by Ian Stewart
solving, 78–79, 91–92, 115
Radiation, 202
Radicals, 72, 83, 89, 97–98
Ramond, Pierre, 251
Ramses II, 18
Rate of change, 162
Rationals, 132
Ravelli, Carlo, 255
Ray optics, 140
Rayleigh-Jeans law, 201
Rays, 175
Re, 17
Real numbers, 143
as division algebras, 157
Reality, 222
Reflection, 141–142
of time, 187
Refraction, 176
Relativity, xiii, 184, 189–190, 193, 212
consequences of, 191–192
quantum theory and, 221–222
Religion, 223
Representation theory, 122–123, 219
Revue Encyclopédique, 109
Ricci-Curbastro, Gregorio, 195
Rich, Claudius, 6
Richard, Louis-Paul, 100
Richelot, F. J., 136
Richmond, H. W., 136
Riemann, Georg Bernhard, 73, 194
Riemannian manifolds, 194
Right angles, 147
Root systems, symmetry in, 168
Roots, 106, 117–118. See also
Cube roots; Square roots
Roots of unity, 68
Rosenfeld, Boris, 272
Rotation, 119, 120, 121, 163
of Earth, 187–188
Rothman, Tony, 110
Rubaiyat (Khayyám), 33, 38–39
Ruffini, Paolo, 78–79, 87, 88, 256
proof of, 80–81, 83–84
Sabah, Hasan, 37, 39
Scherk, Joel, 251
Schonen, Richard, 246
Schrödinger, Erwin, 203–204, 205–206, 208, 209
Schrödinger, Rudolf, 204
Schrödinger’s cat, 205, 209
Schwarz, John, 251
Sedenions, 265–266
Seleucid period, 7
Seti I, 18–19
7-gons, 27
17-gons, 30, 63, 135–136
Sexagesimal system, 12, 145
Shamash, 8
Sight, 174–175
Simonsen, Anne Marie, 84–85
Simonyi, Charles, 244
Sirius, 21
Siwa, 17, 18
Smith, Willoughby, 186
Smolin, Lee, 255
Smoluchowski, Marian, 186
SO(2), 163, 239
SO(3), 239, 240, 268
Solutions, presence of, 146
Sommerfield, Arnold, 208
Space, 186
Space, Time, and Gravitation (Eddington), 212
Space-time, 191
curvature of, 192, 193–194, 195, 197
extra dimensions of, 229–230
Minkowski, 192
properties of, xiii
shape of, 253
symmetries of, 192
Speciation, 241
Spectrum, 217
Spin, 236
Spinors, 214, 273
Spontaneous symmetry-breaking, 218
Square numbers, 21
Square roots, 3, 4, 14, 47, 145
of minus one, 146
of negative numbers, 59–60, 260
Squaring the circle, 125, 129–130
Steinhardt, Paul, 257–258
Stevin, Simon, 144–145
Stobaeus, 21
Straightedge, 25, 26, 27, 29, 30, 33, 63, 126, 127, 128, 129, 134, 150
String theory, 251, 252, 255, 257, 259, 263, 272, 273
backlash against, 254
bosonic, 252
Strominger, Andrew, 253
Strong anthropic principle, 257
Structure, 118–119
defining, 119
SU(2), 239, 268
SU(3), 239
Subgroups, 112–113, 114–115, 115
of permutations, 114
Sumer, 1
Sun, 197
Superstrings, 249, 251, 256–258, 259
types of theory, 253–254
Supersymmetry, 230, 246, 247, 248, 249, 251, 253
Surveying, 48
Sylow, Ludwig, 159
Symbolism, in algebra, 35
Symmetry, 157, 162, 197, 230, 231, 236
in algebra, 121
defining, 118
gauge, 233
inertial frames and, 189
local, 231
mathematics and, 279–280
of Maxwell equations, 191
multiplying, 121
permutations and, 113
in protons, 239
in root systems, 168
of space-time, 192
speciation and, 241
spontaneous, breaking, 218
as transformation, ix
of triangle, 120
Symmetry groups, 160
Symplectic groups, 168
Tait, Peter, 154, 155
Talmud, Max, 182
Tartaglia. See Fontana, Niccolo
Taton, René, 101
Temperature, 241–242
Tensors, 195, 197
Terquem, Orly, 100
Theaetetus, 21
Theorems, 25
Theory of Everything, 222, 223, 240–242, 254, 263, 273, 276
Thermodynamics, 205
Tignol, Jean-Pierre, 77
Tigris, 1
Time, 141, 187, 226
Babylonian measurement of, 12
reflection of, 187
translation of, 187
Tits, Jacques, 271
Tool-building, 29
Topology, 225, 245, 251
Tower of Abel, 91–92
Tower of Babel, 2, 91
Towers, 89–90
Transcendental numbers, 130, 131
Transformation, 118–119, 121–122
defining, 119
Translations, of time, 187
Trattato della Pittura (da Vinci), 269
Treatise on Light (Huygens), 177
Tree of Life, 241
Triangles, 118–119
inequality, 193
symmetries of, 120
Triangular numbers, 21
Trigonometry, 49, 128–129
Trisections, 28–29, 125, 128–129
Truth
beauty and, 188, 263, 275
mathematics and, 275
Tunneling theory, 257–258
Turok, Neil, 257–258
Typhus, 81
Ultraviolet catastrophe, 202
Unification, 140–141
Unified field theory, 198
Universe
harmony of, 21
mathematics and, xiii
University of Königsberg, 134
Uruk, 2
Vacuum energy, 257
Vandermonde, Alexandre-Thóphile, 75
Vector addition, 150
Vector algebra, 154
Vectors, 273
Veneziano, Gabriele, 250
Vibration patterns, 217–218, 250
von Neumann, Janós, 215, 216, 220, 259
Wallis, John, 146, 147, 149
Wantzel, Pierre Laurent, 126–127, 129, 135
Watson, James, 205
Wave optics, 140
Wavelengths, 180
Wavicles, 203
Weak anthropic principle, 257
Weakons, 237
Weather, 226
Weber, Heinrich Friedrich, 184, 216
Weber, Wilhelm, 72–73
Wecklein, Anna, 206
Wecklein, Nikolaus, 206
Weierstrass, Karl, 160, 166, 200
Wessel, Caspar, 148
Wessel, Ole, 148
Wessel plane, 148
Western world, 19
Weyl groups, 168
Weyl, Hermann, 217
What Is Life (Schrödinger), 204–205
Whittaker, 213
Wien, Wilhelm, 201
Wigner, Antal, 215, 216
Wigner, Eugene, x, 215, 216, 217, 219–220, 259, 277
Wiles
, Andrew, 36
William the Silent, 144
Witmer, Richad, 53–54
Witten, Edward, 244, 248, 252
Wolff, Christoph, 207
Woodward, Bob, 243
Wordsworth, William, 139–140
World line, 192, 249
Worldsheets, 249–250
x, 34, 47
Yang, Chen Ning, 238
Yang-Mills field, 238
Yau, Shing-Tung, 246
Zagros Mountains, 1
Zero, 144
Zimmerman, E. A. W., 66
Zorn, Max, 266