The Mathematical Writings of Evariste Galois (Heritage of European Mathematics)

Before he died at the age of twenty, shot in a mysterious early-morning duel at the end of May 1832, Évariste Galois created mathematics that changed the direction of algebra. This book contains English translations of almost all the Galois material. The translations are presented alongside a new transcription of the original French and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the testamentary letter and the first memoir (in which Galois expounded on the ideas that led to Galois Theory), which are the most famous of the manuscripts. These are followed by the second memoir and other lesser known manuscripts. This book makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the nineteenth century, presented in its original form. The primary aim is to establish a text of what Galois wrote. The details of what he did, the proper evidence of his genius, deserve to be well understood and appreciated by mathematicians as well as historians of mathematics. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society TeX output 2011.10.11:1353 Preface 7 Contents 9 List of facsimiles 11 Chapter I Introduction 13 I.1 Évariste Galois 1811–1832, revolutionary mathematician 13 I.2 What Galois might have read 16 I.3 The manuscripts 18 I.4 Publication history of Galois’ mathematical writings 20 I.5 The reception of Galois’ ideas 22 I.6 Scope of this edition 23 I.7 Editorial ambition and policy 24 I.8 Translation and interpretation 29 I.9 A ‘warts and all’ transcription 39 I.10 The transcription: editorial conventions 43 Chapter II The published articles 45 II.1 A theorem on continued fractions 47 II.2 Abstract of an article on the algebraic solutionof equations 61 II.3 A note on the numerical solution of equations 67 II.4 On the theory of numbers 73 II.5 On some points of analysis 89 Chapter III The Testamentary Letter of 29 May 1832 95 III.1 The letter 95 III.2 Notes on the letter 113 Chapter IV The First Memoir 117 IV.1 Text of the First Memoir 117 IV.2 Notes on the First Memoir 157 IV.3 A letter of complaint and enquirysent on 31 March 1831to the President of the Academy 177 Chapter V The Second Memoir 181 V.1 Text of the Second Memoir 181 V.2 Notes on the Second Memoir 207 Chapter VI The minor mathematical manuscripts 211 VI.1 Dossier 6: An 1830 version of Proposition I of the First Memoir 213 VI.2 Dossier 7: An 1830 draft of Proposition V of the First Memoir 221 VI.3 Dossier 8: A torn fragment 231 VI.5 Dossier 10: Publication project and note on Abel 245 VI.6 Dossier 11: Preface for two memoirs 257 VI.7 Dossier 12: On the progress of pure analysis 271 VI.8 Dossier 13: Here, as in all the sciences 281 VI.9 Dossier 14: Science, Hierarchy, Schools 287 VI.10 Dossier 15: Fragments on the theory of permutations and equations 291 VI.11 Dossier 16: Fragments relating to Proposition I of the First Memoir 313 VI.12 Dossier 17: Fragments on the theory of equations 323 VI.13 Dossier 18: Note on non-primitive equations 335 VI.14 Dossier 19: Addition to the memoir on solution of equations 341 VI.15 Dossier 20: On the division of elliptic functions 347 VI.16 Dossier 21: On the integration of linear equations 359 VI.17 Dossier 22: On surfaces of the second degree 367 VI.18 Dossier 23: On eulerian integrals 379 VI.19 Dossier 24: A theorem of Abel 385 VII Epilogue: myths and mysteries 395 VII.1 Myths 395 VII.2 Mysteries 397 VII.3 Last words 402 Bibliography 403 Index 417 Unbenannt 3