GENERAL INDEX

A Beautiful Mind, 68, 106

Abelian integrals, 233

Abstraction, 48–49

Academy of Science (French), 234

Academy of Science (Russian), 235

Academy of Science (Swedish), 235

Acta Mathematica, 75, 164, 234

Algebra, 18, 27, 116, 117, 132, 169, 171, 186, 196, 199, 209, 210, 217, 232, 236–238, 276, 285, 305, 306, 306, 310, 319–327

Algebra Project, 312–314, 322, 329

Algeria, colonial war, 111

Algorithm, 166, 310

American Association of University Professors, 83

American Association of University Women, 83

American Institute of Mathematics, 178

American Mathematical Monthly, 292

American Mathematical Society, 100, 106, 168, 169, 209, 219, 256, 277, 279, 282, 283, 289

Analysis, 217, 259, 264

Anonymous Group (Budapest), 191–193, 315

Applied mathematics, 38, 186, 264, 265

Arithmetic, 10, 54, 230, 309, 321

Asian Journal of Mathematics, 71

Asian students, 21

Association for Women in Mathematics, 5, 177, 218–220, 240

Australia: Szekeres, 191, 192

Austria: Austro-Hungarian army, 94

Olga Taussky-Todd, 169

Automorphic functions, 194

Axioms, axiomatics, 146, 157, 177, 278

Balance (emotional), 125, 336

Bell Labs, 244

Berlin: and Weierstrass, 139, 140

Betti numbers, 116, 119

Black issues, 273–275, 279, 283, 284, 289, 322

Blessed Virgin, vision of, 90

Bounded mean oscillation, 208

Bourdeu, Algebra, 232

Braids, 116, 244

Brazil: and street vendors, 308

Buckinghamshire: and Dyson, 92

Budapest: and Fejér, 35

and Lutheran gymnasium, 11, 26, 34

Calabi-Yau, 71

Calculus, 81, 84, 164, 182, 186, 232, 282, 319, 320, 323, 324

Category theory, 107, 108, 118—121, 182

Chains, ascending, 237

Chaos, 66, 69, 74–78

Charenton Hospital, 4, 132

Childhood interests, 19

in puzzles, 21, 25

Chinese students, 315

Circles, 117, 210

Clarity, 334, 335

Class field theory, 197

Clay Foundation, 73

Cohomology, 119

Collaboration: and aging, 263, 265

Lenore Blum, Steven Smale, and Mike Shub, 246

Bourbaki, 5, 51, 60, 122, 177, 181–191, 238

Grace Chisholm and Will Young, 5, 139, 159, 166

Paul Erdős and Mark Kac, 156

G. H. Hardy, John Littlewood, and Srinivasa Ramanujan, 139, 143–150

Emmy Noether, Helmut Hasse, and Richard Brauer, 238

Andrew Wiles and Richard Taylor, 64

College Mathematics Journal, 319

Combinatorics, 103, 104, 179, 192

Community, 334

Anonymous, 191–193

AWM, 218–223

Bourbaki, 5, 51, 60, 122, 177, 181–191, 238

Courant Institute, 204–209

Göttingen, 193–204

Jewish People’s University; 216–218

Mekh-Mat, 209–216

Competition, 280

Complex analysis, 55, 131, 132, 139, 182, 217

Computers, computing, computability, 62, 154, 280, 318

Conservation laws, 236

Constructionist theories, 308–311

Count Down, 23

Cours d’analyse, 144

Covariant, 236

Creativity, 52

Culture, 47

Curve, 277

Cycloid, 90

Danbury Prison, 96

Differential equations, 98, 252, 257

Diophantine equations, 13, 116, 117, 166

Discrete mathematics, 192

Discrimination in education, 323

Distant teachers: Poincaré, 40

Distributions, 112

Division of labor, 165, 191

DuPont, 282

Dynamical systems, 39, 74, 75, 76–78

Elasticity, 231

Eléments de Géométrie Algébrique, 114

Emotions and feelings: awe, 41

and childhood, 10, 11

curiosity, 23

desire for certainty, 47

despair, 62

engagement, 323

exaltation, 51

insecurity, 41

intrinsic motivation, 72

extrinsic motivation, 72

self confidence, 23

and thought, 1

Equation, 16, 61, 126, 319

Erlangen program, 194

Essai sur le Théorie des Nombres 229

Ethical aspects of mathematics, 337

Everyday cognition and mathematics, 308

Extremal problem, 98, 104

Fermat’s last theorem, 3, 14, 18, 64, 66, 69, 230, 231, 283

Fifteen puzzle, 304

Flow (Csikszentmihalyi), 52

Formulas, 57, 61, 236

Foundations of mathematics, 195

Four-color theorem, 61, 62

Fourier analysis, 35

Fractals, 49

Fractions, 59, 305, 311, 320, 321

Frames of Mind, 328

Function theory, 74, 131, 132, 177, 181

Functional analysis, 94, 112, 163

Galois theory, 181

Gender: career patterns, 260

discrimination, 26, 27, 82, 218–220, 241

stereotypes, 223, 242

Geodesic, 277

Geometry, 18, 35, 54, 132, 161, 185, 194, 195, 210, 238, 265, 276, 277, 319, 320, 326, 327

algebraic, 108, 113, 117

descriptive, 93

differential, 38

Euclidean, 116

non-Euclidean, 62, 74, 116, 116

projective, 17, 83, 93, 94, 104, 116

German mathematics school, 183

Graph theory, 192

Group cohesion, 188

Hahn-Banach theorem, 94

Harmonic analysis, 265

Hilbert’s problems, 100

Hilbert’s tenth problem, 13, 166

Homoclinic tangle, 75, 78

Horseshoe map, 77

Humanistic approaches, 321, 325–327

Hungarian labor force, 102, 103

Ideal, 117

primary, 237

Idealtheorie in Ringbereichen, 237

Images, 50, 51, 55

Immigrant students, 21–22

Inequality, 90, 91, 208

Infinitesimals, 16

Infinity, 10, 58, 59, 116, 140

Insanity, 126–136

Institut des Hautes Études Scientifiques (IHES), 112, 113, 120, 122

Institute for Advanced Study, 70, 80, 134, 154, 156, 239, 289, 290

Integral equations, 195

Integration, 163, 182

Intel Science Search, 21

International Congress of Mathematicians, 120, 122, 142, 166, 198

International Math and Science Study (IMSS), 316

International Mathematical Union, 165

International Mathematical Olympiad, 20

Internet, 70

Invariants, 236

IQ, 54, 328

Japanese attractor, 78

Jewish issues and mathematicians: identity, 111, 154, 169, 201, 203, 217

Jewish tradition, 21, 52

persecution, 102, 109, 192, 215, 218, 281, 289

Knots, 116, 244

Language: Piraha, 49

Latin Quarter: Bourbaki, 181

Latino, 322

Lawrence Berkeley National Laboratory, 312

Lebesgue integral, 163

Lego, 21

Lie groups and algebras, 182, 186, 310

Limits, 16

Linear algebra, 97, 185, 238

Linear functional, 94

Logic, 56, 62, 107, 133, 134, 135, 153, 157, 186, 195, 213, 238, 261, 264, 306, 335

Logical positivism, 190

London Mathematical Society, 164, 254

Love for students, 293

Lutheran Gymnasium of Budapest, 26, 34

Manifold, 69, 76, 94, 118

Mapping, 118

Martingales, 90

Math Counts, 28

Mathematical Association of America, 277, 282, 287, 296

Mathematical beauty, 58–63, 254

Mathematical conversations, 63, 64

Mathematical education and educators, 354, 358, 381

Mathematical friendships: Peter Lax and Louis Nirenberg, 138

Arthur Cayley and James Joseph Sylvester, 138

George Polya and Gábor Szegő, 138

Hermann Minkowski and David Hilbert, 139, 141–143

Karl Weierstrass and Sonia Kovalevskaya, 139–141

G. H. Hardy, John Littlewood, and Srinivasa Ramanujan, 143–150

Andrei Kolmogorov and Pavel Aleksandrov, 151–153

Stan Ulam and John von Neumann, 153–154

Albert Einstein and Kurt Gödel, 156–158

Emmy Noether and Olga Taussky, 169–171

Mathematical genealogy, 277

Mathematical Intelligencer, 96

Mathematical interests, 13, 18

in adolescence, 12, 14, 16

Mathematical physics, 140, 237

Mathematical reform, 309–314, 322

Mathematical stories, 66–68

Mathematical styles: analogue, 55

analytic, 55

problem solvers, 56–57

theorizers, 56–57

Mathematical symbols, 48, 49

Mathematical systems: in Kenya, 307

in New Guinea, 49

in Mozambique, 308

in Papua, 49

among Piraha, 49

Yoruba, 305

Mathematicians: African-American, 171–172, 177, 284–290, 364, 366, 367, 369, 376, 377, 383

Austrian, 360, 361, 362, 368, 378

Belgian, 356

Bulgarian, 29

Canadian, 257, 354, 361

Chinese, 36, 72

Danish, 352

Dutch, 352, 358, 377

English, 263, 354, 355–357, 362, 365, 367–369, 372, 373, 377, 378, 382, 383, 385

Finnish, 368, 371

French, 349, 351, 352, 354, 356, 358, 360, 365, 366, 367, 369, 371, 374, 379, 384

German, 350, 352, 354, 355, 357, 358, 362, 363, 366, 367, 369, 372, 373, 381

Greek, 293, 349, 357

Hungarian, 34, 40, 153, 154, 196, 352, 357, 361, 365, 370–372, 377, 379, 380, 382

Indian, 372, 380

Israeli, 257, 372, 384

Italian, 373

Irish, 361, 362, 377

Japanese, 363, 378, 379

Lebanese, 350

Mozambican, 308

Norwegian, 156, 181, 374

Russian, 349, 351, 363, 364, 369, 370, 375, 376, 377

Swedish, 257, 260, 265

Swiss, 201

United States, 349–382

Ukrainian, 201, 384

Uruguayan, 97–101

Mathematicians as prisoners: Accinelli, Elvio, 100

Davis, Chandler, 96–97

Helly, Eduard, 94

Kerrich, J. E., 95

Leray, Jean, 95

Markarian, Roberto, 99

Massera, J. L., 97–101

Radó, Tibor, 94

Poncelet, Jean Victor, 4, 92, 95, 104

Turán, Pal, 102–104

Vietoris, Leopold, 94

Weil, André, 95–96

Math phobia, 302

“Math Wars,” 317

Mathematics as a filter, 6, 323, 324, 327

Matrix theory, 98

McCarthyism, 96

Measure theory, 83, 84, 265

Mechanics, 132, 206, 209, 234, 235

Medical school, 323

Mentoring, 22, 23, 276

Lipman Bers and Tilla Weinstein, 37

S. S. Chern and Louis Auslander, and Philip Griffiths, 35–37

Richard Courant, Kurt Friedrichs, Fritz John, and Cathleen Morawetz, 201, 203–204

Wilhelm Magnus and Rebekka Struik, 38

Marston Morse and Herbert Robbins, 32

Kazimir Kuratowski and Stan Ulam, 32–33

Jerzy Neyman and George Dantzig, 33

Norbert Wiener and Norman Levinson, 31–32

Moderne algebra, 183

Monte Carlo method, 154

Moore method, 277–281

More Mathematical People, 279

Multiple intelligences, 328

Music and mathematics, 13, 26, 60, 80

National Academy of Sciences, 82, 168, 206, 243, 277, 283, 289, 290

National Association of Mathematicians (NAM), 174, 177, 288

National Medal of Science, 3, 206

National Science Foundation, 34, 38, 178, 251

Nazis, 238, 289, 310

n-body problem, 74–76

New Mexico State Penitentiary Minimum Security Facility, 320

New York Review of Books, 91

New York Times, 128, 130, 267, 316, 319

New Yorker, 72, 255

“No Child Left Behind” Act, 302, 321

Notices of the American Mathematical Society, 207

Number theory, 84, 103, 132, 144, 169, 192, 197, 229, 230

Numbers: algebraic, 197

complex, 55, 116

negative, 9

real, 246

Numerical Analysis, 92, 246, 248, 262, 265

Parabola, 12

Partial differential equations, 37, 138, 212, 243, 257

Penal de Libertad (prison in Uruguay), 98

Permutations, 181

Personality characteristics of gifted mathematicians, 23–26

Physics, 157, 158, 232, 236, 186

Poincaré’s conjecture, 69–72

Point-set theory, 277, 278, 287

Pollution, 128

Polyhedra, 159

Polymath Project, 179

Polynomials, 13, 117, 166, 181

Potsdam model, 7, 275, 292–299

Pre-calculus, 323

Prime numbers, 11, 59, 156, 230

Principia Mathematica, 306

Prizes: Cole Prize, 283

Crafoord Prize, 124

Fields Medal, 54, 71, 72, 120, 179, 198

Gung and Hu Award, 296

MacArthur Fellowship, 243

Math Counts, 35

Nobel Prize, 267

Westinghouse Talent Search, 30

Probability and statistics, 32, 33, 95, 156, 252, 261, 265, 289

Problem solving, 23, 28–30, 34, 52–57, 281

Prodigies, 19, 20

Proof, 57, 59

Proof (play), 69

Prussia, 193, 194

Pyrenees, 108, 126

Quadratic formula, 61

Quantum mechanics, 116, 158, 186

Quaternions, 115

Ramsey theory, 192

Reasoning skills, 328

Récoltes et Semeilles, 108, 109, 110, 125

Relativity, 74, 195, 196

Ricci flow, 70

Riemann surfaces, 37

Ring theory, 117, 237

Rockefeller Foundation, 98, 239

Role models, 29, 292

Rosenwald Fellowship, 2

Royal Air Force, 91

Royal Flying Corps, 164

Royal Society of England, 149, 150, 163

SACNAS (Society for Advancing Chicano and Native American Science), 177

Saratov, 92, 93

Saturn’s rings, 233

Schemes, 118, 121

Scholastic Aptitude Test, 18

Science, 71

Scottish Café in Lwów, 153

Seifert conjecture, 80, 81, 84

Séminaire de Géométrie Algébrique, 114

Sets, set theory, 27, 186

Sheaves, 95, 117, 119

Siberia, 108

Singapore textbooks, 317

Sloan Foundation, 20

SMSG (School Mathematics Study Group), 185, 296

Social aspects of mathematics, 336

Spaces, 115, 119

Banach, 112

Hilbert, 112

infinite-dimensional, 116

metric, 277

metrizable, 119, 277

non-Euclidean, 116

topological, 119, 277

Spatial visualization, 21, 25, 50, 79

Spheres, 55, 69, 188

Statistics, 34, 91, 181, 282, 287

Strange attractor, 76

Study groups, 17

Su Do Ku, 304

Symmetry, 194, 236

Tangent, 118

TBI’s (traditionally Black institutions), 275

The Great Prisoners, 101

Thought collectives, 191

TIMSS (Trends in International Mathematics and Science Society), 315

Topology, 66, 67, 75, 77, 94, 95, 98, 117, 126, 186, 209, 217, 238, 244, 257, 261, 263, 277, 282, 287, 288, 310

Topos, 118, 119

Torus, 118

Triangles, 11, 112

Trigonometry, 232, 282, 305, 323, 324, 327

Tupamaros (Uruguay), 99

Unabomber, 128

Universities/Colleges: Aberystwyth, 164

Alabama, 80

Barnard, 244, 261

Baylor, 249, 284

Berlin, 233, 234

Bishop, 249

Braunschweig, 200

Breslau, 239

Bryn Mawr, 27, 170, 239, 240

Budapest (Loránd Eőtvős), 94

California Institute of Technology, 297

University of California at Berkeley, 247, 290, 298, 315

University of California at Los Angeles, 19, 179

Cambridge, 17, 64, 146, 147, 159, 161, 162, 163, 164, 170, 176, 179, 203, 204, 252, 267

Carleton, 294

Chicago, 276, 287, 311

Chicago State, 295

Clarkson Institute of Technology, 293

Collège de France, 122

Columbia, 70, 249, 267

Cornell, 11

Dartmouth, 297

DePauw, 320

École Normale Supérieure, 111

École Polytechnique, 229

Erlangen, 235, 240

ETH (Eidgenössische TechnischeHochschule (Zürich)), 368

Fisk, 249

Göttingen, 5, 143, 154, 160, 162, 176, 183, 186, 193–204, 206, 233, 235, 237, 315, 336,

Girton, 150

Harvard, 257, 282

Harvey Mudd, 297

Heidelberg, 233

Howard, 249, 287, 289, 290

Illinois, 33

Indiana, 225, 271

Jewish People’s University (Moscow), 177, 218

Johns Hopkins, 9, 275, 276

Johnson C. Smith, 274, 295

Kansas, 27

Königsberg, 41

Lincoln, 275, 295

Manchester, 17

Maryland, 284

Massachusetts Institute of Technology, 38, 66, 76, 90, 315

Michigan, 96, 128, 274

Mills, 247, 260

Montevideo, 98

Montpellier, 111, 122

Morgan State, 275, 276, 291, 294, 295

Moscow, 5, 199, 209–218

Nancy, 111

Nebraska, 163

New Mexico, 258

New York, 37, 38, 97, 112, 172, 177, 203–209, 211, 244, 251, 266, 335, 336

Nice, 122

Northeastern, 217

Northwestern, 276

Ohio State, 95

Oxford, 80, 146

Paul Quinn, 249

Pennsylvania, 276, 277, 287, 289

Prairie View, 275, 276, 291

Princeton, 66, 80, 98, 134, 152, 154, 157, 170, 276, 289, 290, 297, 315

Rhode Island, 258

Rice, 284

Richmond, 26,

Rutgers, 123, 126, 130

Sarah Lawrence, 27

Shaw, 275

Smith, 251

Spelman, 297

Stanford, 30, 98, 127, 156

State University of New York at Geneseo, 29

State University of New York at Potsdam, 276, 294–299

Stockholm, 234

Sussex, 258

Szeged, 94, 253

Texas (Austin), 171, 172, 243, 249, 276, 277, 284, 287, 298

Texas A & M, 282

Tomsk, 239

Toronto, 97

Tufts, 22

Tuskegee, 287

Utrecht, 310

Vienna, 169

Warwick, 80

West Virginia State, 288

Wilberforce, 275, 287

Wisconsin, 163, 249, 260

Yale, 128

U. S. Constitution, 96

U. S. Math Olympiad, 28

U. S. Supreme Court, 283

Varieties, 119

Volga River, 92

Wall Street Journal, 130

Washington Post, 305

Weil conjectures, 115–116, 119

Women in mathematics, 281

discrimination, 241, 242

pregnancy, 240, 243

self-confidence, 247, 294, 321, 329

World War I, 94, 132, 148, 164, 182, 197, 200, 201

World War II, 10, 92, 154, 162, 195, 199, 222