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William Hopkins (1793–1866) was the fi rst of two remarkable private tutors at Cambridge, who dominated the teaching of the university while remaining detached from the formal tuition provided by the colleges. His outstanding successes were matched only by those of his former student and successor Edward J. Routh. Figure 1 shows an engraved portrait of Hopkins, aged perhaps in his mid-fi fties. His long face, clean-shaven in a much bewhiskered age, has a rather prominent nose, and his eyes seem clear and piercing below dark brows. An oil portrait of a somewhat older Hopkins, by Henry William Pickersgill R.A. (1782–1875) and now hanging in the Fellows’ Parlour in Peterhouse, Cambridge, is reproduced in Plate 1 of Chapter 6. It is recognisably of the same man, tall, dignifi ed, straight, and slim. This may have been painted to mark Hopkins’ retirement in 1860.

For much of Hopkins’ time, the B.A. (Batchelor of Arts) honours degree was awarded on the sole basis of performance in the Mathematical Tripos examinations. The lists of successful honours candidates were each year divided into three categories, called “Wranglers”, “Senior Optimes” and “Junior Optimes”. In present-day parlance, these categories correspond to fi rst-, second- and third-class honours. Within each category, candidates were listed in order of merit. The senior wrangler was top of the list, followed by the second and third wranglers, etc. These order-of-merit listings began in 1747 and ceased in 1909.

Evidence of student life in the unreformed university comes from a variety of sources, offi cial and unoffi cial. Of several fi rst-hand accounts by students, the most notable is that of the American Charles Astor Bristed, whose book, (Bristed 1852), was published in New York to describe to his compatriots just what university life in England was like. Bristed’s book has been described as “the most detailed and the most thoughtful memoir of Cambridge undergraduate life ever penned.”4 Rather earlier student recollections are those of Solomon Atkinson and his nearcontemporary John M.F. Wright, who took the Tripos examinations in 1821 and 1819, respectively.

John Venn was equal sixth wrangler in 1857 and later became the President of Gonville & Caius College, a post second only to the Master. His book (Venn 1913) concludes with a delightful appendix on “College Life and Ways Sixty Years Ago”, vividly describing his own student experiences in the 1850s. The writer Sir Walter Besant also makes interesting remarks on his education, fi rst at King’s College, London and then at Cambridge during the 1850s (Besant 1902). By way of introduction, we use the writings of Atkinson, Wright, Bristed, Venn and Besant to illustrate student life and students’ views of the university: two from just before the period of Hopkins’ wranglers, and three towards its end.

The 1830s were a politically turbulent time. Governmental power oscillated between the Whigs and Tories, and radical groups were increasingly vigorous and vociferous. In the aftermath of the Napoleonic Wars, the wages of the working class had decreased whereas taxes and the price of food had increased to meet the huge fi nancial deficit.

It is incorrect to think of the Tories, on the one hand, as the party of the aristocracy and wealthy landowners; and of the Whigs, on the other, as the party of the meritocracy, intent on reforming out-dated practices and vested interests. In fact, Earl Grey’s Whig cabinet of 1830 was composed entirely of aristocrats.30 Leading Tories were Lord Wellington, Viscount Palmerston and Sir Robert Peel (the younger); and prominent Whigs were Earl Grey, Lord John Russell, Lord Henry Brougham and Viscount Melbourne. All just mentioned, except the brilliant but unpredictable Brougham, served periods as Prime Minister. Though some Whigs were keen reformers, many were reluctant to associate with more extreme radicals who shared some of their opinions. Only later, from 1847 and under the leadership of W.E. Gladstone, did the whole Whig party become identifi ed with Liberalism.

In the early nineteenth century, the quality of education and the conduct of examinations at Cambridge were haphazard. There were no set academic criteria for entry, and students arrived from disparate backgrounds and with disparate ambitions. Sons of the nobility and of wealthy, landed gentry often had little interest in study and much in self-indulgence. But they formed only a small, if prominent and rowdy, minority. Many students were hard-working and came from backgrounds that were not particularly affl uent. The long-term aim of many was to secure a Church of England living. The most able set their sights on obtaining a college fellowship, for which a high place in the fi nal Mathematical Tripos examinations was virtually essential. (Only Trinity College had separate fellowship examinations, which were not restricted to mathematics. Other colleges awarded fellowships on the basis of the Tripos results, including, from 1824, the Classical Tripos.) From the comfortable position of a fellowship, a graduate might train for the priesthood, enter one of the Inns of Court to embark on a law career, or seek a tutorship or professorship in Cambridge or elsewhere. Those wishing to hold a fellowship for more than a few years had to become ordained as Anglican priests, and many fellowships could thereafter be held for life, if the fellow remained unmarried. This situation persisted until 1861, when many changes negotiated by the Statutory Commissioners during 1856–59 came into effect.

William Hopkins was born at Kingston-on-Soar, Derbyshire on 2 February 1793, the son of a gentleman farmer. His early education was desultory and designed to train him in farming. His father gave him a small estate near Bury St Edmunds in Suffolk, but William found its management unrewarding and uncongenial. After the early death of his fi rst wife, a Miss Braithwaite, he sold the estate and, aged nearly thirty, entered St Peter’s College (Peterhouse), Cambridge in 1822 as an undergraduate. In 1827, he was placed seventh wrangler, in the same class as Augustus De Morgan (who came fourth), later London University’s fi rst professor of mathematics.

While still a student, Hopkins married his second wife, Caroline Frances Boys (by whom he later had a son and three daughters), and so he could not be elected to a Fellowship; but he was promptly appointed a mathematical lecturer of St Peter’s College, and also Esquire Bedell to the University. The duties of this latter post included carrying a ceremonial mace when accompanying the Vice-Chancellor on public occasions, and carving the joint for him at offi cial dinners. Hopkins held this position from 1827 until his death in 1866, receiving an annual salary and gratuities amounting to more than £100. Henry Gunning, a previous Esquire Bedell, thought highly of the new appointee’s respectability, if not that of some former holders of the offi ce, “men whom I blush to recollect as my colleagues.” And the announcement of Hopkins’ death in newspaper stated that: “The offi ce [Esquire Bedell] which Mr Hopkins fi lled in the University was one on which he conferred more dignity than it gave to him.

The portrait album, mentioned in the Preface as residing in Trinity College’s Wren Library, was little known for many years. It is a very large, well-bound volume, with each portrait mounted on its own stout page. (Henceforth, it is referred to as the “Wren Library album”.) The portraits are the midnineteenth century equivalents of modern-day graduation photographs: each subject wears an academic gown and holds a mortar board. All fi gures are shown three-quarters length, seated. Though the bodies and backgrounds are freely and rapidly sketched, in rather conventional poses, the heads are drawn with great skill and finesse.

There are forty-one numbered portraits, all of William Hopkins’ pupils: forty of them are of students who obtained fi rst, second or third place in the Mathematical Tripos examinations. The remaining portrait is of a fourth wrangler (A. Barry), who won the second Smith’s Prize and also gained First Class honours in the Classical Tripos. Five more portraits, all of graduates of Trinity College, are added at the back of the album: four duplicate other portraits and one is of a further second wrangler. An accurate list of contents states that the fi ve additions were made in 1931. The portraits are of varying sizes, the largest being 13.75″×10.5″ (height×width in inches) and the smallest 9″×7″. Most within a rectangular border are signed and dated by Thomas Charles Wageman, whereas the smaller ones are usually octagonal and unsigned. The latter may possibly be by another artist, but are in similar style. Many portraits were made in the subject’s year of graduation as B.A., but some are from later: the longest delayed are those of Colenso, fourteen years later, and G. Budd, fi fteen years later. The portraits are bound in partial chronological order, haphazardly at fi rst, but by year of graduation from 1844 onwards.

What did a high wrangler gain from his Cambridge education? The pressurised coaching necessary for success certainly gave the top candidates a sound drilling in elementary mathematics, a good knowledge of some more advanced topics, and a familiarity with applications to the physical sciences. The best students were brought to the point at which they could contemplate conducting original research, and several went on to do so. However, some probably felt that the emphasis of their training on amassing examination marks was unworthy of higher intellectual aspirations. Though William Hopkins did what he could to stress the more philosophical aspects of the subject, he knew that speed and profi ciency in examination technique were essential to ensure success, and he trained his students accordingly, with regular written tests.

The physical and intellectual demands on these students were great. Habits of intense and protracted study were inculcated, and the best students learned to work both accurately and very fast. Those who succeeded demonstrated stamina and resilience, the ability to work at a high level under severe stress, the capacity to assimilate rapidly a mass of technical information, and to express themselves on paper clearly and succinctly. These assets were to serve them well in later life, often in fi elds far from mathematics.

As illustrations of the diverse lives of the wranglers, we fi rst discuss three scientists and one divine whose careers were spent in England. The largely selfeducated George Green, the mathematical astronomer John Couch Adams, and the mathematical physicist George Gabriel Stokes are famous for their contributions to science. But Stokes was also a leading Anglican, who shared many of the preoccupations of our fourth subject, the scientifi cally trained divine Harvey Goodwin, regarding the connections and confl icts between science and religion.

As already stated, attention is not now confi ned to individuals known to have been tutored by William Hopkins. Of the four, only Stokes and Goodwin were Hopkins’ students; but Hopkins took an interest in the mature student Green and may well have given him informal advice. Adams seems to have had no direct contact with Hopkins, being tutored mainly by John Hymers of St John’s College. Green features here because of his unusual background and his key place in the evolution of Cambridge mathematical physics, though he held a junior fellowship for only a short time. Stokes and Adams were the fi rst two wranglers of what may be termed the “Hopkins era” to become Cambridge professors in mathematical subjects, and both did work of great distinction. And Goodwin was a fellow and mathematical tutor for a time, before attaining high positions in the Anglican Church.

Cambridge University and Its Colleges Top wranglers graduating B.A. between 1829 and 1856 who spent more than just a few early years of their careers in Cambridge are shown in Table A of Appendix B, pp. 356–358. They are more than fifty in number. Just a few lowerranked wranglers who went on to high offi ce are included in the Table: even the eighteenth wrangler Henry Latham published a text on mathematics and became head of a college. Nearly all were fellows and tutors of their colleges; ten went on to become college heads, and several others held senior college appointments or were noted private tutors. Nine of the fi fty became professors of the University in a range of subjects that encompasses mathematics, astronomy, physics, chemistry, physic (medicine), political economy, moral philosophy and divinity.

Six of our top wranglers served the Church, education and the law in Australia. And a seventh, James Cockle, though a lowly wrangler, was an able mathematician and jurist. The Bishop of Melbourne during 1847–76 was Charles Perry (1st, 1828), senior wrangler in the year after De Morgan and Hopkins. Perry coincided in Melbourne with William Parkinson Wilson (1st, 1847), when the latter was professor of Mathematics at Melbourne University during 1854–74; and also with the lawyer James Wilberforce Stephen (4th, 1844). Stephen became a member of the Victoria Legislative Assembly and then a Judge of the Supreme Court. He was active in promoting education in Victoria; he also served as Chancellor of the Anglican Diocese of Melbourne, and was a member of the Council of the University of Melbourne.

Alfred Barry (4th, 1848) became Bishop of Sydney in 1884, quite late in his career at the age of fifty-eight. He was appointed to the Senate of the University, where two other wranglers and contemporaries had long worked. But Morris Birkbeck Pell (1st, 1849) had died before Barry’s arrival, and William Scott (3rd, 1848) had retired. The three had known one another as students, and Scott and Barry surely met again, thirty-six years later on the other side of the world.