Index

Aaboe Academy, 6

Abbott, Edwin Abbott, 52

Abel, Niels Henrik, 258

Adams, Frank, 228

Adeboye, Adeniran, 204

Ahlfors, Lars Valerian, 100, 140–41, 269–70

Ahlfors’s distortion theorem, 142

Alexander, James Waddell, 103–4

algebraic geometry, 235–36

algebraic K-theory, 228–29

algebraic topology, 243

Allendoerfer, Carl Bennett, 49

Almgren, Frederick J., Jr., 274, 280, 284

Altschiller-Court, Nathan, 83, 90

American Association for the Advancement of Science, 100, 274, 280

American Institute of Mathematics, 254

American Mathematical Monthly, 86, 88, 103

American Mathematical Society, 93, 96, 99, 105, 128, 250, 274, 288

analytic number theory, 32, 41, 254

Archimedean solids, 174

Archimedes, 84, 86, 317

Arrow’s impossibility theorem, 247

Artin, Emil, 105

Artin, Michael, 105

Association for Computing Machinery, 96

Athens, University of, 38

Aumann, Robert, 96

Ayoub, Raymond George, 185

Bacher, Robert F., 32

Barbeau, Edward J., 121

Barnard College, Columbia University, 215, 237

Bateman, Paul T., 299

Beatles, The, 160–61

Beckenbach, Edwin Ford, 97

Bell, Eric Temple, 33

Bellman, Richard Ernest, 200

Berlekamp, Elwyn R., 170, 174–75

Bers, Lipman, 1

Bhargava, Manjul, 158

Birkhoff, Garrett, 100

Birkhoff, George David, 11

Birmingham University, 179

Blackwell, David, 210

Blinn, Jim, 40–41

Boas, Ralph Philip, Jr., 97, 114, 139, 243

Bochner, Salomon, 101, 144

Bohnenblust, Henry Frederic, 33, 101

Bohr, Harald, 43–44, 264–65

Bohr, Niels, 43–44, 101

Borel spreads, 139

Bott, Raoul, 297

Bottema, O., 88

Bourbaki, Nicolas, 102

Bowdoin College, 49

Brandt, Rudoph “Dutch,” 45

Brauer, Richard Dagobert, 153

Brauer-Fowler theorem, 153

Brown University, 52, 66–67, 74

Brun, Viggo, 255

Bryn Mawr College, 198, 200

Bulletin of the American Mathematical Society, 240, 250

Burgstahler, Sylvan, 163

Caius College, Cambridge, 169

California, University of: Berkeley, 17, 31, 45, 49, 63–65, 88, 281, 283, 294

Irvine, 240, 247

Los Angeles, 83, 90

Santa Barbara, 63–64

Santa Cruz, 185, 284

California Institute of Technology, 17, 32–34, 36

Cambridge University, 47, 129, 133, 139, 141–42, 169–70, 215, 221, 226, 229, 232–33, 256, 266

Capone, Alphonse “Al,” 45

Carathéodory, Constantin, 9

Caraus, Iurie, 299

Carleman, Torsten, 264

Carnegie-Mellon University, 111, 120, 122–23

Carroll, Lewis, 84

Cartan, Élie, 317

Cartwright, Mary, 232

Cauchy-(Bunyakovskii)-Schwarz inequality, 50

Cave-Browne-Cave, Frances E., 139

Cayley, Sir Arthur, 177

Cayley graphs, 157–58

celestial mechanics, 243

Cesari, Lamberto, 31

Cesàro, Ernesto, 31

Chachere, Gerald, 204

Chavez, Ben, 82

Chazy, Jean, 245

Chebyshev, Pafnuti L., 256

Chebyshev inequality, 256

Chern, Shiing-shen, 63, 65, 282, 299, 317

Chern-Weil homomorphism, 63

Chevalley, Claude, 101

Chicago, University of, 159

Chopin, Frédéric, 94

Christ Church, Oxford, 130–31, 133

Church, Alonzo, 101

Coddington, Earl Alexander, 32

College Mathematics Journal, 161

Collingwood, Ernest Foyle, 142

Columbia University, 196, 215, 237

Colwell, Rita, 310–11

combinatorics, 107, 174, 176–77

complex analysis, 30–31, 34, 60, 243

complex function theory, 1, 61

complex manifold theory, 1

Conway, John Horton, 162, 170, 174–75, 179, 226

Cornell University, 123–24

Courant, Richard, 30, 33

Courant Institute of Mathematical Sciences, 201

Coxeter, Harold Scott Macdonald, 49, 91, 287

Cramér, Harald, 267

Curtiss, David Raymond, 96, 99

Curtiss, John, 96, 143

Dalí, Salvador, 77–78

Daubechies, Ingrid, 302

Davenport, Harold, 47–48, 176

Dedekind cuts, 259

Denjoy, Arnaud, 6

Denjoy conjecture, 5–6

Descartes, Blanche, 189

Dickson, Leonard Eugene, 177, 259

differential equations, 32, 143, 243, 191

differential geometry, 63–64, 296

Dirichlet series, 41, 257

discrete mathematics, 111, 124

Dixmier, Jacques, 228

Dodge, Clayton, 87, 92

Dodgson, C. L. See Carroll, Lewis

Donaldson, James, 203–4

dynamical systems, 235, 243, 250

Dyson, Freeman John, 106

Edge, W. L., 169

Edinburgh, University of, 226

Eilenberg, Samuel, 184

Einstein, Albert, 89, 98, 101, 103, 317

Eisenhart, Luther Pfahler, 101–3

elliptic functions, 31, 41

Erdélyi, Arthur, 33

Erdős, Paul, 90–92, 102, 170, 172, 176, 178, 184, 189–90

Erdős-Mordell theorem, 90

Erdős number, 85, 178

Escher, Maurits Cornelis, 178

Euclid, 219, 260–61, 317

Euler, Leonhard, 177, 260, 273, 307

Euler’s formula, 260

Euler’s inversion formula, 60

Eves, Howard, 86, 90

Fan, Ky, 59–62, 64–65

Federov, E. S., 287

Fefferman, Charles, 302

Fermat, Pierre de, 317

Fermat equation, 269

Feynman, Richard, 102

Fields Medal, 11–12, 174, 204, 269–70

Flatland, 52, 55, 70

Fleming, Wendell, 66

Floer theory, 236

foliations, 247

Ford, Lester R., 46

fourth dimension, 52, 68–72

fractals, 71

Freedman, Benedict, 41

Friedman, Avner, 244

Frobenius, Ferdinand Georg, 177

functional analysis, 228, 243, 247

Galilei, Galileo, 317

Galois, Évariste, 317

game theory, 96, 107, 173–74, 176, 244–45

Gardner, Martin, 83, 87, 122, 127

Garfunkel, Jack, 85

Gasper, George, 241

gauge theory, 236

Gauss, Carl Friedrich, 177, 258, 260, 269, 317

Gelfand, I. M., 215, 225–28, 233–34

Gell-Mann, Murray, 32

geometric function theory, 1

geometry: algebraic, 235–56

differential, 63–74, 296

global, 63

symplectic, 215, 235–36

Georgetown University, 58

Gill, Tepper, 204

Girton College, Cambridge, 129, 138–39, 141–42, 229–30, 232

Gödel, Kurt, 103

Goldbach problem (conjecture), 268–69

Goldberg, Michael, 189

Goldman, Alan, 124

Goldsmiths College, 170, 181–83, 188

Golomb, Solomon, 88–90

Goodstein, David, 40

Göttingen University, 97, 263

Graham, Ronald Lewis, 92, 159–60, 162

graph theory, 173, 176, 189

Graustein, William Caspar, 7

groups: abelian, 31

finite, 156, 162

infinite, 156

Kleinian, 1

Guy, Michael, 173–74

Hadamard, Jacques Salomon, 191, 256

Halmos, Paul Richard, 266, 295

Hamiltonian circuit, 158

Hardy, Godfrey Harold, 129, 136–39, 143, 243, 256, 261, 266–68, 273

Harvard University, 1, 7, 10, 12, 32, 58, 63, 65–66, 96, 100, 153, 294, 297

Harvey Mudd College, 107, 122, 127–28

Hayman, Walter Kurt, 142

Heaslet, M. A., 83

Hecke, Erich, 257, 273

Hecke operators, 257

Hejhal, Dennis, 254

Helsinki, University of, 1, 3, 7

Herstein, I. N., 282

Higgins, Aparna, 161

Hilbert, David, 98–99, 317

Holmes, Cecil T., 49

homological algebra, 236

Howard University, 193, 203–4, 212

Hurwitz, Adolf, 30, 97

hydrodynamics, 169

Illinois, University of, Urbana-Champaign, 45, 299–301

infinite products, 41

Ingham, A. E., 261

Institute for Advanced Study, 65, 101, 235, 237, 254, 264–65, 271

International Congress of Mathematicians: Berkeley (1986), 93

Cambridge (Massachusettts) (1950), 254, 270

Madrid (2006), 299, 316

Nice (1970), 284

Oslo (1936), 10, 254, 270

Vancouver (1974), 271

Zürich (1932), 140.

Jackson, Dunham, 47

Jacobson, Nathan, 100

John Carroll University, 124

Johns Hopkins University, The, 107, 126, 243

Kelly (Barnes), George “Machine Gun,” 45

King’s College, Cambridge, 219

Klamkin, Murray, 88, 91

Kleinian groups, 1

Kline, Morris, 49

Knopp, Konrad, 28, 61

knot theory, 14

Korevaar, Pia Pfluger, 49

Krantz, Steven G., 286

Kreider, Donald Lester, 160

Kronstein, Karl, 153

Kuhn-Tucker theorem, 96

Kuiper, Nicholaas H., 64, 66

Kummer, Ernst Eduard, 269

Ladies’ and Gentlemen’s Diary, 83

Lagrange, Joseph Louis, 317

Lamb, Sir Horace, 169

Landau, Edmund, 137, 273

Lang, Serge, 229

Laplace, Pierre Simon, 317

Lefschetz, Solomon, 100–104, 143–44

Lehmer, Derrick Henry, 27, 32, 49, 184

Lehmer, D. N., 29

Leibniz, Gottfried Wilhelm von, 271, 317

Leibniz’s formula, 259

Leitzel, James R., 161

Levinson, Norman, 32

Lewis, Donald J., 302

Lie algebras, 258

Lindelöf, Ernst Leonhard, 1, 4–5, 7

Lindgren, William, 52

Littlewood, James Edensor, 129, 138–43, 145, 243, 256, 261, 266, 273

Llull, Ramon, 78

Loewner, Charles (Karl), 299

London Mathematical Society, 129, 137, 140–41

London University, 170

Lovácz, Lázsló, 177

Luce, Duncan, 245, 247

Mackey, George, 65

Maclaurin expansion, 51

Magdelan College, Oxford, 187

magic squares, 29

Maki, Daniel, 241

Massachusetts Institute of Technology, 32, 96, 105, 230, 284

Mathematical Association of America, 93, 96, 99, 107–8, 114, 161–63

mathematical economics, 244

Mathematical Gazette, 87, 186–87

mathematical psychology, 244

Mathematical Sciences Research Institute, 216

Mathematics Magazine, 85, 91, 156, 161

McDuff, Dusa Waddington, 144

Medusa, 221–22

Michal, A. D., 35

Michigan Technological University, 241

Milner, Eric, 183–84, 186

Milnor, John Willard, 233, 235

mirror symmetry, 235

Mnatsakanian, Mamikon, 41

Montel’s normal families, 142

Montgomery, Hugh, 271

Moody, Michael, 125

Morawetz, Cathleen, 198

Mordell, Louis Joel, 90, 181

Morris, Brent, 108, 123

Morse, [Harold] Marston, 100, 103, 106

Morse theory, 229

Morton, V. C., 136

Moser, Leo, 90, 184–85, 187

Mount Holyoke College, 279–80, 288

n-body problem, 243, 245, 247

Nash, John Forbes, Jr., 96

National Academy of Sciences, 240, 315

National Bureau of Standards, 96

National Institute of Standards and Technology, 193, 204, 274

National Science Foundation, 41, 52, 294, 299, 309–11, 315

Neumann, John von, 103–5, 227, 239, 317

Nevanlinna, Rolf Herman, 5, 7, 297

New College, Oxford, 136–37

Newman, Maxwell H. A., 143

Newnham College, Cambridge, 133

Newton, Sir Isaac, 285

New York, City College of, 79, 82

New York Mathematics Society, 202

New York University, 49, 82, 201, 203

Nicholson, John William, 136

Niven, Ivan, 69

North Carolina, University of, 126

Northwestern University, 96, 241, 243

Norwegian Institute of Technology (Trondheim), 255

Notices of the American Mathematical Society, 237

Notre Dame University, 58, 60, 62, 153

number theory, 30, 41, 107, 158–59, 176–77, 229, 250, 254, 265, 268

analytic, 32, 41

Open University, 182

operations research, 224–25

Oppenheim, Sir Alexander, 183–84

Øre, Oystein, 83

Oregon, University of, 49

Osborn, Howard, 51

Oslo, University of, 254

Oxford University, 129–30, 134, 137–38, 256

Pacific Journal of Mathematics, 97

Paley, R.E.A.C., 139

Pappus, 84

Pascal, Blaise, 56

Pearson, Karl, 139

Pell equation, 256, 270

Perelman, Grigory, 273

Pétard, H., 103

Pfluger, Albert, 49–50

Pi Mu Epsilon Journal, 79, 88–89, 92

Poe, Edgar Allen, 119

Poincaré, Henri, 317

Pollard, Harry, 243

Pólya, George, 5, 31, 46, 48–50, 178, 256, 265, 267

Polytechnical Institute, Helsinki, 1

Price, G. Baley, 152

Prime Number Theorem, 254

Princeton University, 96, 106, 137, 143–44, 267, 284, 301–2

prisoner’s dilemma, 96, 105

Project MATHEMATICS!, 40

Project NExT, 161–62

Purdue University, 242–43

Pythagorean triples, 80

quasiconformal mappings, 1

quaternions, 168

Quillen, Daniel G., 228

Quinn, Jennifer, 108

Rademacher, Hans Adolph, 255

Raiffa, Howard, 245

Ramanujan, Srinivasa, 256, 261, 273

Ramsey theory, 178

Randi, James, 115

Rees, Mina, 144

Reid, G. A., 226, 258

Riemann, [Georg Friedrich] Bernhard, 317

Riemann hypothesis (conjecture), 268–69, 271

Riemann zeta function, 254

Ringel, Gerhard, 186

Robinson, Raphael Mitchell, 31, 101

Rogers, L. J., 136

Ross, Arnold, 61, 63

Royal Society of London, 129, 144, 215

Rudin, Walter, 282

Ruskai, Beth, 291

Russell, Bertrand, 101

Rutgers University, 274

Salamon, Dietmar, 234

Sarnak, Peter, 254, 266, 302

Scheinerman, Edward R., 124

Schoenberg, Isaac Jacob, 49

Schwartz, Laurent, 265

Scientific American, 83, 87

Scripta Mathematica, 87

Segal, Graeme Bruce, 229–30

Seidel, Vladimir P., 61

Selberg: asymptotic formula, 254

identity, 254

sieve, 254, 270

trace formula, 254, 270

zeta function, 254, 270

Selfridge, John, 184–85

Senechal, Marjorie, 287

Serre, Jean-Pierre, 191, 229, 265

Serret, Joseph Alfred, 256

Siegel, Carl Ludwig, 264, 273

sieve, 254–55, 270

Simon, Marsha, 284

Singer, Isadore Manual, 232

Skolem, [Albert] Thoralf, 264

Smith, Cedric, 188–89

Sonneborn, Lee, 152

Sonnenschein, Hugo, 244

Southern California, University of, 79, 82

Spanier, Edwin Henry, 63–64

State University of New York, Stony Brook. See Stony Brook University

Steenrod, Norman, 101

Stein, Elias, 302

Stein, Marjorie, 284

Steinhaus, Hugo, 89

Sternberg, Shlomo, 66

Stevens, Christine, 161

Stone, Arthur, 189

Stony Brook University, 232, 236

Størmer, Carl, 256, 259

string theory, 14

Sundman, K. F., 243

Sunseri, Mary Virginia, 43

Sylvester, James Joseph, 177

symplectic geometry, 215, 234–36

Szegő, Gábor, 31

Szemerédi, Endre, 177

Taliaferro, R. Catesby, 60

Tamarkin, Jacob David, 100

Tarski, Alfred, 31

Tata Institute, Mumbai, 272

Tauberian theorems, 243

Taussky-Todd, Olga, 33

Thales, 317

Thébault, Victor, 85–87

Thom, René F., 225

Titchmarsh, Edward Charles, 129, 137

topology, 296: algebraic, 243

general, 60

low-dimensional, 236

Trigg, Charles, 83, 85, 88, 90

Trinity College, Cambridge, 138, 142, 189, 229

Tripos examination, 139, 226

Tucker, Alan C., 96–97, 302

Tucker, Albert W., 96, 102–3, 301

Tucker, Thomas W., 96–97, 302

Tukey, John Wilder, 144

Turku, University of, 251

Tutte, William T., 189

Uspensky, James Victor, 83

Utah, University of, 26–27, 202

Valiron, Georges, 139

Vallée-Poussin, Charles Jean de la, 256

Van der Pol, Balthasar, 142

Van der Pol’s equation, 129

Veblen, Oswald, 104–5, 132

vector fields, 168

voting theory, 244–45, 247

Ward, Morgan, 33–34

Warwick, University of, 283–84

Washington, University of, 26–27, 36, 49

Watson, George Neville, 136, 261

Weaver, Warren, 100

Wedderburn, Joseph Henry, 99, 101

Weil, André, 270

Wells, H. G., 215, 222

Wetzel, John E., 45

Weyl, [Claus Hugo] Hermann, 5, 103, 105, 273, 317

Whitney, Hassler, 100

Whittaker, Edmund Taylor, 136

Wiener, Norbert, 32, 100–101, 105, 317

Wigner, Eugene Paul, 101

Wiles, Andrew J., 273

Wilks, Samuel Stanley, 101

Wisconsin, University of, Madison, 49

Witte theorems, 158

Wolf, Frantisek, 30

Wolf Prize, 12

Wood, Melanie, 157, 159

Wright, Margaret, 309

York University, 142, 229–30

Young, Grace Chisholm, 139

Young, William Henry, 139

Youngs, J.W.T. “Ted,” 185

Zeeman, [Erik] Christopher, 225

Zeitlin, Jacob, 83–84

Zentralblatt für Mathematik und ihre Grenzgebiete, 264

zonohedra, 287

Zuckerman, Herbert Samuel, 27–30

Zürich, University of, 294, 296