Montefeltro, Guidobaldo da, 72
Morgan, Augustus de, 146
motion, laws of, 131
multiplication-of-complex-numbers law, 195, 196
Mysterium Cosmographicum (Kepler), 24, 91
Napier, John, 87–88
Napoleon, 160–61, 166, 170, 175, 176, 177, 178
Nature’s Testimony Against the Atheists (Leibniz), 119
negative numbers, 44, 50, 80
Nemorarius, Jordanus, 79
New Geometry (Klein), 224
New Method for Finding Maxima and Minima (Leibniz), 125
New Methods for Finding Maxima and Minima (Leibniz), 125
Newton, Isaac
background of, 127–28
binomial theorem and, 130
calculus of, 124–26, 130
conic sections and, 31–32
differential calculus of, 131
education of, 128–29, 130
fluxions method of, 130
Gottfried Wilhelm Leibniz and, 114–15, 124–26, 133, 134, 135
integral calculus of, 131
motion laws of, 131
particle-light theory of, 132
Pierre-Simon Laplace and, 172, 173
solving Problem of Apollonius, 31
structure of universe and, 133
studying gravity, 92, 130, 131, 133, 134, 230
“Nine Chapters on Mathematical Art,” 58
Noether, Emmy, 168, 227–29, 232–33
nonagons, 48, 71
non-Euclidean geometry, 152, 224–25, 230, 240
nonorientable surfaces, 225
number mysticism, 11, 12–15
number theory, 154, 220
numerals, Hindu-Arabic, 46, 66, 67, 69
octahedrons, 23, 24
octonions, 195
Oldenburg, Henry, 123
On the Motion of the Stars (al-Battani), 48
On the Sector-Figure (Ibn Qurra), 41
optics, 50, 69, 111, 132
Order of the Rosy Cross, 104
Oxyrhynchus Papyri, 30
Pacioli, Luca, 64–65, 71–74, 72
parabolas, 31, 32, 93, 113
parallel postulates, 51
Pascal, Blaise, 53, 57
Peacock, George, 192
Peirce, Benjamin, 193
Pell, John, 122
pendulums, 123
Perelman, Grigori, 229, 239
perfect number, 13, 14
Pericles, 19, 20
perspective, 69–71
Petersburg Paradox, 141–42
Peter the Great of Russia, 143–44
Philosopher’s Creed (Leibniz), 123
Philosophers of Athens, 20
physics, mathematical, 226, 227, 228
pi, 42, 53, 58
Pisot, Charles, 238
Planck, Max, 226
planetary-motion laws, 90
Plato, 16–17, 18, 23, 24, 36, 91
Platonic solids, 23, 24, 91
Plimpton 322
cuneiform tablet, xviii
Plutarch, 4, 5, 21
Poincaré, Henri, 229, 239–44, 241
Poisson, Siméon-Denis, 187–88
polygons, 73
polyhedron, 70
polynomials, 36, 164, 191, 193
Possel, René de, 238, 239
Poussin, Charles de la Valée, 242
prime numbers, 14, 34, 107–8, 149, 154–56, 191, 242
probability theory, 77, 117, 141, 167, 173, 240, 242
Problem of Apollonius, 31
prosthaphaeresis, 49, 88
Ptolemy, 32, 36, 89
pure mathematics, 35, 111, 112
Pyramids, Battle of the, 178
Pyramids of Giza, xvi–xvii, 5–7, 6
Pythagoras, 8–15, 9, 12, 14, 18–19
Pythagorean triples, xviii, 149
quadratic equations, 42, 44, 46, 50, 53, 113
quantum physics, 226
quartic equations (fourth power), 80, 100, 220
qu a tern ion s, 195, 196, 197
Quesiti et Inventioni Diverse (Tartaglia), 79
quintic equations, 184–85, 191, 220
Ramanujan, Srinivasa, 218–19, 220–24
al-Rashid, Haroun, 40, 45
rates of change, 112, 113, 123, 131
rational numbers, 15, 18, 35
Reign of Terror, 169, 170
relativity theory, 229, 230–32
Rhind Mathematical Papyrus, xix
rhombicuboctahedron, 72
Riemann, G. F. B. (Riemann hypothesis, geometry), 156, 224, 242
Rigaud, Hyacinthe, 121
rigor, mathematical, 149–50
Roomen, Adriaan van, 86
Rosicrucians, 104, 118
Royal Society
at Burlington House, 218–19
Edmond Halley in, 131
Gottfried Wilhelm Leibniz and, 126
Henry Oldenburg in, 123, 126
Isaac Newton in, 131, 132, 134
Leibniz contacting, 119
Rudolph II, 89, 91
Ruffini, Paolo (Abel-Ruffini theorem), 185, 191
Russell’s paradox, 211
Russian Revolution, 247–48
schemes, 253
School of Athens (Raphael), 16–17
Schwartz, Laurent, 251
Science and Method (Poincaré), 240
Sea Mirror of Circle Measurements (Li Zhi), 60
Serre, Jean-Pierre, 244, 255
set theory, 208, 211, 216, 217, 252
Seven Wonders of the Ancient World, 8
sexigesimal number system, xvii–xviii Sforza, Ludovico, 72, 73
Shapiro, Alexander (Taranoff), 246–49, 250
Sieve of Eratosthenes, 34, 107, 154
slide rule, 49, 88
Snayers, Pieter, 105
space-time, 229, 230
square numbers, 13–14, 18, 139
square-root numbers, 18, 19, 81, 212, 221
squaring-the-circle problem, 21, 182, 191
Stairway of Heaven (al-Kashi), 52
Strom, Hélène Jans van der, 109
Summa de Arithmetica, Geometrica, Proportioni et Proportionalita
(Pacioli), 73
Sylvester, James Joseph (Sylvester’s criterion), 193
symmetry in mathematics, 232
Tartaglia (Niccolò Fontana), 74–76, 75, 78, 79, 80
Taylor, Richard, 112
Temple of the Rosy Order, 104
tetrahedrons, 23, 24
Thales, xvi–xvii, 2–7, 6, 8, 9–10, 11, 18
Theon, 35, 36
theoretical physics, 227
theoretical statistics, 151
Theoria Motus Abstracti (Leibniz), 119
Theoria Motus Concreti (Leibniz), 119
Thirty Years’ War, 89, 102, 116, 120
three-body problem, 167, 240
three classical problems of antiquity, 21, 22, 31, 182, 191
topology, 233, 239, 240
topos, 252
triangles, 53, 57, 60–61, 152
triangular numbers, 12, 13, 151
trigonometry, 43, 45, 86, 88
trisecting-an-arbitrary-angle problem, 23, 182, 191
al-Tusi, Nasir Adin, 51, 74
Ulugh Beg, 52, 53
University of Basel, 136–37, 138, 142, 143
University of Göttingen, 226
variation calculus, 146, 167
Viète, François, 84–86, 85, 112
Virgin of the Rocks (da Vinci), 73
Vitruvian Man (da Vinci), 64–65
Voetius, Gisbert, 110
Voltaire, 114–15 volumes, 91
Weierstrass, Karl (Bolzano-Weierstrass theorem), 201, 202, 204, 205, 208, 212
Weil, André, 237, 238, 239, 242, 243–44, 245
Weil, Simone, 237, 238
Wentzel, Johann Friedrich, 123
Werner, Johannes, 69
White Mo
untain Battle, 105
Wiles, Andrew, 36, 112, 113, 191
World, The (Descartes), 107, 108
Wren, Christopher, 122, 131
Yang Hui, 57
Young, Grace Chisholm, 226
Zeno of Elea, 19
Zermelo, Ernst (Zermelo-Fraenkel set t heor y), 216, 217
Zola, Émile, 243