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

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432 Index of names Frobenius, Georg Ferdinand (1849–1917), 280 Galilei, Galileo (1564–1642), 24 Galois, Evariste (1811–1832), 5, 10, 49, 52, 54, 55, 66, 67, 75, 82, 84, 97, 125, 137, 138, 161, 180–187, 390, 395 Garnier, Jean Guillaume (1766–1840), 21, 22 Gauss, Carl Friedrich (1777–1855), 3, 6, 10, 21, 23, 27, 32, 34, 49, 51–54, 58, 72– 80, 82–84, 90, 95–97, 124, 126, 139, 142, 150–154, 157–160, 174, 175, 198– 201, 296, 297, 300, 307, 308, 316– 319, 349, 356, 367, 383 Gergonne, Joseph Diaz (1771–1859), 29, 348, 372, 393 Girard, Albert (1595–1632), 57, 59 Goldbach, Christian (1690–1764), 290 Grabiner, Judith V., 197, 393, 397 Grattan-Guinness, Ivor, 42, 222, 279 Gregory, James (1638–1675), 61, 287 Gruson, Johann Philipp (1768–1857), 32 Gårding, Lars, 171 Göpel, Adolph (1812–1847), 377 Hamilton, William Rowan (1805–1865), 104, 130, 131, 133–136, 138 Hansteen, Cathrine Andrea Borch (1787–1840), 17 Hansteen, Christopher (1784–1873), 22–24, 26–28, 33–36, 40, 97, 125, 224, 225, 246, 250, 297, 331, 339, 348 Heegaard, Poul (1871–1948), 375 Heine, Heinrich Eduard (1821–1881), 280 Hilbert, David (1862–1943), 54 Hindenburg, Carl Friedrich (1741–1808), 218 Hirsche, Meier (1765–1851), 98 Holmboe, Bernt Michael (1795–1850), xviii, 4, 14, 17–22, 31, 34–36, 40, 42, 97, 117, 127, 128, 132–134, 138, 160, 161, 163, 175, 179, 221, 222, 225, 226, 260, 297, 298, 306, 375 Holst, Elling Bolt (1849–1915), 26 Humboldt, Alexander von (1769–1859), 32, 34 Humboldt, Wilhelm von (1767–1835), 32, 41 Huygens, Christiaan (1629–1695), 24 Ivory, James (1765–1842), 42 Jacobi, Carl Gustav Jacob (1804–1851), 6, 17, 36, 42, 44, 45, 49, 55, 97, 155, 157, 290, 294, 298, 300, 302, 307, 309, 310, 331–333, 337, 346, 375, 377, 380, 382, 383 Jahnke, Hans Niels (⋆1948), 391 Jerrard, George Birch (1804–1863), 129–132, 134, 138, 179 Johnsen, Karsten, 76 Kemp, Christine (1804–1862), 17 Klein, Christian Felix (1849–1925), 391 Kline, Morris (⋆1908), 95 Kronecker, Leopold (1823–1891), 51, 136–138, 149, 152, 171, 181 Kuhn, Thomas S. (1922–1996), 11, 13, 400 Königsberger, Leo (1837–1921), 104, 131, 133, 134, 138, 332 Külp, Edmund Jacob (⋆1801), 22, 115–117, 128, 129, 134, 138, 166 l’Hospital, Guillaume-François-Antoine de (1661–1704), 358 Lacroix, Sylvestre François (1765–1843), 21, 186, 198 Lagrange, Joseph Louis (1736–1813), xi, 3, 5, 7, 10, 21, 22, 32, 43, 44, 49–51, 53, 58, 61, 64–73, 75, 81–86, 88, 92, 101, 104, 107, 108, 110, 113, 114, 116, 118, 119, 124, 126, 132, 133, 139, 170, 171, 181, 183, 185, 186, 191, 193, 197, 198, 207, 219, 294, 372, 376, 397 Lakatos, Imre (1922–1974), 11–13, 128, 278, 393, 400 Laplace, Pierre-Simon, marquis de (1749– 1827), 20 Laugwitz, Detlef (1932–2000), 248, 391 Legendre, Adrien-Marie (1752–1833), xiv, 3, 6, 24, 26, 27, 35, 36, 44, 75, 126, 127, 153, 288, 292–297, 299, 307, 309, 310, 321, 325, 327, 331, 333, 336, 337, 339, 375 Lehmus, Daniel Christian Ludolf (1780–1863), 32 Leibniz, Gottfried Wilhelm (1646–1716), 58, 61, 62, 287 Libri, Guglielmo (1803–1869), 348, 361, 375 Lie, Marius Sophus (1842–1899), 244, 245, 252, 325, 328, 329, 375 Liouville, Joseph (1809–1882), 52, 181, 185, 236, 340, 374, 382 Littrow, Karl Ludwig von (1811–1877), 35, 123 Lubbe, Samuel Ferdinand (1786–1846), 32 Lubbock, John William (1803–1865), 130
Index of names 433 Lützen, Jesper, xix, 340 MacCullagh, James (1809–1847), 134 Malfatti, Gian Francesco (1731–1807), 88, 125 Malmsten, Carl Johann (1814–1886), 171 Maurice, Jean Frédéric Théodor, 127 Mertens, Franz (1840–1927), 247 Mittag-Leffler, Magnus Gustav (1846–1927), 379 Newton, Isaac (1642–1727), 24, 59, 70–72, 195, 203, 286, 287 Ohm, Georg Simon (1789–1854), 31 Ohm, Martin (1792–1872), 31–33, 206, 218 Olivier, Louis, 126, 206, 265–272, 393, 396, 399, 400 Ore, Øystein (1899–1968), 14, 261 Poisson, Siméon-Denis (1781–1840), 21, 186, 206, 226 Popper, Karl Raimund (1902–1994), 12 Rasmussen, Søren (1768–1850), 20, 23, 24, 26, 27, 36, 40, 339 Riemann, Georg Friedrich Bernhard (1826– 1866), xiv, 219, 236, 247, 250, 369, 373, 388, 391 Rosenhain, Johann Georg (1816–1887), 377 Rudio, Ferdinand (1856–1929), 390, 391 Ruffini, Paolo (1765–1822), 5, 10, 50, 53, 54, 83–92, 97, 100, 101, 107, 108, 110, 112, 119–125, 128, 135, 137, 139 Saigey, Jacques Frédéric (1797–1871), 123 Schlesinger, 296 Schmidten, Henrik Gerner v. (1799–1831), 29 Schneider, 200 Schumacher, Heinrich Christian (1784–1873), 24, 28, 297, 331, 346 Seidel, Philipp Ludwig von (1821–1896), 217, 279, 280 Serret, Joseph Alfred (1819–1885), 133 Simonsen, Anne Marie (1781–1846), 18 Skau, Christian, 106, 171 Spalt, Detlef, 280 Stokes, George Gabriel (1819–1903), 217, 279, 280 Stubhaug, Arild (⋆1948), xix, 14, 17, 18, 24 Sylow, Peter Ludvig Mejdell (1832–1918), 14, 26, 32, 42, 122, 155, 167, 169, 171, 175, 176, 180, 243, 245, 252, 253, 306, 307, 351, 355, 357, 358, 361, 362, 365, 366, 373 Tartaglia, Niccolò (1499/1500–1557), 59 Taylor, Brook (1685–1731), 202, 222 Thune, Erasmus Georg Fog (1785–1829), 25 Tralles, Johann Georg (1763–1822), 32 Tschirnhaus, Ehrenfried Walter (1651–1708), 61, 80 Vandermonde, Alexandre-Théophile (1735– 1796), 49, 64, 66, 99 Viète, François (1540–1603), 59, 71 Volkert, Klaus, 398 Wallace, William (1768–1843), 196 Wantzel, Pierre Laurent (1814–1848), 89, 135, 247 Waring, Edward (∼1736–1798), 51, 59, 70– 72, 80, 82, 88, 133, 143 Weber, Heinrich (1842–1913), 185 Weierstrass, Karl Theodor Wilhelm (1815– 1897), 44, 45, 219, 223, 228, 246, 248, 250, 280, 327, 382, 388 Wessel, Caspar (1745–1818), 261 Wussing, Hans, 64, 186 Young, Thomas (1773–1829), 42
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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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12.3. Convergence 231 and {εm} was
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12.4. Continuity 233 it followed th
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12.4. Continuity 235 Actually, if t
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12.4. Continuity 237 DIRICHLET intr
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12.5. ABEL’s “exception” 239
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12.6. A curious reaction: Lehrsatz
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12.7. From power series to absolute
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12.7. From power series to absolute
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12.8. Product theorems of infinite
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12.8. Product theorems of infinite
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12.9. ABEL’s proof of the binomia
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12.10. Aspects of ABEL’s binomial
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12.10. Aspects of ABEL’s binomial
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266 Chapter 13. ABEL and OLIVIER on
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Chapter 14 Reception of ABEL’s co
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14.1. Reception of ABEL’s rigoriz
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14.2. Conclusion 281 of basic notio
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Part IV Elliptic functions and the
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286 Chapter 15. Elliptic integrals
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300 Chapter 16. The idea of inverti
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Chapter 17 Steps in the process of
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17.1. Infinite representations 323
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17.2. Elliptic functions as ratios
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17.2. Elliptic functions as ratios
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17.3. Characterization of ABEL’s
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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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Page 434 and 435: 404 Appendix A. ABEL’s correspond
Page 437 and 438: Appendix B ABEL’s manuscripts Man
Page 439 and 440: 1. Précis d’une théorie des fon
Page 441 and 442: Bibliography Abel (MS:351:A). “M
Page 443 and 444: Bibliography 413 in: Journal für d
Page 445 and 446: Bibliography 415 — (1990). “Geo
Page 447 and 448: Bibliography 417 — (1830). “Mé
Page 449 and 450: Bibliography 419 — (1768). “Ins
Page 451 and 452: Bibliography 421 Grattan-Guinness,
Page 453 and 454: Bibliography 423 Jahnke, H. N. (198
Page 455 and 456: Bibliography 425 Legendre, A. M. (1
Page 457 and 458: Bibliography 427 Rosen, M. (1981).
Page 459: Bibliography 429 Toti Rigatelli, L.
Page 465 and 466: Index École Normale, 40, 187 Écol
Page 467: Index 437 Lagrange interpolation, 3
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