RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

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282 Chapter 14. Reception of ABEL’s contribution to rigorization slightly marginal and not universally appreciated. Mathematicians who subsequently adhered to the rigorization program may have included ABEL among their heroes and have certainly adopted some of his notions and results but ABEL’S direct role was far from the role of the key initiator of the rigorization — CAUCHY.
Part IV Elliptic functions and the Paris mémoire 283
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RePoSS: Research Publications on Sc
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The Mathematics of NIELS HENRIK ABE
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The Mathematics of NIELS HENRIK ABE
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Contents Contents i List of Tables
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8.3 Refocusing on the equation . .
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V ABEL’s mathematics and the rise
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List of Figures 2.1 NIELS HENRIK AB
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List of Boxes 1 The algebraic reduc
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Summary The present PhD dissertatio
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Preface to the 2004 edition For thi
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in connection with the Abel centenn
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items published in the same year ar
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the Mittag-Leffler archives in Djur
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Chapter 1 Introduction In the after
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1.2. The mathematical topics involv
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1.3. Themes from early nineteenth-c
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1.4. Reflections on methodology 9 l
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1.4. Reflections on methodology 11
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18 Chapter 2. Biography of NIELS HE
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Chapter 3 Historical background The
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3.2. ABEL’s position in mathemati
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3.3. The state of mathematics 43 tr
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3.4. ABEL’s legacy 45 As can be s
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Chapter 4 The position and role of
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4.1. Outline of ABEL’s results an
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4.2. Mathematical change as a histo
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4.2. Mathematical change as a histo
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58 Chapter 5. Towards unsolvable eq
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98 Chapter 6. Algebraic insolubilit
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100 Chapter 6. Algebraic insolubili
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Chapter 7 Particular classes of equ
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7.1. Solubility of Abelian equation
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7.2. Elliptic functions 153 Figure
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7.2. Elliptic functions 155 7.2.1 T
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7.3. The concept of irreducibility
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7.3. The concept of irreducibility
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7.4. Enlarging the class of solvabl
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164 Chapter 8. A grand theory in sp
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Part III Interlude: ABEL and the
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192 Chapter 9. The nineteenth-centu
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194 Chapter 10. Toward rigorization
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208 Chapter 11. CAUCHY’s new foun
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Chapter 12 ABEL’s reading of CAUC
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12.1. ABEL’s critical attitude 22
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12.3. Convergence 229 12.3 Converge
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Page 263 and 264: 12.4. Continuity 233 it followed th
Page 265 and 266: 12.4. Continuity 235 Actually, if t
Page 267 and 268: 12.4. Continuity 237 DIRICHLET intr
Page 269 and 270: 12.5. ABEL’s “exception” 239
Page 271 and 272: 12.6. A curious reaction: Lehrsatz
Page 277 and 278: 12.7. From power series to absolute
Page 279 and 280: 12.7. From power series to absolute
Page 281 and 282: 12.8. Product theorems of infinite
Page 283 and 284: 12.8. Product theorems of infinite
Page 285 and 286: 12.9. ABEL’s proof of the binomia
Page 291 and 292: 12.10. Aspects of ABEL’s binomial
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Page 307 and 308: Chapter 14 Reception of ABEL’s co
Page 309 and 310: 14.1. Reception of ABEL’s rigoriz
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Page 351 and 352: Chapter 17 Steps in the process of
Page 353 and 354: 17.1. Infinite representations 323
Page 355 and 356: 17.2. Elliptic functions as ratios
Page 357 and 358: 17.2. Elliptic functions as ratios
Page 359 and 360: 17.3. Characterization of ABEL’s
Page 361 and 362: Chapter 18 Tools in ABEL’s resear
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18.1. Transformation theory 333 The
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18.1. Transformation theory 335 Obv
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18.1. Transformation theory 337 Sum
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18.2. Integration in logarithmic te
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18.3. Conclusion 345 Summary. ABEL
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Chapter 19 The Paris memoir N. H. A
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19.1. ABEL’s approach to the Pari
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19.2. The contents of ABEL’s Pari
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19.3. Additional, tentative remarks
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19.3. Additional, tentative remarks
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19.4. The fate of the Paris memoir
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19.6. Conclusion 377 hyperelliptic
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Chapter 20 General approaches to el
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20.2. Other ways of introducing ell
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20.3. Conclusion 383 All these four
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Chapter 21 ABEL’s mathematics and
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21.1. From formulae to concepts 389
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21.1. From formulae to concepts 391
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21.2. Concepts and classes enter ma
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21.3. The role of counter examples
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21.4. Conclusion 401 It is beyond t
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404 Appendix A. ABEL’s correspond
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Appendix B ABEL’s manuscripts Man
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1. Précis d’une théorie des fon
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Bibliography Abel (MS:351:A). “M
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Bibliography 413 in: Journal für d
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Bibliography 415 — (1990). “Geo
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Bibliography 417 — (1830). “Mé
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Bibliography 419 — (1768). “Ins
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Bibliography 421 Grattan-Guinness,
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Bibliography 423 Jahnke, H. N. (198
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Bibliography 425 Legendre, A. M. (1
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Bibliography 427 Rosen, M. (1981).
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Bibliography 429 Toti Rigatelli, L.
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432 Index of names Frobenius, Georg
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Index École Normale, 40, 187 Écol
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Index 437 Lagrange interpolation, 3
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