How Math Explains the World.pdf

predictions

author’s, 241– 42

of limitations of knowledge and 

achievement in the physical world, 

30–31

preference intensity method, 207

presidential elections, U.S., 205–6, 216,

218, 228

prey-predator populations, interplay 

between, 180–82

prime numbers, xvi–xvii, 76

Princeton University, 124

Principia (Newton), 106, 144, 145

principle of mathematical induction,

120 –22

Principles of Political Economy (New-

comb), 30

priority-list scheduling, 4–7, 157, 241

probabilistic concept of expectation, 29

probability, 51, 169, 170, 192

probability density functions, 136–37

Proceedings of the American Mathemati-

cal Society, 107 

Proclus, 103, 104

product, 91

progress in mathematics, cumulative, 

82 

proofs, mathematical, xv

impossible solutions and continued 

formulation of, 71

indirect, 101–2, 104

naming of, 20

proper subset, 15, 16

propositional logic, 117–19.123, 164

Protagoras, 13

pseudosphere, 112

Pták, Vlastimil, 107

Pták-Stein theorem, 107

Ptolemy, 111

publication of results, 106–7, 110, 111

punctuated equilibrium theory, 217

pyramid investment clubs, 17

Pythagoras, 42, 67, 74

Pythagorean theorem, 42

Q

quadratic equations, solution of, 83

quadratic formula, 83

quantum chromodynamics, 146,

148 – 49

quantum computing, 167, 168

quantum electrodynamics, 146

quantum eraser experiments, 54–55

quantum gravity, theory of, 35, 36

quantum mechanics, xvii, 34–35,

41–54, 148–49, 240

entanglement, 58–63

Planck and, 45

randomness in, 171

uncertainty principle, see uncertainty 

principle

unresolved mysteries of, 62–63

views of Pythagoreans and, 76 –77

wave-particle duality, 46–55

quantum theory of gravity, 146

quaternions, 32

quintic, solution of the, 8–9, 89–97,

240 

insolvability of the general quintic by 

radicals, 93–96, 239

R

radicals, 83

radioactivity, 148

RAND Corporation, 214

randomness, 169, 170 –71, 240

random penny, 171–72, 173

random variable, 170

260 Index