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

436 Index
convergence tests, 265
counter example, 7, 12
crisis, 11
critical attitude, 9
critical revision, xiii, xiv, 9, 191, 192, 281,
392
cumulative nature of mathematics, 281
cyclotomic equation, 52, 79
cyclotomic equation, 72, 83, 142, 150–152,
316
cyclotomic equations, 150
Danmarks Tekniske Universitet, 24
degree of equivalence, 92
degree of substitution, 91
degree of equivalence, 86, 87
delineation problem, 400
delineation of concepts, xiv, 139, 272, 390,
395
delineation of solvable equations, 395
delineation problem, xiv, 341
Den Polytekniske Læreanstalt, 24
descent down string of equations, 148
dialectics, 11
differentiable functions, 395
Dirichlet boxing-in principle, 109
disciplinary matrix, 400
divergent series, 265, 267
division of the lemniscate, 315
division problem, 155, 157, 313
for circular functions, 150
for the lemniscate, 154
for elliptic functions, 142, 150, 153
for the circle, 6, 74, 151, 154
for the lemniscate, 154
of the circle, 150
domain of rationality, 159
elementary symmetric relations, 59
epistemic configuration, 13
epistemic object, 13
epistemic technique, 13
equality
arithmetical, 9
formal, 9
Euclid’s division algorithm, 142
Euclid’s division algorithm, 141, 158, 159
Euclidean construction, 74
Euler’s hypothesis, 80
exception, 7, 396
exception barring, 12
exceptions, xiii
false roots, 57
falsification, 12
Fermat primes, 79, 318
fictuous roots, 57
form of expression, 67
formal concept of equality, 9
formula based mathematics, xiii, xiv, 13, 263,
373, 374, 378, 387–392
French Revolution, 3, 40, 43
functional equations, 261
Fundamental Theorem of Algebra, 5, 10, 58,
80, 82, 95, 159
Galois theory, 99
Grand prix, 375
groupe, 75
habituation, xiii, xiv
hyperbola, 285, 287
hyperelliptic functions, 377
hyperelliptic integrals, 350, 351, 376, 377
hypergeometric series, 198–201, 296
identical substitution, 91
imagined roots, 57
imprimitive groups, 86
indecomposable functions, 158
indeterminate series, 265, 267
index, 87
index of a function, 92, 93
indicative divisor, 92
inertia of mathematical community, 80
inherited property, 148
Institut, 348
Institut de France, 90, 181, 186, 348
intransitive groups, 86
irreducibility, 157
irreducible equations, 159
irreducible Abelian equations, 176
irreducible Abelian equations, 52
irreducible equations, 52, 141, 142, 146, 158
Journal, 33, 35–37, 39, 122, 126, 128, 129, 155,
223, 244, 261, 265, 269, 278, 299, 300,
303, 337, 339, 341, 376, 377
Journal d’École Polytechnique, 90
Journal de mathématiques pures et appliquées,
181, 236
Journal für die reine und angewandte Mathematik,
4, 5, 29, 73, 98, 126
Königlichen Friedrichs-Gymnasium, 135
l’Hospital’s rule, 322