John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish : The Mental World of an Early Modern Mathematician

Writing in 19393, the historian of mathematics Herbert Turnbull, described John Pell as ' a mysterious figure' and commented: 'he may well prove to be an unsuspected genius, for his manuscripts appear to survive, unexamined, in the British Museum.' Turnbull's expectations were pitched a little too high: although Pell was a man of unusual intellectual abilities, and one of the leading mathematicians of his day. His work does not merit any use of the term 'genius'. The term 'mysterious', on the other hand, was well deserved; and no less mysterious is the fact that the great majority of Pell's voluminous manuscripts have remained almost entirely unexamined for more than sixty years after Turnbull published those comments. This first full-length biography of John Pell (1611-1685) by Malcolm and Stedall reconstructs the life and times of this central and enigmatic mathematician and scholar. The text consists of over 600 pages and is presented in three parts: Part 1 "The Life of John Pell (1611-1685)" is a thoroughly researched new account of Pell's life; Part 2 "The Mathematics of John Pell" explores Pell's contribution to mathematics; and Part 3 "The Pell-Cavendish correspondence" is the first complete edition of Pell's correspondence, with detailed annotations. For historians of mathematics and science, philosophers, social and political historians and early modern intellectual historians, this superb work of scholarship is essential reading. The mathematician John Pell was a member of that golden generation of scientists Boyle, Wren, Hooke, and others which came together in the early Royal Society. Although he left a huge body of manuscript materials, he has remained an extraordinarily neglected figure, whose papers have never been properly explored. This book, the first ever full-length study of Pell, presents an in-depth account of his life and mathematical thinking, based on a detailed study of his manuscripts. It not only restores to his proper place in history a figure who was one of the leading mathematicians of his day; it also brings to life a strange, appealing, but awkward character, whose failure to publish his discoveries was caused by powerful scruples. In addition, this book shows that the range of Pell's interests extended far beyond mathematics. He was a key member of the circle of the'intelligencer'Samuel Hartlib; he prepared translations of works by Descartes and Comenius; in the 1650s he served as Cromwell's envoy to Switzerland; and in the last part of his life he was an active member of the Royal Society, interested in the whole range of its activities. The study of Pell's life and thought thus illuminates many different aspects of 17th-century intellectual life. The book is in three parts. The first is a detailed biography of Pell; the second is an extended essay on his mathematical work; the third is a richly annotated edition of his correspondence with Sir Charles Cavendish. This correspondence, which has often been cited by scholars but has never been published in full, is concerned not only with mathematics but also with optics, philosophy, and many other subjects; conducted mainly while Pell was in the Netherlands and Cavendish was also on the Continent, it is an unusually fascinating example of the correspondence that flourished in the 17th-century'Republic of letters'. This book will be an essential resource not only for historians of mathematics, science, and philosophy, but also for intellectual and cultural historians of early modern Europe.

writing In 1939, The Historian Of Mathematics Herbert Turnbull Described John Pell As 'a Mysterious Figure' And Commented: 'he May Well Prove To Be An Unsuspected Genius, For His Manuscripts Appear To Survive, Unexamined, In The British Museum.' Turnbull's Expectations Were Pitched A Little Too High: Although Pell Was A Man Of Unusual Intellectual Abilities, And One Of The Leading Mathematicians Of His Day, His Work Does Not Merit Any Use Of The Term 'genius'. The Term 'mysterious', On The Other Hand, Was Well Deserved; And No Less Mysterious Is The Fact That The Great Majority Of Pell's Voluminous Manuscripts Have Remained Almost Entirely Unexamined For More Than Sixty Years After Turnbull Published Those Comments. This First Full Length Biography Of John Pell (1611-1685) By Malcolm And Stedall Reconstructs The Life And Times Of This Central And Enigmatic Mathematician And Scholar. The Text Consists Of Over 600 Pages And Is Presented In Three Parts: Part 1 The Life Of John Pell (1611-1685) Is A Thoroughly Researched New Account Of Pell's Life; Part 2 The Mathematics Of John Pell Explores Pell's Contribution To Mathematics; And Part 3 The Pell-cavendish Correspondence Is The First Complete Edition Of Pell's Correspondence, With Detailed Annotations. For Historians Of Mathematics And Science, Philosophers, Social And Political Historians And Early Modern Intellectual Historians, This Superb Work Of Scholarship Is Essential Reading.

Contents......Page 6 General introduction......Page 8 A note on dates and transcriptions......Page 15 Acknowledgements......Page 16 Abbreviations......Page 17 Part I: The life of John Pell......Page 18 1 Sussex, Cambridge, 1611–1629......Page 20 2 Sussex, London, Sussex, 1629–1638......Page 32 3 London, 1638–1643......Page 68 4 Amsterdam, Breda, 1643–1652......Page 109 5 London, Zurich, 1652–1658......Page 146 6 London, Essex, London, 1658–1665......Page 184 7 Cheshire, 1665–1669......Page 205 8 London, 1669–1685......Page 220 Part II: The mathematics of John Pell......Page 252 Part III: The Pell–Cavendish correspondence......Page 336 Textual introduction......Page 338 The correspondence......Page 342 List of manuscripts......Page 594 Bibliography......Page 608 A......Page 646 B......Page 647 C......Page 648 E......Page 650 G......Page 651 H......Page 652 K......Page 654 M......Page 655 N......Page 656 P......Page 657 R......Page 659 S......Page 661 V......Page 662 W......Page 663 Contents 6 General introduction 8 A note on dates and transcriptions 15 Acknowledgements 16 Abbreviations 17 Part I: The life of John Pell 18 1 Sussex, Cambridge, 1611–1629 20 2 Sussex, London, Sussex, 1629–1638 32 3 London, 1638–1643 68 4 Amsterdam, Breda, 1643–1652 109 5 London, Zurich, 1652–1658 146 6 London, Essex, London, 1658–1665 184 7 Cheshire, 1665–1669 205 8 London, 1669–1685 220 Part II: The mathematics of John Pell 252 Part III: The Pell–Cavendish correspondence 336 Textual introduction 338 The correspondence 342 List of manuscripts 594 Bibliography 608 Index 646 A 646 B 647 C 648 D 650 E 650 F 651 G 651 H 652 I 654 J 654 K 654 L 655 M 655 N 656 O 657 P 657 Q 659 R 659 S 661 T 662 U 662 V 662 W 663 This authoritative work on the 17th-century mathematician John Pell contains new and detailed biographical material and the complete Pell-Cavendish correspondence