How Math Explains the World.pdf

Tilden, Samuel, 228

Time, 143 

topology, 35, 198, 199

tractable problems, 159, 162

tractrix, 112

transcendental numbers, 74–75, 173,

175 

“Transgressing the Boundaries: 

Towards a Transformative 

Hermeneutics of Quantum 

Gravity,” 185

transistor, development of the, 179

transitivity, 210, 218

traveling salesman problem, 159–62, 

163, 240 –41, 241

trigonemetric functions, 97

trisecting the angle, 71, 73

Galois theory and, 95

true-false tables, logic of, see proposi-

tional logic

Turgot, Anne-Robert-Jacques, 208

Turing, Alan, 125, 174

Twelfth Amendment to the Constitu-

tion, 205–6

typhoid fever, 69

U
ultraviolet catastrophe, 9, 44, 45, 46
uncertainty principle, xv, xvii, 37, 
55 –58, 241
consequences of, 57
undecidable propositions, 123, 127, 
239–40
unified field theory, xix, 147, 148
universe(s)
-as-hologram theory, 197–99
four-dimensional, 144
geometry of the, 144 –45
infinity in the, 138

raw materials of the, 186

three-dimensional, 150

University of Berlin, 19

University of California, Berkeley, 163

University of Halle, 19

University of Southern California, 167

unprovable statements, 124

unsolvable and great problems, xiv, xv, 

8 –9, 239, 240, 247

chessboard example, xvii–xviii, 240

leading to unexpected connections 

between mathematics and other 

areas, 76

surprising developments resulting 

from working on, xix, 63, 69–70, 

75–76, 219–20

see also specific problems

V

Van Gogh, Vincent, 19

Vesalius, 111

vocabulary of mathematics, 170

von Lindemann, Ferdinand, 74–75, 116

vote tabulation methods, 205–20, 

223–35, 240

Arrow’s theorem, see Arrow’s theorem

Condorcet paradox, 209, 210, 211, 218

Electoral College, 205–7

insincere voting and, see insincere

voting

preference intensity method, 207

rank-order voting, see rank-order

voting

W

Wantzel, Pierre, 73–74

Washington, George, 228

Washington Redskins, 8

Index 263