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| Hellman H. — Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever |
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| Ïðåäìåòíûé óêàçàòåëü |
Hydrodynamica (Daniel Bernoulli) 91—92
Incompleteness theory 154—155 202 204 208
infinity 4—5 116—118 169 174 See Georg" "Set
Integral calculus 58 59 75
International Congress of Mathematicians, First (1897) 137
International Congress of Mathematicians, Second (1900) 142 164 181
International Congress of Mathematicians, Third (1904) 144 145 181
Introduction to Mathematical Philosophy (Whitehead) 180
Intuitionism 6 155 169 183—184 191—192 198—199 217 See L.E.J." "Kronecker Leopold" "Poincare Jules "Weyl Hermann"
Isochrone 75 83
Jahresbericht (Annual Report) of the DMV 137
Jesus, Cardano's horoscope for 13 22 24
Johns Hopkins University 114—115
Journal for Pure and Applied Mathematics See "Crelle's Journal"
Journal Literaire de la Haye 66
Journey through Genius (Dunham) 16
Kant, Immanuel 201 206
Kasner, Edward 207
Keill, John 52 64—65
Kelvin, Lord (Thomson, William) 101—103
Klein, Felix 123 193
Kline, Morris 2 216—217
Kline, Morris, on absolutism vs. fallibilism 203—205
Kline, Morris, on Ars Magna (Cardano) 8
Kline, Morris, on axiom of choice 153
Kline, Morris, on Cantor and Kronecker 129 140—141
Kline, Morris, on Jakob Bernoulli 82
Kline, Morris, on Poincare 169
Kline, Morris, on Russell 177
Koenig, Jules 144
Kowalevsky, Sonya 120—121 134
Kronecker, Leopold 4 5 117—119 185—186 See Georg"
Kronecker, Leopold, biographical information 118—121
Kronecker, Leopold, death of 137
Kronecker, Leopold, Deutsche Mathematiker-Vereinigung invitation to 135—137
Kronecker, Leopold, legacy of 139—141
Kronecker, Leopold, on Cantor's set theory 127 128—131 133—134
L'Hospital, Guillaume Francois 74 79 87—88
Lagrange, Joseph-Louis 83 85 109—110
Lakatos, Imre 208
Laplace, Pierre Simon 67
Latham, Marcia L. 26
Law of refraction 32 36—38 48
Lebesgue, H. 147—149 151 152
Lecons sur la theorie des fonctions (Borel) 146
Lectures on Ten British Mathematicians of the Nineteenth Century (MacFarlane) 112
Leibniz, Wilhelm Gottfried 3 51—52 216 See Isaac"
Leibniz, Wilhelm Gottfried, Bernoullis and 73—74 83 87
Leibniz, Wilhelm Gottfried, biographical information 56—58
Leibniz, Wilhelm Gottfried, concept of space and time 67
Leibniz, Wilhelm Gottfried, death of 93
Leibniz, Wilhelm Gottfried, on calculus 58—59
Leibniz, Wilhelm Gottfried, on catenary 76
Lemniscate of Bernoulli 79
Life of Virgil (Donatus) 38
Life, Art and Mysticism (Brouwer) 186
Limitation-of-size theory 166 172
Lindemann, Ferdinand 119—120
Liouville, Joseph 127
Lobachevsky, Nikolai 185
Logicism 5 155 162—164 180 187 See Bertrand "Whitehead Alfred
London Mathematical Society 107 166 169
Macfarlane, Alexander 112
Macmillan's Magazine 95
Maddy, Penelope 151
Mahoney, Michael Sean 27 37 40 43—46
Mannichfaltigkeitslehre (Cantor) 161
Mary, queen of Scots 24
Mathematical theory, defined 150
Mathematician's Apology, A (Hardy) 204
Mathematics See also individual names of mathematicians
Mathematics Magazine 199
Mathematics The Loss of Certainty (Kline) 2
Mathematics, absolutism in 203—206 209—211
Mathematics, absolutism vs. fallibilism 200—203
Mathematics, education 105—106 108—114 211—213
Mathematics, fallibilism in 206—211
Mathematics, Russell on 1—2
Mathematics, teaching vs. philosophy of 213—214
Mathematische Annalen 137 146 193—199
Mathesis universalis 29
Matrix concept 107
Maxima/minima 37—38 42 43 49 52 84
Mersenne, Marin 30—31 35 37—43 45
Method of Fluxions and Infinite Series (Newton) 69
Methodus Incrementorum (Taylor) 85 89
Minkowski, Hermann 184
Mirabilis scientiae fundamenta 29
Mittag-Leffler, Goesta 123 124 130 132 134 136—137 140
Monde, Le (The World) (Descartes) 30 37
Montmort, Pierre Remond de 76 89
Moore, Gregory H. 149 152
Morley, Henry 11—12
Mydorge, Claude 40
National Council of Teachers of Mathematics (NCTM) 211
New Problems and Inventions (Quesiti et Inventioni Diverse) (Tartaglia) 18 20
Newman, James R. 90 107 167 207
Newton, Isaac 3 51—52 204
Newton, Isaac, biographical information 52—54
Newton, Isaac, concept of space and time 67
Newton, Isaac, death of 93
Newton, Isaac, on fluxion, fluent 53—54
Newton, Isaac, Opticks 55 63 64
Newton, Isaac, Principia (Mathematical Principles of Natural Philosophy) 55—56 59 62
Newton, Isaac, Taylor and 89
Nicholson, J.D. 46
Nightingale, Florence 106
No-classes theory 157—159 166 172—174
Nordmann, Charles 159
Notation, dot 58—59 61 69
Notation, fluxional 54 59—62 64 69 93
Nova Scientia (Tartaglia) 12
Number theory 116 See Georg"
Number theory, Cantor on 123—124
Number theory, Fermat and 50
Number theory, formalism and 191—192
O'Connor, J.J. 82
Oldenberg, Henry 57
On the Foundations of Mathematics (Brouwer) 187
On the Revolutions of the Heavenly Spheres (Copernicus) 8
On the Structure of the Human Body (Vesalius) 8
Opticks (Newton) 55 63 64
Optics See also "Newton Isaac"
Optics, "Dioptrics" (La Dioptrtque) (Descartes) 32 35—37 39 40 42 46
Optics, Bernoullis and 91
Optics, Fermat on 49 50
Ore, Oystein 10 12—13 15 17
Pacioli, Luca 9
Painleve, Paul 194
Pall Mall Review 101
Pappus 33 35 39
Paradis, James G. 98
Paradoxes See "Set theory"
Paris Academy of Sciences 85
Parshall, Karen H. 105—107
Pascal, Blaise 30 40 41 45
Peano, Giuseppi 164 172 173 185
Penrose, Roger 210
Pepin, Birgit 213—214
Petit, Pierre 38
Philosophical Magazine 105
Philosophical Transactions of the Royal Society of London 55 65
Philosophy of Mathematics Education 201
Pi in the Sky (Barrow) 140
Planck, Max 144
Plato 203 205
Platonists 205—206 See
Poincare, Jules Henri 5 141 153 182 206—207 209 See Bertrand
| Poincare, Jules Henri, biographical information 167—169
Poincare, Jules Henri, Brouwer's views on 187
Poincare, Jules Henri, death of 159 176
Poincare, Jules Henri, Russell criticized by 170—176
Poincare, Jules Henri, Russell's response 173—174
Positivist philosophy 102
Practica Arithmeticae Generalis (Cardano) 15
Principia (Mathematical Principles of Natural Philosophy) (Newton) 55—56 59 62
Principia Mathematica (Principles of Mathematics) (Russell, Whitehead) 152—153 160 163 165—166 176—178 180
Principle of least time 48 50 80
Principle of the excluded middle (PEM) 188—190
Principles of Mathematics (Russell) 160 165—166 176—178
Principles of Philosophy (Descartes) 37
Probability, Jakob Bernoulli on 85—87
Proofs and Refutations (Lakatos) 208
Quarterly Journal of Pure and Applied Mathematics 107
Quesiti et Inventioni Diverse (New Problems and Inventions) (Tartaglia) 18 20
Ramsey, F.P. 157
Rational numbers, defined 126
Real numbers, defined 126
Realism in Mathematics (Maddy) 151
Reid, Constance 184
Religion, Bell on Cantor and Kronecker and 122
Religion, Cantor and 122 135—136
Religion, Cardano's horoscope for Jesus 13 22 24
Religion, Catholic Church 28 30 37
Religion, Church of England 104—105
Religion, Johann Bernoulli and 88—89
Religion, Sylvester and 104—106
Restivo, Sal 141
Revolutionibus, De (Copernicus) 28
Revue de metaphysique et de morale 170 173—174
Riemann, Bernhard 110 185 192 194
Robertson, E.F. 82
Roberval, Gilles Personne de 30 38—41 43 45
Rohault, Jacques 46
Roulet, Geoffrey 214
Rouse Ball, W.W. 43 77
Royal Society 61 63 65 68 106
Royal Society, Cantor and 144
Royal Society, Russell and 165 166 172
Royal Society, Sylvester and 106 107
Rules of Algebra, The (Cardano) See "Ars Magna or The Rules of Algebra (Cardano)"
Rummer, Ernst Eduard 118 119 121
Russell, Bertrand A.W. 1—2 5 155 209—210 216 See Georg"
Russell, Bertrand A.W., "On Some Difficulties in the Theory of Transfinite Types and Order Types" 166 172
Russell, Bertrand A.W., biographical information 159—162
Russell, Bertrand A.W., logicism and 162—164
Russell, Bertrand A.W., on aleph-null 146—147
Russell, Bertrand A.W., paradox of 138 149 156—159 166
Russell, Bertrand A.W., Poincare's criticism of 167—176
Russell, Bertrand A.W., Principia Mathematica (Principles of Mathematics) 152—153 160 163 165—166 176—178 180
Sabra, A.I. 48—49
Sacco, Bartolomeo 22
Schoenfeld, Alan H. 213
Schwarz, Hermann Amandus 121 123 130 144
Science, mathematics vs 94—99 108—114 214 See Thomas "Sylvester James
Scott, J.F. 38
Set theory 4—5 116—118 See Georg"
Set theory, Cantor on 124—127
Set theory, paradoxes in 137—139
Set theory, Poincare on paradoxes of 166 170—173
Set theory, Russell's paradox of 138 149 156—159 166
Set, defined 124
Shakespeare, William 135
Shea, William R. 38
Short Account of the History of Mathematics, A (Rouse Ball) 43
Sierksma, Gerard 88
Simpson, Stephen G. 186
Sine law 32 48—49 80
Sloane, Hans 65
Smith, David E. 26 82—83
Smith, Henry John Stephen 95
Snapper, Ernst 199 217
Spanish Inquisition 23—24 30 37
Springer, Ferdinand 196
Sylvester, James Joseph 3—4 119 See Thomas
Sylvester, James Joseph, at Johns Hopkins University 114—115
Sylvester, James Joseph, biographical information 103—108
Sylvester, James Joseph, British Association speech by 96 108—114
Symbolism, Descartes and 35
Symbolism, dot notation by Newton 58—59 61 69
Symbolism, Hilbert and 182
Symbolism, Leibniz and 58—59
tangents 40 42 43
Tartaglia (Niccolo Fontana) 10—12
Tartaglia (Niccolo Fontana), Ars Magna (Cardano) and 7 8 14—16
Tartaglia (Niccolo Fontana), Nova Scientia 12
Tartaglia (Niccolo Fontana), on cubic equations 16—17
Tartaglia (Niccolo Fontana), views on Cardano 20—24
Tautochrone 75 83—84
Taylor series 90
Taylor, Brook 85 89—90
Theory of equations 34—35
Theory of invariants 107
Thermodynamics 101
Thiele, Rudiger 78
Thom, Rene 201 214
Thomson, William (Lord Kelvin) 102—103
Toulouse, E. 168
Transcendental numbers 119—120
Transfinite set theory 137 138 207 See Georg"
Tyndall, John 101
Ulysses 48
Uniformitarian theory 100—102
United States, mathematics promoted in 105—106 114—115
University of Basel 73 80 87 91
University of Gottingen 118 119
University of Gottingen, Cantor and 123
University of Gottingen, Hilbert and 184 195
University of Gottingen, Zermelo and 144 145
University of Halle 123—124 129 132 136
University of Virginia 105
van Dalen, Dirk 183—184 186—187 191 194 197 198
Van der Waerden, Bartel L. 189 198
van Schooten, Frans 43 44
Varignon, Pierre 85
Velaria curve 77—78
Vico, Giambattista 209
Viete, Francois 8 34 39 45 50
Virgil 38
Voltaire 71
Wallis, John 45 53 59—62 69
Ward, James 161
Weak law of large numbers 85—87
Weierstrass, Karl Theodor 118—121 123 128 129 140
Well-ordering principle 143 145 150—155 See
Weyl, Hermann 155 184—185 189—192
Whitehead, Alfred North, Introduction to Mathematical Philosophy 180
Whitehead, Alfred North, logicism and 155
Whitehead, Alfred North, Principia Mathematica (Principles of Mathematics) 152—153 157 160 163 165—166 176—178
Wilberforce, Samuel (bishop of Oxford) 100
Works (Wallis) 60—62 69
World of Mathematics, The (Newman) 107
World, The (Le Monde) (Descartes) 37
Wu, H. 211—212
Wykes, Alan 18 20 23
X Club 108
Zermelo's Axiom of Choice (Moore) 149
Zermelo, Ernst Friedrich Ferdinand 4—5 184
Zermelo, Ernst Friedrich Ferdinand, biographical information 144—145
Zermelo, Ernst Friedrich Ferdinand, Borel's criticism of 146—149
Zermelo, Ernst Friedrich Ferdinand, Cantor's well-ordering principle and 142—144
Zermelo, Ernst Friedrich Ferdinand, on axiom of choice 145
Zermelo, Ernst Friedrich Ferdinand, on axiomatization of set theory 149—152
Zermelo, Ernst Friedrich Ferdinand, paradoxes 152—155 See Bertrand
Zero, concept of 16
Zigzag theory 166 171—172
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