Abacus 258
Abbott, Edwin 228
Abel, Niels 149, 152, 179, 180, 184
Abstract algebra 187-99
Abstract groups 192
Adam, Douglas 267
Alberti, Leone Battista 161
Algebras 195
Algebraic symbolism 64
Algoriths 262
Al-Kindi 46
Analyst, a Discourse Addressed to an Infidel Mathematician, The 117
Analytical Mechanics 227
Analytical Theory of Heat, The 150
A Plea for the Mathematician 225
Arabian mathematics 6, 47, 75, 175
Arbuthnot, John 252
Archimedean spiral 87
Aristarchus 71
Arithmetic Logarithmica 79
Arithmetic 40-53
Arithmetica 98
Arnold, Vladimir 269
Ars Conjectandi 251
Ars Magna 63
Art 161
Aryabhata 44
Astronomy 72
Atomic bomb 259
Babbage, Charles 258
Babylonian mathematics 6, 13-15, 21, 30, 175, 176
Barlow, William 182
Barrow, Isaac 114
Base ten logarithms 78
Belbruno, Edward 277
Beltrami, Eugenio 223
Berkeley, Bishop George 117, 149
Bernoulli, Daniel 153
Bernoulli family 88
Bernoulli, Jacob 251-3
Bessel functions 153
Bessel’s equation 153
Bhaskaracharya 74
Binary numbers 229
Biology 276
Bolyai, Janos 168
Bolyai, Wolfgang 167
Bolzano, Bernard 149, 152, 157
Boolean algebra 197
Borcherds, Richard 197
Brahe, Tycho 111
Brahmagupta 44
Bravais, Auguste 183
Briggs, Henry 78
Brunelleschi, Filippo 161
Burgi, Jobst 79
Burrough, Peter 276
Byron, Lord 260
Calculus of Extension, The 221
Canon Mathematicus 75
Cardano, Girolamo 62-5, 139, 175, 179, 250
Carroll, Lewis 243
Cartesian coordinates 86
Cartwright, Mary Lucy 269, 271
Cauchy, Augustin-Louis 144, 146, 152, 157, 203
Cauchy-Riemann equations 146
Cayley, Arthur 192, 193, 223, 236
CDs 199
Cellular automaton 275
Chandas Shastra 251
Chaos theory 266-78
Chinese mathematics 49
Chou, Hui-Hsien 276
Christoffel, Elwin Bruno 223
Chuquet, Nicolas 67
Classes 235
Classification Theorem for Surfaces 209
Clay Institute 214
Closed universe 170
Cogitata Physica-Mathematica 96
Cohen, Paul 241
Colmar, Thomas de 259
Combinations 250
Complex analysis 141
Complex numbers 137-47
Complex systems 273-6
Comptes Rendus de l’Academie Francaise 146
Computational mathematics 257-65
Computers 258
Conic sections 34
Continuous functions 151
Conway, John 197
Copernicus, Nicholas 110, 111, 122, 238
Cotes, Roger 143
Cowan, George 273
Coxeter, Harold Scott MacDonald 192
Coxeter diagrams 192
Craig, James 77
Cuneiform numerals 21
Dedekind, Richard 193, 194, 232-4
Del Ferro 175
Della Pittura 161
Der Census Räumlicher Complexe 206
Desargues, Girard 163
Desargues’s Theorem 163
Descartes-Euler Formula 203
Descartes, Rene 66, 67, 84-7, 114, 140, 202, 218, 221
De Triangulis 75
Dialogue Concerning the Two Chief Systems of the World 114, 238
Die Grundgesetze der Arithmetik 236
Die Grundlagen der Arithmetik 236
Differential equations 120, 123-36
Differential geometry 222
Discours de la Méthode 84
Discourses and Mathematical Demonstrations Concerning the Two New Sciences 113
Disquisitions Arithmeticae 99
Dodgson, Charles Lutwidge 243
DVDs 199
Dyck, Walther van 193
Dynkin diagrams 192
Dynkin, Eugene 192
e 79
Eddin, Nasîr 75
Edgeworth, Ysidor 255
Egyptian mathematics 15-17
Einstein, Albert 169, 195, 213, 222, 223, 227, 242, 244
Electromagnetic Theory 221
Electromagnetism 127
Elements of Vector Analysis 221
Ellipses 33
Engel, Friedrich 191
Eratosthenes 35
Erlangen Programme 169
Escher, Maurits 169
Euclid 22, 25-9, 37, 83, 93-5, 160, 166, 169, 172, 201, 242, 243, 254, 262
Euclidean geometry 21-39, 69-81
Euclides ab Omni Naevo Vindicatus 165
Euclid’s Fifth Postulate 161
Eudoxus 22
Euler, Leonhard 93, 127, 143, 150, 155-7, 202, 204, 205, 207, 260
Fedorov, Evgraf 182
Fermat, Pierre de 83, 97, 114, 140, 250
Fermat’s Last Theorem 93, 102, 177, 188, 194, 196-8, 241
Fermat’s Little Theorem 97
Ferrari 175
Fibonacci 47
Fibonacci Sequence 61
Fields 194
Fior 175
Fischer, Bernd 197
Flatland 228
Flat universe 170
Fluid dynamics 131
Four-dimensional space 217
Fourier analysis 148-58
Fourier, Joseph 129, 149-51, 182, 232
Fowler, David 29
Functions 87
Fundamental Theorem of Algebra 206
Furtwängler, Philipp 245
Galileo, Galilei 107, 113, 122, 238-41
Galois, Evaristel, 174, 180-5, 190, 193, 196, 197, 199
Games of chance 249
Gauss, Carl Friedrich 93, 141, 144-6, 166-8, 170, 177, 178, 193, 206, 212, 219, 222
Gaussian integers 193
Gaussian numbers 193
Gell-Mann, Murray 274
General Theory of Equations 178
Geology 276
Geometry 21-39, 69-81, 159-72, 200-215, 216-29
Germain, Marie-Sophie 103
Gibbs, Josiah Willard 221
Global positioning system 18
Gödel, Kurt 244-6
Gödel’s incompleteness theorem 244-7
Godfrey, Thomas 90
Goldbach, Christian 97
Golden mean 28
Gordan, Paul 242
Gorenstein, Daniel 196
GPS 18
Grassmann, Hermann Günther 220
Gravity 128
Grebogi, Celso 277
Greek numerals 41
Greek mathematics 22-37, 41, 62, 83, 175
Griess, Robert 197
Group theory 173-86
Grundlagen der Geometrie 243
Hadley, John 90
Hamiltonian 134
Hamilton, Richard 213
Hamilton, William Rowan 134, 219
Hamming, Richard 230
Harrison, John 90
Heat 129
Heaviside, Oliver 221
Heiberg 31
Helmholtz, Hermann von 223
Hermes, J. 103
Hertz, Heinrich 135
High-dimensional geometry 216-29
Hilbert Problems 242-5
Hindu mathematics 43-6
Hippasus 24
Hitchhiker’s Guide to the Galaxy, The 267
Hölder, Otto 184
Huntingdon, Edward 193
Hypatia 37
Hyperbolas 34
Hypothesis testing 256
Imaginary numbers 137-47
Incompleteness theorem 244-7
Indian numerals 43
Integers 138
Introduction to Mathematical Philosophy 245
Introduction to Plane and Solid Loci 83
Irrational numbers 24
Jordon, Camille 182-4
Jupiter table 14
Karaji, Al 251
Kauffman, Stuart 276
Kepler, Johannes 7, 107, 110, 112, 113, 122, 132
Kepler’s Laws of Planetary Motion 112
Khayyám, Omar 62, 63, 175, 251
Klein bottle 209
Klein, Felix 169, 188-90, 192, 198, 209
Kline, Morris 6
Kolmogorov, Andrei 254
Königsberg Bridges puzzle 202
Kovalevskaya, Sofia Vasilyevna 133
Kummer, Ernst Eduard 194
Kutta, Martin 260
Lacaille, Abbe Nicolas Louis de 81
La Géometrie 84
Lagrange, Joseph-Louis 93, 133, 134, 177, 182, 227
Lagrangian 134
L’Algebra 139
Lambert, Johann Heinrich 30, 166, 167
Lame, Gabriel 194
Laplace’s equation 130
Lasers 153
Laskar, Jaques 262
Law of Large Numbers 253
Lebesgue measure 254
Lectures on Lineal Extension 221
Legendre, Adrien-Marie 164
Leibniz, Wilhelm Gottfried 107, 118-120, 124, 142, 143, 202, 258
Lejeune-Dirichlet, Peter 194
Levi-Civita, Tullio 223
Liber Abbaci 61
Lie groups 190-2
Limits 152
Listing, Johann 206
Li, Tien-Yien 269
Littlewood, John 269
Lobachevsky, Nikolai Ivanovich 167
Logarithmorum Canonis Constructio 78
Logarithmorum Chilias Prima 78
Logarithms 76-80
Logic 231-47
Longitude 90
Lorenz, Edward 269
Luminet, Jean Pierre 171
Maclaurin, Colin 128
Mahavira 44
Mandelbrot, Benoir 272
Marconi, Guglielmo 135
Mathematics of Plato’s Academy, The 29
Mathematical Reviews 9
Mathematical Syntaxis 73
Matrix algebra 223
Maxwell, James Clark 128, 135, 221
Maxwell’s equations 135
Mayan numerals 51
Meinhardt, Hans 276
Mengenlehre 238
Meré, Chevalier de 250
Mersenne primes 96
Mesopotamian symbols 10
Method of Fluxions 107
Method of Fluxions and Infinite Series 117
Method of Mechanical Theorems 32
Millennium Mathematics Problems 214
Minkowski, Hermann 224
Minkowski space-time 224
Mirimanoff, Dimitri 194
Möbius, Augustus 206
Möbius band 206
Möbius transformations 169
Moivre, Abraham de 253
Monstrous Moonshine Conjecture 197
Moore, Eliakim 193
Morgan, Augustus de 28
Muller, Johannes 75
Multidimensional space 225
Music 127
Mysterium Cosmographicum 110
Napier, John 76
Napierian logarithms 77
Napier’s Rods 76
Natural irrationalities, theorem on 179
Navier-Stokes equations 264, 270, 271
Negative numbers 49
Neumann, John von 275
New Logarithmes 79
Newton, Isaac 7, 67, 76, 90, 107, 116-18, 120, 122, 124, 128, 132, 136, 140, 154, 254, 259, 261, 267
Noether, Emmy Amalie 195
Noether’s Theorem 195
Non-Euclidean geometry 159-72, 200-215
Nonlinear dynamics 266-77
Notions sur la Machine Analytique de Charles Babbage 260
Number theory 92-105
Numerical analysis 257-65
Odhner, Willgodt T. 259
On Plane Loci 83
On the Revolutions of the Heavenly Spheres 110
On the Sizes and Distances of the Sun and the Moon 71
On the Sphere and the Cylinder 30
Open universe 170
Ott, Edward 277
Pacioli 250
Parabolas 34
Pascal’s triangle 251
Pearson, Karl 256
Perelman, Grigori 213
Peuerbach, George 75
Phidias 71
Plane trigonometry 77
Planetary motion 112
Playfair, John 164
Plea for the Mathematician, A 225
Poincaré, Jules Henri 174, 210-14, 246, 269, 270, 274
Pol, Balthazar van der 268
Polyhedrons 202
Portsmouth Papers 107
Power series 155
Primes 93-7
Principia Mathematica 107
Probability 248-56
Probability theory 251
Prosthapheiresis 77
Pythagorean triples 96
Ptolemy’s Theorem 73
Pythagoras’s Theorem 22, 26, 83, 96, 155, 224
Quaternions 219
Quetelet, Adolphe 255
Recorde, Robert 68
Reed, Irving 199
Reed-Solomon codes 199
Reggia, James 276
Regiomontanus 75
Regular polyhedra 27
Rhabdologia 78
Rhaeticus, George Joachim 75
Ribet, Kenneth 198
Ricci-Curbastro, Gregorio 213, 223
Ricci tensor 213
Richardson, Lewis Fry 273
Richelot, F.J. 103
Riemann 156, 189, 207, 222, 246
Riemann Hypothesis 156
Rings 194
Roman numerals 41
RSA code 104
Ruelle, David 270
Runge, Carl 260
Runge-Kutta methods 260-1
Russell, Bertrand 236, 237, 245
Russell’s paradox 237
Salmon, George 223
Satnav 18
Schlick, Moritz 245
Schmandt-Besserat, Denise 10
Schönflies, Arthur 182
Science and Hypothesis 210
Science and Method 210
Sets 235
Sharkovskii, Oleksandr 269
Sharkovskii’s Theorem 269
Sierpinski, Waclaw 272
Smale, Stephen 269
Snoflake curve 272
Solomon, Gustave 199
Speidell, John 79
Statistics 248-56
Staudt, Karl von 206
Stetigkeit und Irrationale Zahlen 232
Stokes, George Gabriel 132
Summerian numerals 12
Sylvester, James Joseph 225
Syllogism 243
Symbolic Logic 243
Symmetry 173-86
Symmetry of a quadratic 176
Takens, Floris 270
Taniyama-Shimura conjecture 196
Taniyama-Weil conjecture 197
Taylor, Richard 196
Tentamen Juventum Studiosam in Elementa Matheseos 168
Theorie Analytique de la Chaleur 130
Thurston, William 211
Time Machine, The 217
Topology 200-215
Traité de Substitutions et des Équations Algébriques 182
Transformationsgruppen 191
Triangles 69-81
Treatise on the Quadrilateral 75
Trigonometry 69-81
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme 245
Universe, shape of 171
Value of Science, The 210
Varahamihira 74
Vieta 66-8
Vorstudien zur Topologie 206
Walther, Bernard 75
Wantzel, Pierre 178
Was Sind und was Sollen die Zahlen? 232
Wave equations 126
Weil, André 198
Wells, Herbert George 217
Wessel, Caspar 141
Whetstone of Witte, The 66
Whitehead, Alfred North 237
Wilkinson Microwave Anisotropy Probe 171
Wisdom, Jack 262
Zermelo, Ernst 245
Zuse, Konrad 275