Mathematical Tripos

According to the study Masters of Theory: Cambridge and the Rise of Mathematical Physics by Andrew Warwick[7] during this period the style of teaching and study required for the successful preparation of students had a wide influence:

• on the development of 'mixed mathematics' (a precursor of later applied mathematics, descriptive geometry and mathematical physics, with emphasis on algebraic manipulative mastery)[7][4]
• on mathematical education
• as vocational training for fields such as astronomy
• in the reception of new physical theories, particularly in electromagnetism as expounded by James Clerk Maxwell

Since Cambridge students did a lot of rote learning called "bookwork", it was noted by Augustus De Morgan and repeated by Andrew Warwick[7]^: 152 that authors of Cambridge textbooks skipped known material. In consequence, "non-Cambridge readers ... found the arguments impossible to follow."

From the 1820s to the 1840s, analytic topics such as elliptical integrals were introduced to the curriculum. Under William Whewell, the Tripos' scope changed to one of 'mixed mathematics', with the inclusion of topics from physics such as electricity, heat and magnetism. Students would have to study intensely to perform routine problems rapidly.[4]

The early history is of the gradual replacement during the middle of the eighteenth century of a traditional method of oral examination by written papers, with a simultaneous switch in emphasis from Latin disputation to mathematical questions. That is, all degree candidates were expected to show at least competence in mathematics. A long process of development of coaching—tuition usually outside the official University and college courses—went hand-in-hand with a gradual increase in the difficulty of the most testing questions asked. The standard examination pattern of bookwork (mostly memorised theorems) plus rider (problems to solve, testing comprehension of the bookwork) was introduced.

The list of wranglers (the candidates awarded a first-class degree) became in time the subject of a great deal of public attention. According to Alexander Macfarlane[8]

To obtain high honours in the Mathematical Tripos, a student must put himself in special training under a mathematician, technically called a coach, who is not one of the regular college instructors, nor one of the University professors, but simply makes a private business of training men to pass that particular examination. Skill consists in the rate at which one can solve and more especially write out the solution of problems. It is excellent training of a kind, but there is not time for studying fundamental principles, still less for making any philosophical investigations. Mathematical insight is something higher than skill in solving problems; consequently the senior wrangler has not always turned out the most distinguished mathematician in after life.

William Hopkins was the first coach distinguished by his students' performances. When he retired in 1849, one of his students, Edward Routh became the dominant coach. Another coach, William Henry Besant published a textbook, Elementary Hydrostatics, containing mathematical exercises and solutions such as would benefit students preparing for Tripos. After Routh retired in 1888, Robert Rumsey Webb coached many of the top wranglers. Warwick notes that college teaching improved toward the end of the 19th century:

The expansion of intercollegiate and university lectures at all levels through the 1880s and 1890s meant that, by 1900, it had become unnecessary for coaches either to lecture students or even to provide them with manuscripts covering the mathematical methods they were required to master. The prime job to the coach now was to ensure that students were attending an appropriate range of courses and that they understood what they were being taught. … This curtailment of responsibility made it virtually impossible for a private tutor to dominate undergraduate training the way that Hopkins, Routh, and Webb had done.[7]^: 282

A fellow of Trinity College, Robert Alfred Herman then was associated with several of the top wranglers as their coach; evidently the university was finally providing their students with education.

When A. R. Forsyth wrote his retrospective in 1935, he recalled Webb, Percival Frost, Herman, and Besant as the best coaches. Other coaches that produced top wranglers include E. W. Hobson, John Hilton Grace, H. F. Baker, Thomas John I'Anson Bromwich, and A. E. H. Love.

Apart from intellectual preparation, the challenge of Tripos was its duration: "The examinations themselves were intended partly as tests of endurance, taking place on consecutive mornings and afternoons for four and five days together."[7]^: 186 Brisk walking was taken up by many candidates to build up their stamina. As the nineteenth century progressed walking turned to athletics and other competitive sports including rowing and swimming. The coaches set the example: Routh had a two-hour constitutional walk daily, while "Besant was a mountaineer, Webb a walker, and Frost was extremely proficient in cricket, tennis, running and swimming."[7]^: 200 By 1900, there were twenty-three recognized sports contested at Cambridge.

In 1873, Sarah Woodhead became the first woman to take, and to pass, the Mathematical Tripos.[9]

In 1880, Charlotte Angas Scott obtained special permission to take the Mathematical Tripos, as women were not normally allowed to sit for that exam. She came eighth on the Tripos of all students taking them, but due to her sex, the title of "eighth wrangler," a high honour, went officially to a male student.[10] At the ceremony, however, after the seventh wrangler had been announced, all the students in the audience shouted her name. Because she could not attend the award ceremony, Scott celebrated her accomplishment at Girton College where there were cheers and clapping at dinner, a special evening ceremony where the students sang "See the Conquering Hero Comes", received an ode written by a staff member, and was crowned with laurels.[10] After this incident women were allowed to formally take the exam and their exam scores listed, although separately from the men's and thus not included in the rankings. Women obtaining the necessary score also received a special certificate instead of the BA degree with honours.

In 1890, Philippa Fawcett became the first woman to obtain the top score in the Mathematical Tripos.[11][12]