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We have seen how Cambridge University, at a low intellectual ebb at the start of the early nineteenth century, underwent a revival that by the 1850s established it as the pre-eminent British university for mathematics and its applications. This revival involved several distinct processes. The fi rst was criticism from outside Cambridge, and particularly from Edinburgh, of the oldfashioned mathematical instruction that was offered, and of the poor level of understanding in Britain of recent (and not so recent) continental advances. There were also calls for more general reforms from anxious parents and disaffected former students, who accused the University and colleges of neglecting their duties. The next advance was the adoption of textbooks on trigonometry and astronomy written by Robert Woodhouse; and the student-driven attempt, by the short-lived Analytical Society, to modernise the mathematical syllabus and to foster analytical research. The subsequent election to college fellowships of two of these students, George Peacock and Richard Gwatkin, enabled them, as Tripos moderators and examiners, to introduce the continental notation of the calculus into the examinations. [ABSTRACT FROM AUTHOR]

By the 1830s, the main areas to which mathematics had already been successfully applied were mechanics, planetary astronomy, hydrostatics and hydrodynamics, and optics. All of these were prominently represented in the Tripos; and so it was these topics that mainly attracted the interest of the wranglers. To set the scene (and at great risk of oversimplifi cation), the evolution of the mathematical sciences before 1830 is fi rst summarised; then many of the major advances made during the period 1830-80 are reviewed, with emphasis on the work of our wranglers. Mechanics is the study of the equilibrium and motion of bodies under applied forces. (In the mid-twentieth century, this was renamed "classical mechanics" to distinguish it from the new fi elds of statistical, relativistic, and quantum mechanics.) It naturally subdivides into statics and dynamics. Statics is the study of mechanical systems in equilibrium under applied forces, and dynamics concerns the motion of bodies induced by applied forces. Frequently, a solid body can be regarded as a mass concentrated at a single moving point, to which Newton's laws are directly applicable. Calculation of the motion of such "point particles", acted on by a constant gravitational force, adequately describes the paths of solid projectiles (including objects such as cannon-balls). Isaac Newton himself improved on this by incorporating a drag force to model air resistance. Numerical tables of such trajectories were long used in warfare for range-fi nding of artillery. Other early theoretical developments included the laws of impact of colliding bodies, and the motion of pendulums under gravity: the latter crucial to the development of accurate clocks, and for detecting local variations of the force of gravity itself. [ABSTRACT FROM AUTHOR]

In the mid-nineteenth century, scientifi c research did not have a prominent place in the British universities. A record of scholarship and of original contributions to the subject was notionally demanded of appointees to chairs; but, in practice, there were many instances of appointment of inferior candidates over better scholars, through political and personal infl uence. In all British universities and colleges apart from Oxford and Cambridge, the number of teaching staff was small, and most professors had heavy teaching loads. In Oxford and Cambridge, however, the professors and most college fellows had light teaching duties and ample time to devote themselves to advancing their subject if they were so inclined. But, as already noted, some professors became absentees, taking on other, usually Church, commitments that absorbed their time; and many fellows sank into a comfortable, and often indolent, life in college. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]