Cardano, Girolamo 58–9, 62–7, 114, 118, 119
Ars magna 64, 65
formula 60–7
Opera omnia 66
Practica arithmeticae generalis 62
Cartan, Elie 112, 175–6
Cauchy Augustin-Louis 115
Cavalieri, Buonaventura 82–3
chaos theory 194–203
Chebyshev, Pafnuty 131
Chern, Shiing–Shen 175–81
Chern-Gauss-Bonnet theorem 176–81
Cohen, Paul 1923
complex numbers 65
Copernicus, Nicolaus 68–9
Crelle, Leopold August 115
Crelle’s Journal 115, 125
cubic equations 64–7
cuneiform script 24, 27
Davis, Philip 25
del Ferro, Scipio 62
della Nave, Annibale 62
Descartes, René 75, 88, 92
La Géométrie 129
differential geometry 174–81
Diophantus of Alexandria 21
Dirac, Paul Adrien Maurice 169, 167–73
Dirac’s formula 164–73, 180
Dunham, William 80
Einstein, Albert 67, 160, 152–63, 193
light-quanta hypothesis 155–6, 163
theory of general relativity 161–2, 162, 174, 176
theory of special relativity 127, 159–63
Escher, M.C. (Maurits Cornelis) 77, 78
Euclid 22, 61, 66, 122
Elements 18, 34
Geometry 122
Eudoxus of Cnidos 51
Euler, Leonhard 44, 76, 96–103
Mechanica 99
the Basel problem 103
the infinitude of prime numbers 102
f-hat 140–41
Faraday, Michael 145
Fermat, Pierre de 74–9
Fermat’s last theorem 74–9
Ferrari, Lodovico 58–9, 64–5, 118, 119
Feynman, Richard 12–15
Fiore, Antonio Maria 62
Fizeau, Armand 148
Fourier, Joseph 135–41, 140
Fourier series 135–41
Fraenkel, Abraham 189
French Academy of Sciences 82, 96, 117, 134
Frénicle de Bessy, Bernard 75–6
Fresnel, Augustin 144
Fundamental Theorem of Calculus 80–9
Galilei, Galileo 68–70
Galois, Évariste 114, 116–21, 117
Gauss, Karl Friedrich 90, 115, 123, 127, 127, 128–31, 133, 174, 182
Gauss-Bonnet theorem 177–8
Gell-Mann, Murray 121
Gerlach, Walther 166
Gibbs, Josiah Willard 111
Gleick, James 198, 202
Gödel, Kurt Friedrich 24–5, 189–193, 190
Gödel’s Incompleteness Theorem 191
Gou-gu theorum 36–9
Graves, John 111, 112
Gray, Jeremy 103
Gregory-Leibniz formula 44
Grimaldi, Francesco 144
group theory 114, 118–21
Hadamard, Jacques 132
Halley, Edmund 92, 94
Hamilton, William Rowan 106–13, 110, 168
heat equation 137–41
Heaviside, Oliver 111
Heisenberg, Wolfgang 170
Heisenberg Uncertainty Principle 191
Hénon, Michel 198
Hermite, Charles 119, 121
Hersh, Reuben 25
Hertz, Heinrich 154
hexadecimal arithmetic 45
Hilbert, David 22, 183, 187–9
Hooke, Robert 92, 143
Hooley, Christopher 133
Huygens, Christian 92
hyperbolic geometry 125–7
imaginary numbers 65
irrational numbers 35
Jefferson, Thomas 19
Jones, William 44
Kassouf, Sheen 206
Kepler, Johannes 69–73, 92
first law 70–71, 92
Harmony of the World 73
second law 71–3
third law 73
Khayyam, Omar 61
Kronecker, Leopold 22, 36, 187
Kummer, Ernst 77
Lafayette, Marquis de 116
Lagrange, Joseph Louis 139–41
Lambert, Johann 45, 123
Lamé, Gabriel 77
Legendre, Adrien-Marie 115, 123
Leibniz, Gottfried Wilhelm 44, 84
calculus 80–9
Lenard, Philipp 154
Lindemann, Ferdinand 45
Littlewood, John 200
Liu Hui 38–9, 42–3
quadrature 82
Lloyd, Humphrey 108
Lobachevski, Nikolai
Ivanovich 124–5, 127, 174
Lorenz, Edward 195–8
Lorenz Attractor 196, 200, 202
Lyapunov, Aleksandr 200
Madhava 44
magnetic fields 145–9, 146
Mandelbrot, Benoit 202
Manhattan project 152
Marconi, Guglielmo 149
Markus, Willem 198
Maxwell, James Clerk 145–9
Maxwell’s equation 145
Maxwell’s theory of fields 147
May, Robert 198
Mersenne, Marin 74–5, 82
Merton, Robert 204–13
Michelson, Albert 159
Millikan, Robert 156
Minkowski, Hermann 153
Morley, Edward 159
Napoleon Bonaparte 134–6
Napoleon’s theorem 135
Newton, Isaac 44, 93
calculus 80–9
light 143
Law of Universal
Gravitation 91
laws of motion 81, 91, 94
method of fluxions and infinite series, The 87, 89
Principia 92
theory of gravity 147
Nine Chapters on the Art of Mathematics 36–8, 41–3
non-Euclidean geometry 22, 122–7, 174
number theory 128–33
Ørsted, Hans Christian 145
Pacioli, Fra Luca 61
parallel postulate 122–5
Parmenides 35, 46
Peano, Giuseppe 22
perfect numbers 32
pi 40–45, 45, 88
Planck, Max 156
Plouffe, David 45
Poincaré, Henri 199–200
Pólya, George 97
prime number theorem 128–33
prime numbers 32, 130
Ptolemy 66, 71
Pythagoras 30–6, 37
quadratic formula 60–61, 63
quantum mechanics 65, 158, 164–73
quartic equations 64–7
quaternions 106–13, 113, 168
quintic equations 67, 118–21
Ribet, Kenneth 78
Riemann, Bernhard 127, 131–133, 174
Riemann’s hypothesis 132
zeta function 131–3
Roman numerals 14–15, 26
Roosevelt, Franklin 152
Ruelle, David 198
Russell, Bertrand 22, 188
Principia Mathematica 24
Scholes, Myron 204–13 Shanks, William 44
Sharkovsky, Olexandr 202
Shelley, Mary 107
Singer, Isadore 180
Smale, Steven 200
Somayaji, Nilakantha 44
Spivack, Michael 175
Stern, Otto 166
Takens, Floris 198
Taniyama-Shimura conjecture 78
Tartaglia, Niccolò 58–9 62–5
Taylor, Richard 79
Taylor’s formula 13
Theodorus of Cyrene 35
Thomson, William (Lord Kelvin) 112, 149
Thorp, Edward 206
Vallée–Poussin, Charles de la 132
van der Pol equation 200
Volta, Count Alessandro 144
Voltaire 82, 91
von Neumann, John 194–5
Weil, André 76, 79, 178
Whitehead, Alfred North 24
Principia Mathematica 24
Wilczek, Frank 170
Wiles, Andrew 78–9
Wren, Christopher 92
Wu Hung-Hsi 181
Yorke, James 202
Young, Thomas 143
Zeno of Elea 35, 46–8, 49
Zermelo, Ernst 189
Zermelo-Fraenkel set theory 189–193
Picture credits
Alamy: pp. 37, 54, 160, 207; The Art Archive: p. 104; The Art Archive/British Museum: p. 16; The Art Archive/Kharbine-Tapabor/Photo Boistesselin p. 23; The Art Archive / Bibliothèque des Arts Décoratifs Paris / Gianni Dagli Orti: p. 127; Corbis: pp. 24, 66, 93, 99, 217; Getty: pp. 10, 54, 72, 87, 120, 136, 157, 162; Science Photo Library: Endpapers, pp. 2, 33, 49, 58, 113, 117, 133, 140, 145, 146, 150, 166, 169, 171, 179, 188, 190, 196, 200, 211; Topfoto: pp. 78, 84, 88, 100.