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| Hellman H. — Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever |
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| Ïðåäìåòíûé óêàçàòåëü |
"Classical" mathematics 182
"Dioptrics" (La Dioptrique) (Descartes) 32 35—37 39 40 42 46
"Free mathematics" 139
"Intuitionistic Set Theory" (Brouwer) 189
"Kuhnian revolution" 201—202
"Mathematical Creation" (Poincare) 206—207 209
"Mathematical insanity" 4
"Meteors" (Les Meteores) (Descartes) 32 35
"Mock Recantation, A" (Horace) 48
"Notorious axiom" 4—5 145 See
"On Quadrature" (Newton) 63 69
"On Some Difficulties in the Theory of Transfinite Types and Order Types" (Russell) 166
"On the Cube and First Power Equal to the Number" (Ars Magna) 16—17
"On the Unreliability of the Logical Principles" (Brouwer) 188
"War of the Frogs and the Mice" 6 193—199
2001 A Space Odyssey (movie) 215
Absolutism 200—206 209—211
Academia, early practices in 9—10
Acta Eruditorum, Bernoulli, Jakob 75 85
Acta Eruditorum, Bernoulli, Johann 80
Acta Eruditorum, Leibniz 59 61 62 64
Acta Mathematica 124 130—131 134—135
Aczel, Amir D. 121
Advances in Mathematics (Hersh) 213
AJAX 48
Aleph-null  125—126 131 See Georg" "Zermelo Ernst"
Aleph-one  131 143
Algebra See "Cardano Girolamo" "Sylvester James "Tartaglia"
American Journal of Mathematics 114—115 175
Analyse des infiniment petits (L'Hospital) 74 79 88
Analysis with Infinite Series (De Analyst) (Newton) 54
Analytic geometry 26 35 38 40 50 See Rene" "Fermat Pierre
Apollonius 33 39
Arithmetica Infinitorum (Wallis) 53
Ars Conjectandi (Art of Conjecture, The) (Jakob Bernoulli) 85—87
Ars Magna or The Rules of Algebra (Cardano) 2—3 7—8 13—19
Ashforth, Albert 101—102
Autobiography (Russell) 159—160
Axiom of Choice 4—5 145 149—150 153 See Ernst"
Bacon, Francis 135
Baire, Rene 147—149 151
Ballistics, Tartaglia on 12 14
Barner, Klaus 44
Barrow, Isaac 53 54
Barrow, John D. 140 203 205—206 210
Barton, Catherine 63
Beaugrand, Jean 30 36 38—40 45
Beeckman, Isaac 28—29
Begriffsschrift (Frege) 161—163
Beitrag (Cantor) 128—129
Bell, Eric Temple 43 107
Bell, Eric Temple, on "notorious axiom" 145
Bell, Eric Temple, views on Cantor and Kronecker 122 133 139
Bell, Eric Temple, views on Jakob Bernoulli 81—82
Bell, Eric Temple, views on Sylvester 105
Bennett, Charles E. 48
Bernays, Paul 205
Bernoulli's principle 92
Bernoulli's theorem 85—87
Bernoulli, Daniel (Johann's son) 74 90—93
Bernoulli, Jakob 3 72—75
Bernoulli, Jakob, brachistochrone solution and 80—84
Bernoulli, Jakob, catenary solution and 76—78
Bernoulli, Jakob, death of 85—87
Bernoulli, Jakob, Fermat and 50
Bernoulli, Jakob, integral calculus 75
Bernoulli, Jakob, Leibniz and 60
Bernoulli, Jakob, on isoperimetric figures 84—85
Bernoulli, Jakob, on probability 85—87
Bernoulli, Jakob, relationship to father 78—79
Bernoulli, Johann 3 72—75
Bernoulli, Johann, brachistochrone solution and 80—84
Bernoulli, Johann, brother's death and 85—87
Bernoulli, Johann, catenary solution and 76—78
Bernoulli, Johann, L'Hospital and 87—88
Bernoulli, Johann, Leibniz and 60 61 66
Bernoulli, Johann, on isoperimetric figures 84—85
Bernoulli, Johann, on velaria 77—78
Bernoulli, Johann, relationship to father 78—79
Bernoulli, Johann, relationship to son Daniel 74 90—93
Bernoulli, Johann, religious criticism of 88—89
Bernoulli, Johann, Taylor and 89—90
Bernoulli, Nicholas (Johann's son) 74 86 90—92
Bibby, Cyril 112
Bieberbach, Ludwig 187 196
Biquadratic algebraic equations 7
Blumenthal, Otto 194—197
Bolyai, Janos 185
Boorstin, Daniel 51
Borel, Emile 4—5 145—149 151 153 See Ernst"
Born, Max 197
Brachistochrone 60—61 80—81
Bridgman, Percy W. 207
British Association for the Advancement of Science 96 108—114
Brougham, Lord 106
Brouwer, L.E.J. 6 141 155 178 186—187
Brouwer, L.E.J., as constructivist 201
Brouwer, L.E.J., early intuitionism and 183—184
Brouwer, L.E.J., formalism term coined by 182
Brouwer, L.E.J., Hilbert disagreement and 187—193
Brouwer, L.E.J., on Mathematische Annalen editorial board 193—199
Bulletin de la Societe Mathematique (Zermelo) 147
Bullialdus, Ismael 86
Burali-Forti, Cesare 169
Cajori, Florian 78
Calculus 51—52 See Jakob" "Bernoulli Johann" "Leibniz Wilhelm "Newton Isaac"
Calculus of variations 84
Calculus, Continental European vs. English adherents 59—69 72
Calculus, Descartes, Fermat on analytic geometry and 50
Calculus, Newton's, Leibniz's simultaneous development of 52—59 70—72
Calculus, Principia (Newton) and 52—56 59 62
Calinger, Ronald 8
Cambridge University Press 165
Candide (Voltaire) 71
Cantor, Georg 4 116—118 203 207 216
Cantor, Georg, Beitrag and 128—131
Cantor, Georg, biographical information 122—124
Cantor, Georg, continuum hypothesis of 131—132 142—144
Cantor, Georg, Deutsche Mathematiker-Vereinigung and 135—137
Cantor, Georg, legacy of 139—141
Cantor, Georg, mental illness of 132—135
Cantor, Georg, on set theory 124—127
Cantor, Georg, on theory of numbers 123—124
Cantor, Georg, paradoxes in set theory of 137—139 149—155
Cantor, Georg, Poincare's views on 170
Cantor, Georg, well-ordering principle 143 145
Caratheodory, Constantin 194—196
Cardano, Aldo (son) 23 24
Cardano, Chiara (daughter) 22 24
Cardano, Giambattista (son) 22—23
Cardano, Girolamo 12—14
Cardano, Girolamo, alleged promise of secrecy to Tartaglia 17—18
Cardano, Girolamo, Ars Magna 2—3 7—8 13—19
Cardano, Girolamo, Descartes and 33—34
Cardano, Girolamo, Morley's views on 12
Cardano, Girolamo, on cubic equations 16—17
Cardano, Girolamo, Practica Arithmeticae Generalis 15
Cardano, Girolamo, Tartaglia's views on 20—24
Cartesian coordinate system 26—27 33—35
Cassirer, Ernst 51
Catenary curve 76—78
Catholic Church 28 30 37
Cavalieri, Francisco Bonaventura 64
Cayley, Arthur 106
Charraud, Nathalie 135
Charta Volans (Leibniz) 66
Church of England 104—105
Cicero 47
Clarke, Arthur C. 215
Class, defined 157
| Clerselier, Claude 45—49
Cohen, Paul J. 154—155
Collins, John 57 70
Collins, Randall 141
Commercium Epistolicum (Newton) 66 67 69
Compositio Mathematica 198
Comte, Auguste 102
Consistency, of a mathematical theory 150
Constructivism 201 See
Continuum Hypothesis 131—132 149—150 See Georg" "Zermelo Ernst"
Continuum, The (Weyl) 189
Coolidge, J.L. 33
Copernicus 8 28 30
Courant, Richard 196 198
Couturat, Louis 169 172
Crelle's Journal 119 127—130
Crelle, August Leopold 119
Cubic algebraic equations 7—9 16—17
Cycloid 60
D'Avalos, Alphonso, Marchese del Vasto 14—15
da Vinci, Leonardo 12 75
Darwin, Charles 95 100
Dauben, Joseph W. 117 141 154 207
de Morgan, Augustus 67—68 104 105
Dedekind, Richard 119 123 125—128 140
del Ferro, Scipione 9—10 19
della Nave, Annibale 10 18
Depressed cubic equation 9 11 15 19
Desargues, Girard 40
Descartes, Rene 8 27—31
Descartes, Rene, "Dioptrics" (La Dioptrique) 32 35—37 39 40 42 46
Descartes, Rene, "Geometry" 32—36 40 42 44 45 50
Descartes, Rene, "Meteors" 32
Descartes, Rene, Discourse on Method 26 30 31—36 39
Descartes, Rene, Fermat's criticism of 36—38 41—43 45—49
Descartes, Rene, legacy of 26—27 44—45 49—50
Descartes, Rene, Principles of Philosophy 37
Descartes, Rene, response to Fermat's criticism 39—43
Desmond, Adrian 94 96 112
Detlefsen, Michael 178
Deutsche Mathematiker-Vereinigung (DMV) 135—137 143—144
Diagonalization method 136
Dialogues Concerning Two Mew Sciences (Galileo) 124—125
Differential calculus 7 52—54 58 93
Dirichlet, P.G. Lejeune 118
Discourse on Method (Descartes) 26 30—36 39
Disquisitiones Arithmeticae (Gauss) 123
Donatus 38
Duillier, J.C. Fatio de 74
Duillier, Nicolas Fatio 61—62
Dunham, William 16
Education 211—213
Education, mathematics promoted in U.S. 105—106 114—115
Education, science vs. mathematics, Huxley vs. Sylvester on 94—99 108—114 214
Edward VI, king of England 13
Edwards, Harold M. 140 141
Einstein, Albert 6 184 194 195 197 198
Emperor's New Mind, The (Penrose) 210—211
Encyclopaedia Britannica 78
Ennius 38
Equal-time problem 75
Equiangular spiral 87
Ernest, Paul 201 208—209 212—214
Euclid 33
Euclid, Hilbert's views on 185
Euclid, on whole as greater than part 116 125
Euclid, parallel postulate 147
Eudoxus of Cnidus 216
Euler, Leonhard 74 83 85 91 92
Evolutionary theory 95 100
Exercitationes Mathematicae (Daniel Bernoulli) 90
Fallibilism 200—203 206—211
Fellman, E.A. 84
Fermat, Pierre de 27 38—39 See Rene"
Fermat, Pierre de, characteristics of 43—44
Fermat, Pierre de, criticism of Descartes by 36—38 41—43 45—49
Fermat, Pierre de, Descartes' response to 39—43
Fermat, Pierre de, last theorem of 41
Fermat, Pierre de, least time principle 48 50 80
Fermat, Pierre de, legacy of 49—50
Fermat, Pierre de, letters to Clerselier from 45—49
Fermat, Pierre de, on maxima/minima 52
Ferrari, Ludovico 16 18 20—21
Fior, Antonio Maria 10 11 19
Fleckenstein, J.O. 84
FLUENT 54
Fluxional notation 54 59—62 64 69 93
Fontana, Niccolo 10—11 See
Formalism 6 155 181—184 191 198—199 See David"
Fortnightly Review 95 102—103
Foundations of Geometry (Grundlagen der Geometrie) (Hilbert) 149 180 185
Fraenkel, Abraham Adolph 153
Frege, Gottlob 161—163
French Academy of Sciences 63—64 107
Friederich, Karl 117
Galileo 30 37 53 80 124—125
Galton, Francis 92
Gambling, Cardano on 13
Gassendi, Pierre 30
Gaukroger, Stephen 31
Gauss, Carl Friedrich 110 123 185
Gentzen, Gerhard 191
Geological theory, uniformitarianism in 100—102
Geometry 185 See Rene" "Fermat Pierre "Hilbert David"
Geometry (Descartes) 32—36 40 42 44 45 50
Geostatics (Beaugrand) 36
Goedel, Kurt 154 198—199 202 204 205 208 216
Gregory, James 53 64 90
Groningen 80 88—89
Grosholz, Emily R. 35
Grundgesetze der Arithmetik (Frege) 162 163
Grundlagen der Arithmetik (Frege) 162
Grundlagen der Geometrie (Hilbert) 149 180 185
Hadamard, Jacques 147—149 151 152 204
Hall, Rupert 64
Halley, Edmund 55
Hamilton, Archbishop John 24
Hardy, G.H. 204
Harriot, Thomas 45
Heine, Eduard 123—124 132
Heliocentric theory 28 30
Hermite, Charles 204 209
Hersh, Reuben 6 213
Heyting, Arend 192
Hilbert, David 6 117 140 155 184—186 207
Hilbert, David, Brouwer disagreement and 187—193
Hilbert, David, early formalism and 181—184
Hilbert, David, on axiomization of set theory 149—150
Hilbert, David, on continuum hypothesis 142
Hilbert, David, on Mathematische Annalen editorial board 193—199
Hirst, Thomas Archer 108
History and Origin of the Differential Calculus (Leibniz) 66
Hobbes, Thomas 38
Hofmann, J.E. 79
Hollingdale, Stuart 83
Hooke, Robert 55 63
Hooker, Joseph Dalton 95
Horace 48
Hulsius, Paulus 89
Husserl, Edmund 144
Huxley, Thomas Henry 3—4 182
Huxley, Thomas Henry, at Johns Hopkins University 114
Huxley, Thomas Henry, biographical information 96—97
Huxley, Thomas Henry, on evolutionary theory 100
Huxley, Thomas Henry, on importance of science over mathematics 94—99
Huxley, Thomas Henry, on Positivist philosophy 102—103
Huxley, Thomas Henry, on uniformitarian theory 100—102
Huxley, Thomas Henry, Sylvester's speech to British Association speech and 96 108—114
Huygens, Christiaan 55 61 75 76 83
Hydraulica (Johann Bernoulli) 92
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