Why Beauty is Truth (64 page)

Engel, Friedrich,
167

Enlil,
9

Equations,
5–6
,
34
.
See also
Quadratic equations

complex numbers and,
68

theory of,
101

Equivalence principle,
194

Eratosthenes,
20

Eridu,
2

ETH (Eidgenössiche Techhnische Hochschule),
183
,
184

Euclid,
19–21
,
28
,
31
,
49
,
182
,
193–194
,
270

axioms of,
24–25

innovations of,
22–23

life of,
20–21

omissions of,
26–28

Eudoxus,
21

Euler, Leonhard,
66–67
,
68
,
69
,
76
,
85
,
132
,
148
,
264

Euphrates,
1
,
2

Exner, Franz,
204

Experimental Researches
(Faraday),
179

Fano plane,
262
,
270

Fantini, Luigi,
79

Faraday, Michael,
177
,
178
,
179

Ferdinand, Carl Wilhelm,
66
,
67

Fermat, Pierre de,
36
,
141
,
264

Fermat primes,
135

Fermat's Last Theorem,
36
,
86
,
126
,
207

Fermi, Enrico,
236

Fermions,
236
,
239

Ferrari, Lodovico,
54
,
55–56

Fontana and,
55–56

Ferrari Tower,
90–91

Fertile Crescent,
1–2

Feynman diagrams,
249–250
,
250

Fibonacci.
See
Leonardo of Pisa

Fibonacci sequence,
49

Fields Medals,
246
,
248

Fields, ordered,
156

Fifth postulate,
22–23

Fifth roots,
68–69
,
114

Fior, Antonio Maria,
54

Fitzgerald, Edward,
33

Flatland
(Abbott),
227

Fontana, Niccolo,
45
,
55

Cardano, Girolamo, and,
53–54

Ferrari and,
55–56

Forces,
233–235
.
See also
Electromagnetism
;
Gravity
;
Nuclear force

characteristics of,
238

Formulas, breeding of,
89

Four Squares Theorem,
76
,
77
,
264–265

Fourier, Joseph,
103

Fourth dimension,
225
,
226

Fractions,
144

in Babylonian times,
12–13

France, Prussia and,
161

Frank, Amelia,
219

French Revolution,
76–77

Freudenthal, Hans,
271

Fridrichsen, Henriette,
95

Fundamental particles, x,
230

Fundamental Theorem of Algebra,
70

G
₂
-manifolds,
254

Galileo,
56
,
277

Galois, Évariste, ix, xi,
98–99
,
101
,
104–105
,
107
,
162
,
275

arrest of,
105–106

duel of,
109–110

education of,
99–100

innovations of,
110–111

proofs of,
106

Galois group,
113
,
116–117

limitations of,
117

Galois, Nicolas-Gabriel,
99

Galois test, xii

Galois's Theory of Algebraic Equations
(Tignol),
77

Garrone, Lorenzo,
183

Gauss, Carl Friedrich,
63–64
,
83
,
88
,
127
,
134–135
,
166

death of,
73

education of,
64–65

fame of,
71

theorems of,
70

Gauss, Gebhard Dietrich,
64

Gauss plane,
148

General Theory of Equations
(Ruffini),
79

General Theory of Terrestrial Magnetism
,
72–73

Geodesics,
196

Geometry

Euclidean,
22–28

noncommutative,
255

of quadratic equation,
15–16

Germain, Sophie,
105

Gibbs, Josiah Willard,
154
,
155

Gjerstad,
84

Global Positioning System,
180

Gluons,
237

Göttingen,
71
,
72
,
160

Gout,
154

Grand Unified Theories (GUTs),
240
,
248

Grassmann, Hermann,
154
,
155

Graves, John,
261–262
,
263
,
265
,
266

Graviton,
237

Gravity,
193
,
195
,
196
,
197
,
225
,
233
,
234
,
251

electromagnetism and,
223–225

loop quantum,
255–256

The Great Art
(Cardano, G.),
47
,
53–54
,
55
,
60
,
75

Green, Michael,
252

Grossmann, Marcel,
184–185
,
194–195
,
198

Group disease,
219–220

Group theory,
ix
,
xi
,
111–113
,
125
,
161

cubic equation and,
116

quadratic equation and,
116

quartic equation and,
116

Group Theory and Its Application
to Quantum Mechanics of Atomic Spectra
(Wigner, E.),
217

Guigniault, M.,
103–104

GUTs.
See
Grand Unified Theories

Gymnasium,
66

Habilitation thesis,
73
,
204

Hahn, Otto,
201

Halley, Edmond,
76

Hamilton, William Rowan,
137–138
,
140
,
152
,
154
,
260
,
268

on complex numbers,
148–150

education of,
137–138

Hamiltonian systems,
139

Hanging Gardens,
2

Hansteen, Catharine,
95

Hansteen, Christoffer,
85

Hansteen, Johanne,
92

Hardrons,
251

Hardy, Godfrey Harold,
267

Harmony,
21

Harnack, Adolf von,
200–201

Hasenhöhrl, Friedrich,
204

Hashishiyun,
39

Hawkins, Thomas,
167

Heisenberg, August,
206

Heisenberg, Werner,
206–210
,
213
,
221
,
278

Heliocentric theory,
188

Helmholtz, Hermann von,
166
,
189
,
200

Henry VIII,
178

Hermite, Charles,
133
,
134

Hertz, Heinrich,
180
,
186

Hexagons, constructing regular,
30–31

Hilbert, David,
134
,
165
,
197

Hippasus of Metapontum,
47
,
130

Hitler, Adolf,
203
,
204
,
208

Hoesslin, Marga von,
201

Holmboe, Bernt,
85
,
93–94

Holten, Florence Hannah,
211

Homer,
19

Hooke, Robert,
175

Horowitz, Gary,
253

Huguenin, Ulrich von,
136

Humboldt, Alexander von,
71

Hunter-gatherers,
1–2

Hurwitz, Adolf,
157
,
184
,
266

Hutton, Sarah,
137

Huxley, Thomas,
278

Huygens, Christian,
177

Hydrogen,
204

Hyperbola,
40

Hyperspheres,
228

i
,
260

Identity,
120–121

Imaginary numbers,
146
,
148–149

Inertial frames,
188–189

symmetry and,
189

Infantozzi, Carlos,
107

Inference,
229

Infinite decimals,
145

Inquisition,
56

Institute for Advanced Study,
219
,
244
,
245

Invariant theory,
191

Inverse square law,
40

Iraq, rubble mounds in,
6

Irrationals,
130
,
131

Ishtar Gate,
8

al-Jabr w'al Muqâbala
(al-Khwarizmi),
36–37

Jacobi, Carl Gustav Jacob,
67–68

Jean-Louis,
107

Jolly, Philipp von,
199
,
200

Jordan, Camille,
122

Jordan, Pascual,
271

Journal de Mathématiques Pures et Appliquées
,
127

K(9),
240

Kaiser Wilhelm Institute,
216

Kaluza, Theodor,
224–225
,
229
,
253

Kaluza-Klein theory,
230

Kant, Immanuel,
182

Karnak,
18

Kelvin, Lord,
199

Kemp, Christine,
86
,
87
,
93
,
94
,
95

Kepler, Johannes,
40
,
276
,
277

Khayyám, Omar,
33
,
37
,
38–39
,
41–44

al-Khwarizmi, Mohamed ibn Musa,
36–37

Killing, Wilhelm Karl Joseph,
165
,
166
,
167
,
168
,
169
,
170–171
,
272

proofs of,
168–169

Killing's list,
239
,
268

Kinetic theory,
186

Kirchhoff, Gustav,
200

Klein, Felix,
133
,
160

Klein, Oskar,
230

Klein's Elangen program,
270

Kline, Morris,
50

Kollros, Louis,
108

Königsberg,
224

Kragh, Helge,
278

Kronecker, Leopold,
160

Kummer, Ernst,
160
,
166

Küssner, Elizabeth,
134

Lacroix, Sylvestre-François,
103

Lagash,
2

Lagrange, Joseph-Louis,
75–77
,
80
,
81
,
83
,
111
,
264–265

Lambert, Johann,
130

Lambert's proof,
131
,
133

Laplace, Pierre Simon,
77

Lavoisier, Antoine,
77

Law,
3–4

Laws of nature,
x

Le Monnier, Renée-Françoise-Adélaide,
77

Legendre, Adrien-Marie,
93
,
99–100
,
103

Lehrbuch der Algebra
(Weber, H.),
216

Leibniz,
148

Leonardo of Pisa,
49–50
,
264

Levi-Civita, Tullio,
195

Liber Abbaci
(Fibonacci),
49

Lie algebras,
166
,
168
,
169
,
245
,
268

simple,
167

Lie groups,
xii
,
163
,
165
,
214
,
263
,
267
,
271
,
272

exceptional,
169
,
170
,
253
,
254
,
263
,
269
,
270
,
271–272

features of,
164

in physics,
253–254

Lie, Marius Sophus,
159
,
160
,
162
,
170
,
213

Liebniz, Gottfried Wilhelm,
5

Light,
174–175
,
197–198

change of phase in,
232
,
233

speed of,
190
,
191

Limitations,
28

Lindemann, Carl Louis

Ferdinand von,
133–134

Lindemann's proof,
134

Linear equations,
14

Lines,
28
,
122
,
270

Liouville, Joseph Louis,
111
,
127
,
131

Logarithms,
132
,
148

Loop quantum gravity,
255–256

Lorentz group,
192
,
232

Lorentz, Hendrik,
192
,
212

Lorentz invariance,
194

Louis XVIII,
99
,
103

Louis-Le-Grand,
100
,
133

Louis-Philippe,
103
,
104

Ludus Algebrae et Almucgrabalaeque
,
37