the Senate House, went out of his way to denounce 

 the excessive attention given in the University to certain 

 branches of pure mathematics. 



We can thus imagine the Tripos examination based 

 upon the traditions of its predecessors, yet continuing 

 to grow both in extent and difficulty, and with some of 

 its features perhaps somewhat exaggerated. In 1873 a 

 great change had to be made. The University, feeling 

 it was not creditable to it that so little encouragement 

 should be given to the higher branches, and especially 

 to the great modem subjects of mathematical physics, 

 determined that those subjects should be introduced into 

 the Tripos examination. The additions thus made, be- 

 sides considerable extensions in the subjects already 

 existing, included, amongst others. Elliptic Functions, 

 Electricity, Magnetism, and Heat. 



It was thought that in thus extending the examination 

 the students would have a choice of subjects, and that 

 their course of study would thereby be rendered more 

 interesting than it was before. It was certainly never 

 intended that the burdens under which the Tripos can- 

 didate was already staggering, should be increased upon 

 him. But how were these changes met on the part of the 

 students and on the part of the teachers ? The imme- 

 diate result seemed to be that the best candidates at- 

 tempted to know something of all the subjects. The 

 examiners in 1874 were careful to watch for indications 

 as to whether the candidates had devoted themselves to 

 special groups, but they reported that there was no 

 evidence to that effect. The University thereupon passed 

 a Grace enacting that the number of questions in the 

 higher subjects should be increased, the object being to 

 supply a sufficient variety so that a candidate who had 

 confined his studies to a limited group might reasonably 

 expect plenty to occupy him in the examination. This 

 provision has continued operative down to the present 

 time, but it does not appear to have produced the salutary 

 effect intended. There is much reason to fear that the 

 best candidates still push their way through most of the 

 subjects, whilst the next best struggle as far in the same 

 direction as they can. 



There is then a well-defined evil^ to be remedied. 

 For no one can deem it a good education where the 

 student is carried, necessarily with rapidity, over a variety 

 of subjects, many of which he must therefore very imper- 

 fectly comprehend. What changes in the examination 

 are proposed to the University as a remedy we will pre- 

 sently describe. Meanwhile let us glance at the position 

 of the teachers in their relation to. the new state of affairs. 



It must be admitted that the great changes made in 

 1873 found the college lecturers unprepared. There were 

 only one or two of them who ventured to expound the 

 new subjects to college classes. The students were there- 

 fore compelled to depend upon the private tutors, and 

 thenceforth the selection of groups became difficult, if not 

 impracticable. The fact we have just mentioned was, in 

 truth, a misfortune in ifiore ways than one. For the 

 new subjects, and, indeed, the higher subjects generaUy 



