index

Page numbers in italics refer to illustrations

Abel, Niels Henrik 67, 114–16, 118–21

Allendoerfer, Carl 178

Anderson, Carl 170

Arabic numerals 14–15

Archimedes 40–3, 48–51, 52–5, 54

Measurement of the Circle, The 40

On Floating Bodies 53–4

principle 53–4

quadrature 82–3

Quadrature of the Parabola 48–51

Aristarchus of Samos 68

Aristotle 70–71, 92

Atiya, Michael 180

atomic bomb 157, 158

Bachelier, Louis 210

Bacon, Francis 76

Bailey, David 45

Barrow, Isaac 83

Bessel, Friedrich 124

Biot, Jean–Francois 141

Black, Fischer 204–13

Black-Scholes formula 204–13

Blaschke, Wilhelm 175

Bolyai, Janos 124, 127, 174

Bolyai, Wolfgang 123–4

Bombelli, Rafael 66–7

Bonnet, Pierre Ossian 176

Borwein, Peter 45

bosons 170, 172

Brahe, Tycho 70–3

Brahmagupta 27–9, 28, 61

Brownian motion 210, 211

Bryant, Robert 181

butterfly effect 198

calculus 80–9, 100–101

Cantor, Georg 183–8

Cantor’s Continuum Hypothesis 187, 192–3

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

Frey, Gerhard 78

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

Li Tien-Yien 202

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

Theorem 30–9, 33

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