THE ANALYTICAL SOCIETY: MATHEMATICS AT CAMBRIDGE UNIVERSITY ’IN THE EARLY NINETEENTH CENTURY by Philip Charles Enros ■ - i . ' ■ ^ , a Institute for the History and Philosophy of Science and Technology A thesis submitted in conformity with the requirements for the Degree of Doctor of Philosophy in the University of Toronto © Philip Charles Enros 1979 This work is licensed under a Creative Commons Attribution 4.0 International License. % UNIVERSITY OF TORONTO SCHOOL OF .GRADUATE STUDIES PROGRAM OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY OF PHILIP CHARLES ENROS 10:00 a.m., Friday, October 5, 1979 Room 111, 63 St. George Street THE ANALYTICAL SOCIETY: MATHEMATICS AT CAMBRIDGE UNIVERSITY IN THE EARLY NINETEENTH CENTURY Committee in Charge: Professor C.R. Morey, Chairman Professor E. Barbeau Professor M.-Crowe, External Appraiser Professor S. Eisen Professor'R.J. Helmstadter Professor T.H. Levere, /Supervisor Professor I. Winchester Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract The thesis is a study of the Analytical Society (1812- 1813) of Cambridge University. Its purpose i£ to present a detailed history of the Society, of which little has previously been known, in or/3er to obtain an insight into the reasons for the transition in Cambridge mathematics in the early nineteenth century. A large part of. the content^of the thesis is based'on research-in extensive manuscript sources, especially various Charles Babbage and John Herschel collections. Two chap'ters in the thesis are devoted to theNjjackground to the Analytical Society. The curriculum of the University of Cambridge and the prominent position of mathematics there are examined. And the widespread lament about the decline of the mathematical sciences in England (1790-1815) is discussed and shown to have two "Sonnected features: a debate over analytical and synthetical mathematics, and a new view, for England, about the relationship" of mathematics and society. The ’lament along with, the Cambridge curriculum helped^o provoke both the founding of the Analytical Society and the later changes in Cambridge mathematics. The Analytical Society is dealt with in a long chapter. It was a short-lived association of a small but remarkable group of students at Cambridge University. The Society was a manifestation of a larger movement towards Continental analytical methods in-British mathematics. The Analytical Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Society did not attempt to reform Cambridge mathematical studies as is often assumed. However, the Society is -an important illustration of the ways in which various features J s ~ \ of Continental mathematics were being imported into England. >S\ Two other chapters are given over to an examination of the influence (mostly indirect) of the Analytical Society. It promoted and encouraged the mathematical work and vision of some of its members, in particular, the mathematical concerns -of Charles Babbage, John Herschel and Edward BromheadJ f rom 1814 to 1822. Also, several of its former members initiated an informal movement that led to a reform of Cambridge mathematical studies (1813-1820s). This transition to analytics took place through the structure of the studies of Cambridge. Thus not only did some members, of the Analytical Society do creative mathematics after the Society's dissolution, but many former members were also involved in changing Cambridge' mathematics. All of these activities including the formation of the Analytical Society were expressions of the members' image of mathematics. 55 The main theme of the thesis is the importance, for understanding early'nineteenth-century Cambridge mathematics, of an intellectual and social' framework which was composed of three key elements: ideas concerning the nature of mathematics (analytics versus ^synthetics) } ideas about the purpose of a university (a liberal education), and a set of expectations concerning mathematics and science best described as professionalism. The thesis contends that the presence of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. this particular framework in/-early nineteenth-century England explains the activities of the Analytical Society and the revival of Cambridge mathematics. This thesis thus provides a valuable insight- into the stste and nature of mathematics at Cambridge in the early nineteenth century. J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Biographical Sketch <• Philip Charles Enros was born in Chicoutimi, Quebec, August 30th 1950. He received primary and'secondary education in Montreal. He gained a B.Sc. (summa cpm laude") in mathematics from Loyola College, Montreal, in 19 71. From that date he has been a graduate stpdent (M.A. 1973) in' .the Institute for the History and Philosophy of Science and Tethnology, University of Toronto. Mr. Enr|os^ s graduate studies have been supported by a ■' Bell Canada Centennial Fellowship (1971-73), a Canada Council Doctoral Fellowship (1973-76), and an Ontarid Graduate Scholarship (1976-77). He was a Lecturer in-1977-78 in the Department of History, University of New Brunswick., and in ... O 1978-79 in^the Institute for History and Philosophy.of Science and Technology, University of Toronto. In 1978-7.9 he also organized the production of a "Biobibliography of Ontario Scientists, 1914-1939". Mr. Enros is Secretary-Treasurer of the Canadian Society for History and Philosophy of Mathematics, and a member of the History of Science Society'and of the Canadian'Society for History and Philosophy of Science. He has delivered a number of papers^to various conferences: the latest was to the third Workshop on the Social Histor-y of Mathematics, Berlin, July 1979; he y £ s" also been invited to' speak to the Davis Center Seminar on the History of the. professions, Princeton University, in December. Mr. Enros married Pragnya Thakkar- in 19 75. Their son) Madhava, was born in 1976.* Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Courses. M^jor Field: History of Mathematics . s&x 1005 History of Mathematics (A-> K.O. May S&T 1011. History of Physical Science (B+) J. MacLachlan S&T 1021 Intellectual Context of 19c. Science (A-) ■ T.H. Levere S&T 20t>0x Philosophy and Science in the 17-18c. (A-) T. Goudge S&T 2192x Philosophy of Science (A) B.C. van Fraassen t- First Minor: History of Technology S&T 1013 History of Technology (A) B. Sinclair S&T 2013 History of Technology (A^) B. Sinclair \ Second Minor: . ' S&T 1012 History of Biological Science (A> M.P. Winsor Specialist Examination's History of England m the Early Nineteenth Century (R.J Helmstadter), Mathematics (K.O. May) . and Science (T.H. Levere) in the Early Nineteenth Century. Comprehensive Examinations History of the Physical Sciences (T.H. Levere), History of the Biological Sciences (M.P. Winsor), History of Technology (B-. Sinclair), Philosophy of Science (B.C.. van Fraassen). •'* ' ‘ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Publications "Person Index for Delainbre's Rapport Hjstorigue of 1810", Historia Mathematics 3^ (1976) 321-324.| Review of J. Delambre's Rapport Histonque, Historia Mathematica 3 (1976) 342-344. ! •••----------------------- ; * ' i Review of J.M. Dubbey's The Mathematical Work of Charles Babbage, American Scientist 6^(S^ (1978) 639. Review ofJJ.M. Dubbey's The Mathematical WorTc• of Charles- Babbage,' to appear in Historia Mathematica 19 79. "Commentary" on R.A. Jarrell's paper "Courses in the History of .Canadian Science and Technology: Their Purpose and Content", to appear in the Proceedings of the Conference on the Study of the History of Canadian. Science and Technology, Kingston, 1978. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. THE UNIVERSITY OF TORONfO LIBRARY \ MANUSCRIPT THESIS AUTHORITY to d i s t r i b u t e n OTE The AUTHOR will sign in one of the two places indicated. 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