# The History of Mathematics in Cambridge

Mathematics has been studied at Cambridge for a long time. The first figure of note is Robert Recorde (born about 1550) who is credited with the invention of the equality sign "=". He wrote several textbooks in the form of dialogues, but his last book ends with the author being arrested for debt.

Those with less antiquarian interests start their history a century or so later with Wallis, Barrow and Newton. (All three luminaries had interesting

non-mathematical careers. Wallis broke codes for the parliamentary side in the civil war. Barrow was noted for his strength and courage, and once when travelling in the East saved his ship by his own prowess from capture by pirates

. Newton took a very public part in the university's quarrel with King James II.)

The spectacular success of Newton's work had the fortunate effect of establishing the prestige of mathematics in Britain and Cambridge and the unfortunate effect of blinding British mathematicians to progress in mathematics elsewhere. The parochial century that followed was not a very glorious period for Cambridge or British mathematics. However, it witnessed a slow but important change

described in the next paragraph.

Over the years, the syllabus of the Medieval university had lost its relevance and the disputation by which it was examined became a mere formality. Sometime around 1725, a voluntary examination was instituted to help order the better students. At first, the examination was oral and consisted of questions on mathematics and some philosophy. Later, the candidates wrote their answers but the

questions were dictated and finally, in around 1790, the questions were printed. Thus was born the Cambridge Mathematical Tripos, the grandparent of every university examination in the world.

The examinations were held in January in the Senate House — a building which happens to be a very beautiful one, with a marble floor and a highly ornamental ceiling; and as it is on the model of a Grecian temple, and as temples had no chimneys, and as a stove or fire of any kind might disfigure the building, we are obliged to take the weather as it happens to be.

Sometimes the ink froze

in the inkwells.

Since the Mathematical Tripos was the only way in which students could show intellectual prowess, it was taken by many who went on to achieve distinction in other areas. A suitable example, given our present address, is provided by Thomas Clarkson who helped lead the fight against the slave trade. Even when examinations in other subjects became available, the Mathematical Tripos continued to

produce people like Keynes and Bertrand Russell who gained eminence in very different fields.

In the 1820s, a group of young mathematicians including Babbage (of the Analytical Engine) modernised the Tripos to take account of the work of continental mathematicians and the glory days of the examination began.

The details changed but, as described by Galton, the examination lasted five and a half hours a day for eight days. Those in the top class were (and still are) called Wranglers in an echo of the old system of disputation. The candidates were listed in order of marks with the top candidate being 'Senior Wrangler' the next 'Second Wrangler' and so on. In one list that Galton was allowed to

consult, the Senior Wrangler got more than 7,500 marks, the lowest Wrangler got about 1,500 marks and the lowest candidate to get honours (obtaining 'the wooden spoon') got 300 marks. Although the owner of the wooden spoon had 100 people above him, he in turn outclassed 300 'poll men' who failed or, more usually, did not attempt to obtain honours. (Galton was a poll man.)

The Tripos became something of a national event with substantial betting on the outcome. When, in 1890, Miss Fawcett was placed 'above the Senior Wrangler' (i.e. beat all her male competitors) this, according to the Dictionary of National Biography, 'materially advanced the cause of higher education for women and naturally gave her mother the greatest satisfaction'.

It may be doubted that a system in which the best students spent three years training to solve problems against the clock represented the ideal way to teach mathematics. However, this system was the nursery for the great flowering of British physics in the 19th century. Its products included Maxwell (2nd Wrangler), Kelvin (2nd Wrangler), Stokes (Senior Wrangler) and Rayleigh (Senior Wrangler).

On the pure side it produced Sylvester (2nd Wrangler) and Cayley (Senior Wrangler). Pearson, the father of modern statistics, was a 3rd Wrangler.

The 19th century Cambridge system concentrated on undergraduate teaching. Although good research was admired, it was not viewed as a professional duty and the university was not expected to provide support for it. A different view developed in France and then, still more strongly, in the great German universities. Over the course of the 20th century, Cambridge mathematics moved to align itself

first with the German model of a research driven university and then with the successor model presented by the major (post 1950) US universities.

Landmarks in this process include the publication of Hardy's *A Course of Pure Mathematics* (still, as a glance at Amazon will show, a best seller after nearly a century) and the abolition of the order of merit in the Mathematical Tripos in 1909. Present day exams are hard but not ferocious.

Under the old system, the best placed Wranglers could take a further exam in some of the higher branches of mathematics

for a Smith's prize. When Kelvin found an interesting result in three dimensional calculus, he communicated it to Stokes who set it as a question in the Smith's prize exam. It is now known as Stokes' theorem. The Smith's prize exam evolved into the present Part III, a one year postgraduate qualification taken by about 200 students from all over the world. From 1885, Smith's prizes (now supplemented by Rayleigh and Knight prizes) were given for an essay in mathematics instead. Today, this usually presents the student's own work after 4 terms of research. Past winners include Turing, Coxeter, Ingham, Hodge and Hoyle.

Although a Faculty like that of the 1930's which included Dirac, G. I. Taylor, Sir Harold Jeffreys, Phillip Hall, Hardy, Littlewood and Mary Cartwright could hardly be faulted on the grounds of research, the supporting structure seems strange to modern eyes. The Faculty met from time to time to decide who should lecture on what, but there was no communal building and everyone worked in their

own college.

In about 1960, the Faculty was finally organised into departments. These were housed in a very lightly converted old printing house and offices formerly owned by CUP and then awaiting demolition to make way for a new road. After 40 years, it became clear that, not only was the road never going to be built, but the growth of the Faculty had rendered the premises grossly overcrowded.

In an extraordinarily short time, enough money was raised to move both departments to splendid new buildings in the Centre for Mathematical Sciences (CMS) off Clarkson and Wilberforce Roads. (Wilberforce was another Cambridge anti-slavery campaigner.) Of the £61.4 million required for the whole building project, a total of £30.8 million, or 50%, came

from private sources. Another £14 million came from public funds, and the rest from within Cambridge.

Over the last hundred years, the Faculty has grown slowly but steadily and has become more and more international in its staff and students. We hope and expect that these trends will continue. As a result of these and other factors, some of which were discussed above, Cambridge has come to resemble other great mathematical centres much more than it used to. We think, however, that it retains

its commitment to teaching at the undergraduate and graduate level together with a certain mild eccentricity.

A search in the Mactutor archives for articles including the word 'Cambridge' will give a good idea of the mathematicians associated with Cambridge but does not include several important physicists. A search for articles including the word 'Wrangler' will give a good idea of the mathematicians who were undergraduates at Cambridge. The

Oxford Dictionary of National Biography web site can only be accessed by subscription but, if you can access it, a search for biographies including the word 'Wrangler' will reveal the place this distinction occupied in British life. (A search under 'Optime' gives some of those who attained honours at a lower standard.)