Masters of Theory Masters of Theory Cambridge and the Rise of Mathematical Physics ANDREW WARWICK The University of Chicago Press Chicago and London Andrew Warwick is senior lecturer in the history of science at Imperial College, Lon- don. He is coeditor of Teaching the History of Science and Histories of the Electron: The Birth of Microphysics. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2003 by The University of Chicago All rights reserved. Published 2003 Printed in the United States of America 12 11 10 09 08 07 06 05 04 03 1 2 3 4 5 isbn: 0-226-87374-9 (cloth) isbn: 0-226-87375-7 (paper) Library of Congress Cataloging-in-Publication Data Warwick, Andrew. Masters of theory : Cambridge and the rise of mathematical physics / Andrew Warwick. p. cm. Includes bibliographical references and index. isbn 0-226-87374-9 (cloth : alk. paper) — isbn 0-226-87375-7 (pbk : alk. paper) 1. Mathematical physics—History—19th century. 2. University of Cambridge—History—19th century. I. Title. qc19.6 .w37 2003 530.15Ј09426Ј59Ј09034 —dc21 2002153732 ᭺ϱ The paper used in this publication meets the minimum ruirements of the Americanational Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ansi z 39.48-1992. Contents List of Illustrations vii Preface and Acknowledgments ix Note on Conventions and Sources xiii 1 Writing a Pedagogical History of Mathematical Physics 1 2 The Reform Coach Teaching Mixed Mathematics in Georgian and Victorian Cambridge 49 3 A Mathematical World on Paper The Material Culture and Practice- Ladenness of Mixed Mathematics 114 4 Exercising the Student Body Mathematics, Manliness, and Athleticism 176 5 Routh’s Men Coaching, Research, and the Reform of Public Teaching 227 6 Making Sense of Maxwell’s Treatise on Electricity and Magnetism in Mid-Victorian Cambridge 286 7 Joseph Larmor, the Electronic Theory of Matter, and the Principle of Relativity 357 8 Transforming the Field The Cambridge Reception of Einstein’s Special Theory of Relativity 399 9 Through the Convex Looking Glass A. S. Eddington and the Cambridge Reception of Einstein’s General Theory of Relativity 443 Epilogue: Training, Continuity, and Change 501 Appendix A: Coaching Success, 1865–1909 512 Appendix B: Coaching Lineage, 1865–1909 524 Bibliography 527 Index 549 Illustrations 1.1. Derivation of the Poynting Vector 5 1.2. Poynting’s 1876 Examination Script (investigation) 19 1.3. Poynting’s 1876 Examination Script (problem) 20 1.4. Pages fromewton’s copy of Barrow’s 1655 Latin edition of Euclid’s Elements 31 2.1. Cambridge University Senate House 54 2.2. William Hopkins 81 2.3. Title Page of J. M. F. Wright’s The Private Tutor 83 2.4. The “Star of Cambridge” Stagecoach 91 2.5. A College Lecture 93 3.1. Smith’s Prize Questions 121 3.2. A Disputation 123 3.3. Written Examination in Trinity College 124 3.4. Examination Script by William Garnett 165 4.1. “Keeping an Exercise” 193 4.2. Boat Races on the river Cam, 1837 195 4.3. “Training” 196 4.4. St. John’s College Rugby Team, 1881 199 4.5. The Order of Merit in the Times newspaper, 1909 203 4.6. Reading the Order of Merit 204 4.7. Presentation of the Senior Wrangler 207 4.8. Ceremony of the Wooden Spoon 209 vii viii illustrations 4.9. Parading the Wooden Spoon outside the Senate House 210 4.10. The Trinity First Boat 220 5.1. Edward John Routh 232 5.2. Syllabus of the Mathematical Tripos, 1873 239 5.3. The Senior Wrangler in his Rooms 245 5.4. Robert Rumsey Webb 248 5.5. Robert Webb’s Coachingotes 250 5.6. Francis S. Macaulay 259 5.7. Title Page of Wolstenholme’s Mathematical Problems 262 5.8. Professorial and Intercollegiate Lectures in Mathematics, 1880 –1881 268 5.9. Robert Herman 283 6.1. Pedagogical Geography of Mid-Victorian Cambridge 290 6.2. Routh’s Lectureotes on Electrostatics 308 6.3. Examination Script by George Pitt 312 6.4. Examination Script by Joseph Ward 314 6.5. Routh’s Team for the Mathematical Tripos of 1880 316 6.6. W. D.iven 318 6.7. Examination Question, 1886 341 7.1. A Torchlight Procession in Belfast 365 7.2. Tripos Questions, 1901 and 1902 378 7.3. Jeans’s Mathematical Theory, Articles 257, 258 383 8.1. Ebenezer Cunningham 410 8.2. Harry Bateman, P. E. Marrack, and Hilda Hudson 417 8.3. Jeans’s Mathematical Theory, Articles 226, 227 419 8.4. Jeans’s Mathematical Theory, Articles 231, 232 420 8.5. Lecture notes by L. H. Thomas 438 9.1. A. S. Eddington (1904) 450 9.2. Alice through the Convex Looking Glass 466 9.3. Lecture notes by L. H. Thomas 481 9.4. Tripos Problems, 1927 and 1929 488 Preface and Acknowledgments This study offers a new account of the rise of modern mathematical physics. The history of the mathematical sciences has until recently played a rela- tively minor role in the development of social and cultural studies of sci- ence. As an eminent historian in this field remarked to me a few years ago, the project of writing a cultural history of mathematical physics sounded to many like a contradiction in terms. Taking Cambridge University as my ex- ample, I contend in this study that mathematical physics has a necessarily rich culture which is most effectively made visible through the history of training, the mechanism by which that culture has been reproduced and ex- panded for more than two hundred years. We tend to think of “theories” as collections of propositions or fundamental mathematical uations, but this is how they appear to those who have already mastered the physicist’s craft. It takes special aptitude and more than a decade’s education to make human beings who can see a theory in a jumble of mathematical uiggles, and I am interested in how that shared vision is produced. My approach is naturalistic in that it explores theory not in terms of method or logic but through the experience of the student struggling to be- come its master. Nor do I treat theorizing as a unuely cerebral process. Historians of experiment now speak routinely of machines, technicians, and embodied practical skills, but what of the material technology and skilled practices of theoreticians? Cambridge undergraduates in the late eighteenth ix x preface and acknowledgments century found it very odd that they were being ruired to learn by sketch- ing and writing rather than by reading and talking, and to display their knowledge by solving mathematical problems on paper instead of disputing in Latin. Their testimony highlights the peculiarity of mathematical knowl- edge made using hand, brain, paper, and pen. It is part of my task to under- stand how these new skills were taught and learned, and to explore the rela- tionship between drawing, writing, and knowing. I also contend that how and by whom students were taught is as important as what they were taught. The mathematical coaches who trained and motivated the Cambridge elite placed great emphasis on pedagogical technue, and ruired their students to spend long hours rehearsing mathematical methods in the solitude of their college rooms. The mathematician’s body, gender, and sexuality were also implicated in the making of the modern theoretician. Those who would master celestial mechanics in Victorian Cambridge believed that competi- tion on the playing field was as important as competition in the classroom, that irregular sexual activity sapped a man’sstrength, and that women’sminds and bodies could not withstand these trials. I want to understand how these embodied values contributed to what contemporaries characterized as the industrialization of the learning process. Above all, my study is a historical one. A good deal has been written about the rise of big, mainly experimental science in the twentieth century, but mathematical theory got big, at least in relative terms, a century earlier. It did so by successfully colonizing undergraduate studies in the expanding universities. My interest is focused not so much on why that colonization occurred as on its consuences for the emergence of mathematical physics as a discipline. That said, the first half of this study is as much a contribu- tion to institutional and educational history as it is to the history of science. In my opinion historians have yet to take on board the profound changes wrought in the kind of knowledge prized in the universities as essentially medieval practices of teaching, learning, and examining were swept away by a new pedagogical economy of model problem-solutions, private tutoring, and paper-based learning and examination. I am also concerned with the way novel theories are made teachable, the power of training to shape re- search, and the several and contradictory ways in which training regimes are conservative. On the one hand, training provides a mechanism by which the esoteric culture of mathematical physics is preserved and replicated at new sites; on the other, the peculiarities of each site produce distinct and local re- search cultures. Attempts to exchange knowledge across these boundaries are especially interesting as they highlight tacit forms of expertise not car- preface and acknowledgments xi ried in published works. The second half of my study explores these issues by looking at the establishment and operation of Cambridge’s first research school in mathematical physics (electromagnetic theory) and the Cambridge reception of the special and general theories of relativity. These examples il- lustrate my more general thesis that the cultural history of mathematical physics is not an alternative to its technical history but an explanation of how the latter was made possible.