Why Beauty is Truth (65 page)

Magic square,
271

Magnetism,
179
,
187
,
222

Manhattan Project,
220

Manifolds,
73

Map making,
48

Marconi, Guglielmo,
180

Marduk,
8

Maric, Mileva,
185

Marie, Anne,
86

Maskerade
(Pratchett),
205

Mathematical Principles of Natural Philosophy
(Newton),
174

Mathematical Thought from Ancient to Modern Times
,
50

Mathematics

ancient study of,
2

applied,
22

in Babylon,
13–14

beauty and,
278
,
280

competitions,
54

role of,
5

symmetry and,
279–280

truth and,
275

universe and, xiii

Mathias, Hans,
85

Matrix,
122
,
208
,
276

Matter,
186
,
197

Maurice of Nassau,
144

Maxwell equations,
180
,
187–189
,
222

symmetry of,
191

Maxwell, James Clark,
174
,
177
,
178–179
,
184

Maxwell-Boltzmann doctrine,
199

McGovern, George,
244

Mechanico-optical analogy,
142

Mechanics
(Euler),
132

Meitner, Lise,
201

Merck, Marie,
200

Mesopotamia,
1–2

history of,
7

Metric,
195–196

Michelson, Albert,
189
,
191

Michelson-Morley experiment,
189

Micheria, Chiara,
50

Mills, Robert,
238

Minkowski, Hermann,
184
,
192

Minkowski space-time,
192

geometry of,
193

Moon, movements of,
23–24

Morley, Edward,
189
,
191

Morse, Marston,
247–248

Motzfeldt, Ernst,
159

Mowaffak, Imam,
37
,
39

M-theory,
254

al-Mulk, Nizam,
37

Müller, Hermann,
200

Multidimensional spaces,
73

Multiplication,
150

Nabopolassar,
8

Nabu,
8

Naishapur,
37

Nambu, Yoichiro,
249

Napoleon,
77
,
79
,
161

Nature, beauty and,
278–279

Nazis,
203
,
210

Nebuchadnezzar,
6
,
7
,
8

Negative numbers,
144

square roots of,
59–60
,
260

Negatives,
29

Negentropy,
205

Neugebauer, Otto,
13–14

Neusis constructions,
27

Neutrinos,
235–236

Neveu, André,
251

Newton, Isaac,
5
,
174
,
175–176
,
277

physics of,
190

Nichomachus,
35

Nineveh,
2

Nippur,
2

Nixon, Richard,
243

Nobel Prize,
185
,
204
,
209
,
220
,
244

Noether, Emmy,
165

Noncommutative geometry,
255

Notation systems,
10–11
,
144–145

Babylonian,
11–12

Nuclear force,
233
,
235

Nuclear weapons,
210

Number theory,
76

Numbers.
See also
Complex numbers
;
Imaginary numbers
;
Negative numbers
;
Prime numbers
;
Real numbers
;
Square numbers
;
Transcendental numbers
;
Triangular numbers

notation systems for,
10–11

O(1),
240

Observation,
23

Octonions,
xii
,
259–260
,
268
,
273

units of,
262–263

Octooctonions,
272

On the Conditions of Solvability of Equations by Radicals
(Galois),
104–105

On the Revolutions of the Heavenly Spheres
(Copernicus),
56

Opticks
(Newton),
175

Order,
156

Ørsted, Hans,
178

Osiander, Andreas,
56

Oslo Fjord,
84

Osthoff, Johanna,
71

Pacioli, Luca,
50

Pais, Abraham,
174
,
220

Pappus,
21

Parabola,
40

Paris,
87

Particle physics,
231

Pauli principle,
236

Pauli, Wolfgang,
208–209

Pausanias,
18

Peirce, Benjamin,
154
,
155

Perihelion position,
196

Peritonitis,
ix

Permutations,
81
,
111–112

group property of,
121

multiplying,
81–83
,
111

subgroups of,
114

symmetries and,
113

Pfaff, Johann,
67
,
71

Phase,
232

shift,
232

Philip II,
18

Philosophy,
221

Photoelectric effect,
186

Photons,
237

Physics,
149
,
173
,
194
,
199

lie groups in,
253–254

Pi,
132

Piazzi, Giuseppe,
70–71

Planck, Max,
200
,
202
,
203
,
204
,
218–219

Planes,
147

Plasma,
242

Plato,
20
,
21
,
44
,
269
,
277

Plücker, Julius,
159–160
,
165–166

Poetry,
139–140

Poincaré, Henri,
133
,
192

Poinsot, Louis,
103

Poisson brackets,
213

Polchinski, Joseph,
257

Polygons,
29

regular,
29
,
30

Polynomials,
57
,
81

Poncelet, Jean-Victor,
159

Positron,
236

Powers,
35

Practica Geometriae
(Leonardo of Pisa),
49

Pratchett, Terry,
176
,
205

Preserve,
118–119

defining,
119

Prime numbers,
264

Principle of Least Time,
141

Problems of antiquity,
125–126

Projections,
269
,
270

Proofs,
22–23

necessity of,
23–24

Proportion,
118

Proposed Draft of an Attempt to
Treat the Results of a Cone Intersecting a Plane
(Desargues),
271

Protons

stability of,
240

structure of,
238–239

symmetry groups in,
239

Protractors,
128

Prussia, France and,
161

Ptolemy,
20

Pythagoras,
130
,
144

cult surrounding,
21

Pythagorean theorem,
25
,
144
,
193
,
264

Pythagoreanism,
21–22

Quadratic equations,
13–14
,
42
,
57
,
78
,
280

geometric picture of,
15–16

groups and,
116

solving,
90

Quadratic reciprocity,
66–67

Quadratrix,
27

Quadruples,
152

Quanta,
236

Quantum chromodynamics,
233
,
238

Quantum field theory,
245
,
248

Quantum mechanics,
192
,
210
,
213
,
230
,
259

Quantum physics,
x

Quantum theory,
xiii
,
202
,
209
,
230

Copenhagen interpretation of,
205

relativity and,
221–222

Quarks,
237
,
238
,
256

Quartic equation,
61

groups and,
116

solving,
90

Quaternions,
xii
,
142–143
,
153
,
154
,
156
,
214
,
261
,
263

Quateroctonions,
272

Quintic equations,
xi
,
61
,
78
,
83
,
97
,
114
,
117
,
280

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