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
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
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
Austria: Austro-Hungarian army, 94
Olga Taussky-Todd, 169
Automorphic functions, 194
Axioms, axiomatics, 146, 157, 177, 278
Bell Labs, 244
Berlin: and Weierstrass, 139, 140
Black issues, 273–275, 279, 283, 284, 289, 322
Blessed Virgin, vision of, 90
Bounded mean oscillation, 208
Bourdeu, Algebra, 232
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
Childhood interests, 19
Chinese students, 315
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
DuPont, 282
Dynamical systems, 39, 74, 75, 76–78
Elasticity, 231
Eléments de Géométrie Algébrique, 114
Emotions and feelings: awe, 41
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
Erlangen program, 194
Essai sur le Théorie des Nombres 229
Ethical aspects of mathematics, 337
Everyday cognition and mathematics, 308
Fermat’s last theorem, 3, 14, 18, 64, 66, 69, 230, 231, 283
Fifteen puzzle, 304
Flow (Csikszentmihalyi), 52
Foundations of mathematics, 195
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
Geodesic, 277
Geometry, 18, 35, 54, 132, 161, 185, 194, 195, 210, 238, 265, 276, 277, 319, 320, 326, 327
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
Horseshoe map, 77
Humanistic approaches, 321, 325–327
Hungarian labor force, 102, 103
Ideal, 117
primary, 237
Idealtheorie in Ringbereichen, 237
Immigrant students, 21–22
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
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
Japanese attractor, 78
Jewish issues and mathematicians: identity, 111, 154, 169, 201, 203, 217
persecution, 102, 109, 192, 215, 218, 281, 289
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 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
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
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 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
Danish, 352
English, 263, 354, 355–357, 362, 365, 367–369, 372, 373, 377, 378, 382, 383, 385
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
Hungarian, 34, 40, 153, 154, 196, 352, 357, 361, 365, 370–372, 377, 379, 380, 382
Italian, 373
Lebanese, 350
Mozambican, 308
Russian, 349, 351, 363, 364, 369, 370, 375, 376, 377
Swiss, 201
United States, 349–382
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
Mechanics, 132, 206, 209, 234, 235
Medical school, 323
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
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
“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
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
Proof (play), 69
Quadratic formula, 61
Quantum mechanics, 116, 158, 186
Quaternions, 115
Ramsey theory, 192
Reasoning skills, 328
Récoltes et Semeilles, 108, 109, 110, 125
Ricci flow, 70
Riemann surfaces, 37
Rockefeller Foundation, 98, 239
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
Saturn’s rings, 233
Scholastic Aptitude Test, 18
Science, 71
Scottish Café in Lwów, 153
Seifert conjecture, 80, 81, 84
Séminaire de Géométrie Algébrique, 114
Siberia, 108
Singapore textbooks, 317
Sloan Foundation, 20
SMSG (School Mathematics Study Group), 185, 296
Social aspects of mathematics, 336
Banach, 112
Hilbert, 112
infinite-dimensional, 116
metric, 277
non-Euclidean, 116
Spatial visualization, 21, 25, 50, 79
Statistics, 34, 91, 181, 282, 287
Strange attractor, 76
Study groups, 17
Su Do Ku, 304
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
Torus, 118
Trigonometry, 232, 282, 305, 323, 324, 327
Tupamaros (Uruguay), 99
Unabomber, 128
Universities/Colleges: Aberystwyth, 164
Alabama, 80
Bishop, 249
Braunschweig, 200
Breslau, 239
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 State, 295
Clarkson Institute of Technology, 293
Collège de France, 122
Cornell, 11
Dartmouth, 297
DePauw, 320
École Normale Supérieure, 111
École Polytechnique, 229
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
Harvey Mudd, 297
Heidelberg, 233
Illinois, 33
Jewish People’s University (Moscow), 177, 218
Kansas, 27
Königsberg, 41
Manchester, 17
Maryland, 284
Massachusetts Institute of Technology, 38, 66, 76, 90, 315
Montevideo, 98
Morgan State, 275, 276, 291, 294, 295
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
Paul Quinn, 249
Pennsylvania, 276, 277, 287, 289
Princeton, 66, 80, 98, 134, 152, 154, 157, 170, 276, 289, 290, 297, 315
Rhode Island, 258
Rice, 284
Richmond, 26,
Sarah Lawrence, 27
Shaw, 275
Smith, 251
Spelman, 297
State University of New York at Geneseo, 29
State University of New York at Potsdam, 276, 294–299
Stockholm, 234
Sussex, 258
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
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
self-confidence, 247, 294, 321, 329