A

Abel, Niels Henrik, 55–58

Abel Endowment Fund, 55

Abelian groups, 57

Adaptation, 155–156

Aerodynamics, 170–171

Agarwal, Manindra, 133

AIDS research, 108

Alabama paradox, 142, 143

Alexander, James, 94

Alexander the Great, 93, 99

Alfréd Rényi Institute of Mathematics, 44

Algebra, 82, 87, 122, 130, 139

Algebraic groups, 112–115

Algebraic topology, 17–19

Algorithms

data compression, 149–150

encryption key search, 181

prime number certification, 132–133

profitability, 176–177

theory of, 82

Alighieri, Dante, 150

Allais, Maurice, 184

Alternating harmonic series, 40

American Mathematical Association, 33

Annals of Mathematics, 43, 44

Anti-Semitism, 59, 62

Apocalypse predictions, 6–7

Applied Minds, 77–78

Apportionment of representatives

Alabama paradox, 142, 143

Jefferson–d’Hondt–Hagenbach-Bischoff method, 144–145

monotony requirement, 141, 142

population paradox, 142–143

quota rule, 141

remainder distribution, 141

Ariane rocket, 103–104

Arithmetika, 122

Ars Conjectandi (Art of Conjecture), 12

Artificial intelligence, 61, 64

Associative operations, 57

AT&T, 20

Atom bomb, 61, 63

Atomic clocks, 5

Atomic models, 93, 95

Aumann, Robert, 192, 193

Authorship, attribution of, 150–151, 153–154

Axiomatization of physics (Hilbert’s problem 6), 27

Axion of Choice, 82

Axis of symmetry, 125

B

Baby monster groups, 115

Bak, Per, 168

Baker, Alan, 38

Balinsky, Michel, 141

Ballistics, 63

Bar-Hillel, Maya, 191

Bar-Natan, Dror, 191

Basle number series, 42

Basle problem, 42

Batik weaving, 126

Bauke, Heiko, 130

A Beautiful Mind (movie), 64

Bees

honeycombs, 34, 36, 46, 159–160, 175, 177

swarm intelligence, 175–176

waggle dance, 175–177

Behavioral and social sciences, catastrophe theory in, 121

Ben Gurion University, 88

Benedetto, Dario, 150, 151

Bernays, Paul, 59–60

Bernoulli, Daniel, 11, 12–14, 147

Bernoulli, Jakob I, 11, 12, 40–41

Bernoulli, Jakob II, 11

Bernoulli, Johann I, 11, 12, 13, 14, 41, 42

Bernoulli, Johann II, 11

Bernoulli, Johann III, 11

Bernoulli, Nickolaus, 11

Bernoulli, Nickolaus I, 11, 146

Bernoulli, Nickolaus II, 11, 12, 13

Bible

apocalypse predictions, 6

codes, 190–193

Big Bang theory, 127

Binary digits, 181

Binary numbers, random, 130

Biology, 69, 73

evolutionary, 185–186

fly aerodynamics, 170–171

Bonacci, Leonardo, 156

Bonifatius III, Pope, 7

Botany, mathematical applications, 73, 155–157

Bounded rationality theory, 185

Brain

neurophysiology of economic decision making, 188–189

structural analysis, 139

Brenner, Sydney, 76

Buckeyballs (C₆₀ molecule), 67

Butterfly effect, 105

C

Caesar, Julius, 3–4

Caglioti, Emanuele, 150, 151

Calculators, inaccuracies, 102

Calendar adjustments, 3–5

California Institute of Technology, 70, 170

Cambridge University, 18, 37, 66

Cardiology, reverse butterfly effect in, 105

Catalan conjecture, 37

Catalan, Eugène Charles, 37

Catalanian rabbi’s problem, 37–39

Catastrophe theory, 119–121

Catholic Church and Catholicism, 3–4, 7

Catholic University of Nijmegen, 47

Cauchy, Augustin, 56

Cellular automata, 61, 70–74

Center for Palestinian Studies, 161

Center for Rationality, 191

Center of rotational symmetry, 125

Chamberlain, Edward, 172

Chaos theory and phenomena, 28, 104–105, 139

Charlemagne, 7

Chirality, 126–127

Churchill, Winston, 145

Circle Limit I–IV graphics, 67–68

Clay Foundation, 17, 110

Clay Mathematics Institute, 17

Clock face group, 112

Clocks

atomic, 5

10,000-year mechanical, 78–79

Coin tosses, 128, 146

Collatz conjecture, 22–23

Collatz, Lothar, 20–22

Columbia University, 50

Combinatorial theory, 79, 82

Composite numbers, 117

Computers and computer science

algorithms, 72–73, 109–110, 149–150

brain architecture analogy, 64, 76

check sums, 158–159

compression algorithms, 149–154

data encryption, 180–183

error-correcting codes, 158, 159–160

error detection, 158–159

father of, 61, 64

Game of Life, 71

Internet server allocation models, 175–177

knot simulations, 98–100

Nevanlinna Prize, 158

nondeterministic machines, 109

parallel processing, 64, 76, 77

programs to test other programs, 83

proofs with, 43–47

quantum computers, 181–182, 183

random number generators, 128–131

rounding errors, 102–103, 104, 183

software errors, 104

solving NP problems, 109–110

verifying proofs with, 27, 28, 44–47, 51

von Neumann architecture, 64

weather simulations, 104–105

word stacking, 158–160

Connection Machine, 76, 77

Contergan, 127

Control variables, 119–120

Convergence of series, 40

Conway group, 115

Conway, John, 71, 114–115

Cook, Stephen, 110

Cornell University, 50, 82

Coxeter, Harold Scott MacDonald, 66

Crack generation, 73

Cramer, Gabriel, 146–147

Creation of the world, 73

Credit card numbers, encryption, 133

Crelle, August Leopold, 56–57

Crelle’s Journal, 37

Cryptography, 128, 132.

See also Bible codes;

Data encryption

Crystal development, 73

Cubic decompositions, 123–124

Curie, Pierre, 126

Curl, Robert, 67

Cyclotomic fields, theory of, 39

D

Dali, Salvador, 121

Dan David Prizes, 75, 76, 78, 79

Darwin, Charles, 69

Data compression algorithms, 149–150

Data encryption, 128

heat flow–based, 182–183

keys, 180–183

multiplication of prime numbers, 128, 132–133, 180–182

PIN numbers, 180

public keys, 182–183

quantum computers and, 181–182, 183

thermodynamics-based, 182

De imitatione Christi, 152

de Moivre, Abraham, 41

Decomposition

cubic, 123–124

of numbers, 123

singular value, 139

Deligne, Pierre, 46

Demaine, Eric, 109, 110–111

Dendrites, 166

Determinism, 69

Deutsch, David, 183

d'Hondt, Victor, 143–144

Diao, Yuanan, 99

Dice, 58, 66, 113, 128

Dickinson, Michael, 170

Diophantine cubic decompositions, 123–124

Diophantine equations, 122

Diophantus, 122, 123

Discontinuities, 120

Disorder, 138, 149

Dissymmetry, 126–127

Divergence of series, 40

DNA molecule, 85, 152

Drosophila melanogaster, 170

Dunwoody, Michael J., 17, 18–19, 27, 51

E

Earthquakes

frequency and magnitudes, 168

risks and insurance, 106, 107–108

Eckert, John, 63–64

Eckmann, Beno, 85–89

Ecole Normale Supérieure, 120

Economics.

See also Finance;

Stock markets

bounded rationality theory, 185

experimental, 172–174

game theory, 147–148, 184, 185

market efficiency, 172–174

neoclassical theory, 172

ultimatum game, 187–189

Eidgenössische Technische Hochschule (Swiss Federal Institute of Technology), 37, 59, 62, 80, 81, 82, 85, 86, 87, 88, 170, 182

Einstein, Albert, 63, 82, 83, 86

Elections

apportionment of representatives, 140–145

rounding results, 103

Elemente der Mathematik, 181–182

Elliptic functions, 56

Enlightenment, Age of, 40

Enormous theorem, 113

Entropy, 138, 149, 150, 152, 153

Equidistant letter sequences, 190, 191, 193

Eratosthenes, 24

Erdös, Paul, 82–83

Erdös number mathematicians, 82–83

Ergodic theory, 192

Escher, M. C., 34, 67–68, 126

Euclid, 24, 116

Euler, Leonhard, 11, 13–14, 24, 38, 41–42, 117

Evolutionary biology, 185–186

Expected prize, 146, 147

Expected utility theory, 147, 184

Expo 67

F

“Federalist Papers,” 151

Fejes Toth, Gábor, 44

Fejes Toth, László, 35, 36, 44, 177

Ferguson, Sam, 44, 45, 46

Fermat, Pierre de, 116, 122–123

Fermat numbers, 116–118

Fermat’s last theorem, 27, 39, 41, 49, 116–118, 123

Fermat’s little theorem, 133

Festival of Symmetry, 68

Feynman, Richard, 183

Fibonacci series, 156–157

Fields Medal, 50, 120

Fifth–degree equation, 55–56

Finance, 73.

See also Economics;

Stock markets

evolutionary theory, 184–186, 188

irrational decision making, 184–189

trader characteristics, 173–174, 179, 184

Finite groups, classification of, 112–113, 115

Fink, Thomas, 95

Flies, aerodynamics, 170–171

Fluid dynamics, 14

Forest fires, 168

Foundations of Mathematics, 59

Four–color theorem, 43

Fractal theory, 161–163

Fractions, 122, 143

Free will, 69, 73

Freedman, Michael, 18

Friction, 167, 170, 171

Fry, Steven, 170–171

Fuller, Buckmnister, 67

Furstenberg, Hillel, 192, 193

G

Gambling and gamblers, 106–108, 146–147, 148

Game theory, 61, 64, 147–148, 184, 192

Gans, Harold, 191

Gauss, Carl Friedrich, 25, 56, 116, 117–118

German Federal Office for Security in Information, 181

Geodesic domes, 67

Geography, fractal dimension of borders and frontiers, 161–163

Geometrization conjecture, 50

Geometry, 66–68, 87, 116, 125

Georgia Institute of Technology, 175

Gibbs–Thomson effect, 164–165

Gielis, Johan, 156

Glasgow University, 113

Gödel, Kurt, 82, 86

Gödel lecture series, 124

Goldbach, Christian, 94

Goldbach conjecture, 24

Goldston, Dan, 24, 25–26, 27

Gonseth, Ferdinand, 59

Gordian knot, 93, 99

Gorenstein, Dan, 113

Gravity, 167

Greedy algorithm, 176–177

Gregory XIII, Pope, 3–5

Griess, Robert, 115

Group theory and groups, 56

abelian groups, 57

algebraic groups, 112–115

baby monster groups, 115

classification of finite groups, 112–113, 115

clock face group, 112

Conway group, 115

infinite number of elements, 112

lattice symmetries, 113–114, 115

monster groups, 115

nonabelian groups, 57–58

small groups, 112

sporadic simple groups, 113, 115

Gutenberg, Beno, 168

Gyro Gearloose, 75

H

Hagenbach-Bischoff, Eduard, 145

Ha-Hasid, Yehuda, 192

Hailstone sequence, 21–23

Hales, Thomas, 33, 35–36, 43–47, 160, 177

Hamilton, Alexander, 151

Hamilton, Richard, 50

Harmonic series, 40

Harsanys, John, 61, 64

Harvard University, 151, 172

Hasse, Helmut, 21

Hasse algorithm, 21

Heat flow encryption method, 182–183

Hebraeus, Leo, 38

Hebrew alphabet, 192

Hebrew University of Jerusalem, 6, 88, 178, 191

Heisenberg, Werner, 62

Heptadecagons, 117–118

Hermes, Johann Gustav, 118

Herzl, Theodor, 61

Hexagons, 33–36, 160, 165–166

Hidden variables, 83

Hilbert, David, 17, 27, 59, 62

Hilbert’s problem 16, 27–30

Hillis, Daniel, 75–79

Hohenberger, Susan, 109, 110–111

Holes, defined mathematically, 48–49

Holy Roman Empire, 7

Honeycomb conjecture, 34, 36, 46, 159–160, 177

Hopf, Heinz, 85–86

Hsiang, Wu–Yi, 45

Hungerbühler, Norbert, 182

Hydraulica, 14

Hydrodynamica, 14

Hydrodynamics, 63

I

Icicles, structure of, 164–165

Indian Institute of Technology, 133

Inertia, 167, 170, 171

Infinite-element groups, 112

Infinite series, 40–42, 44

Information theory, 137–139

Institute for Advanced Study, 44, 46, 63, 70, 81–82, 86, 94, 147

Institute of Neuroinformation, 170

Insults, neurophysiological response, 188–189

Insurance, 106, 107–108, 148

Integer numbers, 122

Integral calculus, 42

Intel, 26

Intelligence, 73, 175–176

International Congress of Mathematicians, 67, 158

International Court of Justice, 161, 163

International Journal of Mathematics, 45

Internet

data encryption, 132–133

server allocation, 175–177

Irrational numbers, 122

Israel

ideological founder, 61

West Bank security barrier, 161–162, 163

J

Jay, John, 151

Jefferson, Thomas, 144

Journal für Reine and Angewandte Mathematik (Journal for Pure and Applied Mathematics), 56

K

Kabbala, 121

Kahneman, Daniel, 173, 184

Kakutani, Shizuo, 21

Kakutani problem, 21

Kalai, Gil, 191

Kayal, Neerja, 133

Kaye, Richard, 111

Kelvin, Lord, 93, 95

Kempis, Thomas à, 151

Kepler, Johannes, 43, 159, 165

Kepler’s conjecture, 35, 43–47, 159–160

King’s College, Halifax, 6

Knots

classification of, 93–95

cloverleaf, 98, 99

computer models, 98–100

configuration of strings, 97–98

DNA molecule, 85

in four-dimensional space, 97

Gordian, 93, 99

granny, 100–101

mathematical theory, 93–96, 97, 98

minimum length, 98–99

necktie, 95–96

physical theory, 97–101

prime, 93

quanta, 100

Reidemeister manipulation, 94

shoelaces ties, 100–101

square, 101

string theory, 95, 100

trefoil or overhand, 98

unknots, 94, 97

winding number, 99–100

Kochen, Simon, 83

Kroto, Harold, 67

Kummer, Eduard, 39

L

L function, 123

Lagarias, Jeff, 20, 22

Lagrange, Joseph–Louis, 11

Lap loop lop leap year, 5

Laplace instability, 164

Lattices

high-dimensional, 113

hexagonal, 165, 177

order and entropy, 138

snowflake, 165

symmetries, 113–114, 115, 165

Läuchli, Hans, 60

Leap years, 3–5

“Lecture Notes in Mathematics,” 87–88

Lecturing conditions and styles, 8–10, 81

Leech, John, 113–114

Leech lattice, 113–114

Legendre, Adrien–Marie, 25

Legionnaire’s disease research, 108

Leibnitz, Gottfried Wilhelm, 11, 41

Lempel, Abraham, 150

Lempel–Ziv algorithm, 149–150

Leo III, Pope, 7

Liben-Nowell, David, 109, 110–111

Linear operations, 104 n.2, 139

Linguistics, 83, 121

affinity between languages, 151–152

attribution of authorship, 150–151, 153–154

Linné, Carl von, 112

List, John, 173

Logic, 59–60, 80, 82, 83

London Science Museum, 79

Loop lop leap years, 4, 5

Lop leap years, 4

Lorenz, Edward, 104–105

Loreto, Vittorio, 150, 151

Lotteries, 106, 128, 148

M

MacArthur Foundation “genius awards,” 70

MacPherson, Robert, 44, 45, 47

Madison, James, 151

Mandelbrot, Benoit, 162–163

Manhattan Project, 21, 63

Mao, Yong, 95

Massachusetts Institute of Technology, 76, 79, 104, 109, 123

Mathematica, 72

Mathematical models, 72

of social insects, 175–177

Mathematical problems.

See also Proofs;

individual problems

media fanfare, 28–30

most important of 21st century, 17, 23–24

Matter-antimatter disturbance, 127

Mauchly, John, 63–64

Max Planck Institute of Mathematics, 123–124

McKay, Brendan, 191

McLaughlin, Sean, 46, 47

Mengoli, Pietro, 40, 41

Mersenne, Marin, 116

Mertens, Stephan, 130

Mignotte, Maurice, 38, 39

Mihailescu, Preda, 37–38, 39

Millennium Prize problems, 17, 51, 110

Minesweeper game, 111

Mini–max theorem, 64

Missiles and rockets, guidance errors, 103–104

Moby Dick, 191

Monash University, 100

Monster groups, 115

Monte Carlo simulations, 128–129

Morgenstern, Oskar, 64, 147, 184, 185

Morse code, 149

Mosteller, R. Frederick, 151

Muchnik, Lev, 178–179

N

Nakrani, Sunil, 175, 176–177

Nash, John, 64

National Security Agency, 191

National Television Systems Committee (NTSC), 9

Natural disasters, 106, 107–108.

See also Catastrophe theory

Natural selection, 186

Nazi regime, 59

Necktie knots, 95–96

Neural networks, 61, 64

Nevanlinna, Rolf, 158

Nevanlinna Prize, 158

A New Kind of Science, 69–70, 74

New York University, 46

Newton, Isaac, 6–7, 11, 69

Niceley, Thomas, 26

Nobel Prize winners, 61, 64, 67, 75, 85, 126, 172–173, 175, 184, 185

Noether, Emmy, 59

Nonabelian groups, 57–58

Nonlinear Analysis (journal), 28, 29

Nonlinear operations, 104–105

NP problems, 109–111

Number theory, problems in, 20–23, 37–39, 116, 122–124

O

Omniscient algorithm, 176–177

On Growth and Form, 155

One-way function with a trapdoor, 180–181

One-way function without a trapdoor, 182

Optimal-static algorithm, 176–177

Origin of Species, The, 69

Oxenhielm, Elin, 28–30

Oxford University, 70, 123, 175

P

P problems, 109, 110

Pappus of Alexandria, 34, 35

Parisian Academy of Science, 14

Pasteur, Louis, 126

Patriot missiles, 103

Pattern recognition, 139

Pauli, Wolfgang, 85

Pentagrams, 126

Pentium bug, 26

Perelman, Grigori, 49–51

Perko, Kenneth, 94

Persian Gulf War, 103

Peter the Great, 13

Phokas, Emperor, 7

Physics

icicle structure, 164–165

sand avalanches, 167–168

snowflake formation, 165–166

stock market crashes, 168

traffic jams, 168–169

Pi, 41, 42

Pieranski, Piotr, 99

Pintz, Janos, 25–26

Pirandello, Luigi, 150

Planck, Max, 62

Poincaré, Henri, 17, 49

Poincaré conjecture, 17–19, 27, 48–51

Political science, apportionment of representatives, 140–145

Polster, Burkhard, 100

Polya, George, 59

Polygons, regular, 33–36, 116, 117–118

Polyhedra, 66

Polynomial time, 109–110, 133

Polynomials, 28, 94

nondeterministic, 109

Polytopes, 66

Population paradox, 142–143

Presley, Elvis, 73

Prime cousins, 25

Prime knots, 93

Prime numbers, 38

algorithm for certifying, 132–133

data encryption, 128, 132–133, 180–182

distribution of, 25

factorization record, 181

Fermat numbers, 116–118

theory of, 23

twin primes conjecture, 24–26

Princeton University, 62, 63, 64, 66, 83, 115, 184, 188

Principia, 69

Probability theory, 12, 128

Proceedings of the National Academy of Sciences, 190

Proofs

computer–aided, 43–47

verification of, 27, 28, 44–47, 51

Pseudorandom numbers, 129–130

Psychology, catastrophe theory in, 120–121

Pyramids, 66, 125

Pythagoras, 126

Pythagoreans, 126

Q

Quantum computers, 181–182, 183

Quantum mechanics, 62, 73, 83, 95

Quine, Willard van Orman, 82

R

Random number generation/generators, 128–131, 139

Rational numbers, 57

Reagan, Ronald, 108

Reciprocal squared number series, 40–43

Reflection symmetry, 125

Rehnquist, William, 137

Reidemeister, Kurt, 94

Reidemeister manipulation, 94

Research Institute for Mathematics, 24

Reverse butterfly effect, 105

Review of Modern Physics, 71

Ricci flow, 50

Richter, Charles, 168

Riemann conjecture (Hilbert’s problem 8), 27–28

Ripple phenomenon in icicles, 164–165

Rips, Eliyahu, 190–191

Risk perception, 106–108

Rockets. See Missiles and rockets

Rosenberg, Yoav, 190–191

Rotations of symmetrical bodies, 114, 125, 171

Roulette, 107, 129

Rounding errors, 102–105, 140, 143

Royal Society, 115

Royal Statistical Society, 106

Rubinstein, Hyam, 19

Rubik’s cube, 58

Russell, Bertrand, 66

Russia

Academy of Science, 13–14

October Revolution, 5

S

Salk Institute for Biological Sciences, 76

Sand avalanches, 167–168

Saxena, Nitin, 133

Sayaman, Rosalyn, 170

Scalia, Antonin, 138

Scientific American, 71

Scud missiles, 103

Self-organized criticality, 167–169

Selten, Richard, 64

Series expansion of sine function, 42

Set theory, 62–63, 82, 87

Sexy primes, 25

Shannon, Claude, 138

Shapes, coordinate transformations, 155–157

Shock waves, 63

Shoelaces ties, 100–101

Simon, Herbert, 185

Singular value decomposition, 139

Sirovich, Lawrence, 137–139

Smale, Stephen, 18, 28

Small groups, 112

Smalley, Richard, 67

Smith, Adam, 172

Smith, Vernon, 172–173

Snobelen, Stephen, 6–7

Snowflake formation, 165–166

Solomon, King, 126

Solomon, Sorin, 178–179

Space–time continuum, 49

Specker, Ernst, 60, 80–84

Sporadic simple groups, 113, 115

Springer, Julius, 88

St. Petersburg paradox, 146, 147

Stallings, John, 18

Stanford University, 184

Star of David, 126

Stasiak, Andrzej, 99

State, change of, 119

State University of San Jose, 24

Statistical cost-benefit analysis, 108

Statistical Science, 190, 191

Steinhaus, Hugo, 34–35

Steklov Institute, 49

Stevens, John Paul, 138

Stirling, James, 41

Stock markets

crash predictions, 121

entropy measurements, 152

fractal theory and, 163

index rounding errors, 104

turbulence in, 178–179

virtual, 178–179

Stoltenberg, Thorvald, 55

Stonehenge, 125

String theory, 95, 100

Structural stability, 119–120

Struwe, Michael, 182

Sudan, Madhu, 158

Superformula, 156–157

Supreme Court (U.S.) decisions, mathematical analysis, 137–139

Sussmann, Hector, 121

Swiss National Fund, 11

Switzerland

apportionment of Federal Council delegates, 140–145

earthquakes, 107

fractal dimension of alpine landscape, 162

Symmetries

adding, 113–114

combining, 125–126

snowflake, 165–166

types of, 125–126

Symmetry Festival, 126

Syracuse problem, 21

Syracuse University, 21

Szilard, Leo, 63

T

Tait, Peter, 93–94

Talamania system of proportions, 126

Tank, Chao, 168

Technion, 88, 150

Telecommunications, 149

Teller, Edward, 63

Tetris, 109, 110–111

Thalidomide, 127

Theory of Games and Economic Behavior, 147

ThermoCrypto, 182–183

Thermodynamics, 69, 73, 138, 182

Thinking Machines, 76

Thom, René, 120

Thomas, Clarence, 138

Thompson, D’Arcy, 155–156, 157

Three-dimensional manifolds, 49, 50

Three-partition problem, 110–111

Thurston, William, 50

Thurston’s conjecture, 50

Thwaites, Bryan, 22

Thwaites conjecture, 22

Tildeman, Robert, 38

Tile layer’s efficiency problem, 33–36

Topology, 17–19, 44, 48–51, 82, 85, 97.

See also Knots

Toufakji, Khalil, 161

Tovey, Craig, 175, 176–177

Traffic

jams, 168–169

simulations, 128–129

Transformations, 155–157

Translation symmetry, 125

Traveling salesman problem, 109

Trigonometric functions, 42

Trinity College, Dublin, 35

Truncation errors, 103–104

Turbulent fluid flow, 73, 139, 178–179

Turing, Alan, 63

Tversy, Amos, 184

Twin primes conjecture, 24–26, 27

Two-dimensional manifolds, 49

U

Ulam, Stanislaw, 21

Ulam’s problem, 21

United States, apportionment of representatives, 140, 144–145

University La Sapienza, 150

University Louis Pasteur, 38

University of Basle, 11, 12, 145

University of Berlin, 57

University of Birmingham, 111

University of Budapest, 62

University of California, 50

Berkeley, 18, 45

San Diego, 18

University of Chicago, 21

University of Christiana, 55

University of Fribourg, 182

University of Ghent, 144

University of Göttingen, 62, 117

University of Groningen, 12

University of Hamburg, 21

University of Illinois, 72

University of Lausanne, 60, 86, 99

University of Leiden, 38

University of Maryland, 173

University of Michigan, Ann Arbor, 44

University of North Carolina, 99

University of Oslo, 55

University of Paderborn, 37

University of Pittsburgh, 44, 188

University of Southampton, 17

University of Tel Aviv, 75

University of Toronto, 66, 110

University of Zurich, 8–10, 59, 170

Unknots, 94, 97

Utility function, 147–148

V

Volumes of complicated shapes, 129

von Frische, Karl, 175

von Laue, Max, 165

von Neumann, John, 61–65, 70–71, 82, 86–87, 147, 184, 185

von Neumann, Klari, 64

von Neumann, Marietta, 64

W

Wallace, David L., 151

Walt Disney Imagineering, 77

Walter Reed Hospital, 65

Wantzel, Pierre Laurent, 118

War and Peace, 191, 193

Weaire, Denis, 35

Weather simulations, 104–105

Westfall, Richard, 7

Weyl, Hermann, 86

Wiedijk, Freek, 47

Wieferich pairs, 39

Wiesenfeld, Kurt, 168

Wigner, Eugene, 61, 63

Wiles, Andrew, 27, 49, 116

WinZip program, 150–154

Wittgenstein, Ludwig, 66

Witztum, Doron, 190–191

Wolfram, Inc., 72

Wolfram, Stephen, 61, 69–74

World Wide Web, random numbers, 130–131

X

X-ray crystallography, 165

Y

Yale University, 21

Yehuda, Abraham, 6

Yildirim, Cem, 24, 25, 27

Young, Peyton, 141

Yule, George, 151

Z

Zagier, Don, 123–124

Zahler, Raphael, 121

Zeeman, Christopher, 18

Zeta function, 42

Zipf, George, 151

Ziv, Jacob, 150

Zoology, 73