Overview

A few years ago, in the Wren Library of Trinity College, Cambridge, I came across a remarkable but then little-known album of pencil and watercolour portraits. The artist of most (perhaps all) was Thomas Charles Wageman. Created during 1829–1852, these portraits are of pupils of the famous mat- matical tutor William Hopkins. Though I knew much about several of the subjects, the names of others were then unknown to me. I was prompted to discover more about them all, and gradually this interest evolved into the present book. The project has expanded naturally to describe the Cambridge educational milieu of the time, the work of William Hopkins, and the later achievements of his pupils and their contemporaries. As I have taught applied mathematics in a British university for forty years, during a time of rapid change, the struggles to implement and to resist reform in mid-nineteenth-century Cambridge struck a chord of recognition. So, too, did debates about academic standards of honours degrees. And my own experiences, as a graduate of a Scottish university who proceeded to C- bridge for postgraduate work, gave me a particular interest in those Scots and Irish students who did much the same more than a hundred years earlier. As a mathematician, I sometimes felt frustrated at having to suppress virtually all of the ? ne mathematics associated with this period: but to have included such technical material would have made this a very different book.

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Mathematics at the University of Cambridge moved slowly in the 19th century from the low standards of a gentleman's education to something like a professional training for future mathematicians and physicists. Ambitious young students competed with ever greater energy for the honour of graduating top in their year, for the Senior Wrangler, as he would be called, was assured of at least the chance of a prestigious job for life, be it in the university world, law, the Church, or in the service of the British Empire. The distinction of graduating among the top half dozen or so Wranglers was such that those with sufficient ability and dedication drove themselves through their time at Cambridge acquiring the techniques needed to answer demanding questions in exam conditions accurately and at high speed. But the University itself did little to assist the process, although the top colleges took real interest in the results, and the training was conducted by a number of coaches, of whom William Hopkins was the most successful. Indeed, as this book shows, he virtually created the coaching system that turned the best students into Wranglers. Craik takes an admirably broad view of his theme, mixed with a sharp eye for detail and a deft way of weaving information into a larger argument. His opening chapters sketch the story of the university in the first half of the 19th century. Then we meet Hopkins himself, and his views on education. He was interested in science in its many forms, notably geology, and an advocate of specialised mathematical education rather than the old-style Cambridge instruction that fitted people mostly for the Church. His real gift, however, was for cramming technicalmastery into willing students. Then Craik introduces us to some of Hopkins' most conspicuous successes, and in Part II of the book we follow the careers of Hopkins' Wranglers. A few pursued careers in science, notably Adams and Stokes; Green had done his best work before ever going up to Cambridge and was advised by Hopkins but never coached by him. More went into the Church and went out to India, Africa, or Australia as educators; Craik considers a dozen of these. Finally Craik considers the Wranglers' influence on the creation of a research community, not just in England, but in Scotland, Ireland, and across the Empire. It is evident that Cambridge in the period considered was in transition from one social role to another. Craik is particularly sensitive to the place of the Christian Church in Cambridge life, and thence to the shifting views on the purpose of a Cambridge education. This emerges very naturally from his examination of the careers of so many of Hopkins' men, as well as numerous other figures, and as a result his book is a significant addition to the study of the social history of mathematics. It is also accompanied by a wonderful selection of pictures of people, many in colour. Other forces were of course at work reforming Cambridge, from individual professors to Royal Commissions. It was recognised that the undergraduate degree did not encourage the idea that research could be done in mathematics, and the Smith's Prize was promoted to meet that need. Many distinguished natural scientists at Cambridge missed being Senior Wrangler, pipped by a future lawyer or bishop, but took the Smith's Prize a year or so later. Tensions developed later in the century between the needsof mathematicians and physicists, and in the early years of the 20th century the system of Wranglers was abolished because it had become seen to be inimical to deep mathematical understanding. This is very well described in Andrew Warwick's book Masters of theory: Cambridge and the rise of mathematical physics [Univ. Chicago Press, Chicago, IL, 2003; MR2145511 (2006c: 01003)] but that book concentrates on the scientists. Craik's account of the first half of the 19th century is original and highly informative on the education of mathematicians. Mathematical Reviews <p> Groomed for Success <p>A few years ago, Alex Craik, a mathematician from the university of St. Andrews, found an obscure collection of portraits in the Wren Library of Trinity College at Cambridge University. The people depicted all had one thing in common: they had been pupils of the famous 19th-century Cambridge private mathematics tutor William Hopkins. He had taught a group that included George Stokes, William Thomson and James Clerk Maxwell, as well as other less famous but still highly successful scientists. Inspired by this finding, Craik has written Mr Hopkins' Men, which tells the story of Hopkins and his top students. The book provides a fascinating insight into 19th-century Cambridge college life, and charts how the university evolved from an outdated and stagnating institution into the world-renowned centre for mathematical and scientific research it is today. Many of these reforms were, in fact, down to Hopkins and the men he tutored. <p> -Physics World, June 2008

From the reviews: Mr Hopkins' Men is a book which takes the reader on a hike across nineteenth century mathematics in the British Isles. It takes in university reform, the lives of great mathematicians and the cultural influences and religious controversies in Victorian Britain. The author provides an engaging combination of historical colour, breadth of scope and fascinating detail in his narrative. It was a joy to read [Mark McCartney, University of Ulster: BSHM Bulletin] Groomed for Success A few years ago, Alex Craik, a mathematician from the university of St. Andrews, found an obscure collection of portraits in the Wren Library of Trinity College at Cambridge University. The people depicted all had one thing in common: they had been pupils of the famous 19th-century Cambridge private mathematics tutor William Hopkins. He had taught a group that included George Stokes, William Thomson and James Clerk Maxwell, as well as other less famous but still highly successful scientists. Inspired by this finding, Craik has written Mr Hopkins' Men, which tells the story of Hopkins and his top students. The book provides a fascinating insight into 19th-century Cambridge college life, and charts how the university evolved from an outdated and stagnating institution into the world-renowned centre for mathematical and scientific research it is today. Many of these reforms were, in fact, down to Hopkins and the men he tutored. -Physics World, June 2008 This book gives a fascinating view of Cambridge University during the Victorian era. ! The book can be recommended to people who are interested in the history of Victorian Britain in general and in the history of Cambridge University, mathematical education, mathematics, and scientific life and work, as well as the connections of science and religious belief, politics, etc. (EMS Newsletter, June, 2008) The nineteenth century has often been styled the age of reform in Britain and neither higher education nor mathematical curricula were immune to the reforming impulses that have come to characterize the era. ! book that will serve as a resource for those interested both in the role of mathematics in nineteenth century Cambridge and in the lives of many of those who so successfully gamed the Cambridge system. (Karen Hunger Parshall, ISIS, Vol. 100 (3), 2009) The author has researched very well, not only in the published primary and secondary literature but also in various archives. His long bibliography is followed by excellent indices; nearly 50 pages of end matter. He has produced an impressive and attractive book -- and his publisher has matched him in the quality of the reproductions and indeed in the book as a whole, which even carries a ribbon bookmark. Overall this book and Warwick's shed much light on the Tripos, its context and consequences. (The Mathematical Gazette, July 2010)

Author Information

ADD Craik is a well-respected mathematician and an authority on 19th century mathematics. He has contributed a number of well-regarded articles to journals such as ""Historia Mathematica"" and ""Notes and Records of the Royal Society of London"".

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