Creators of Mathematical and Computational Sciences (eBook)

Preface 8
Contents 10
Introduction 22
Number Sense 22
Arithmetic 24
Astronomy 25
Mathematical Science 39
Computing 46
Computational Science 47
Creators 58
Krishna Dwaipayana or Sage Veda Vyasa (Born 3374 BC) 59
Sulbasutras (About 3200 BC) 61
Aryabhatta (Born 2765 BC) 62
Great Pyramid at Gizeh (Erected Around 2600 BC) 64
Cuneiform Tablets (About 2000 BC) 64
Vardhamana Mahavira (Around 1894–1814 BC) 66
Moscow and Rhind Papyruses (About 1850 and 1650 BC) 69
Sage Lagadha (Before 1350 BC) 71
Thales of Miletus (Around 625–545 BC) 71
Anaximander of Miletus (Around 610–547 BC) 73
Acharya Charak and Acharya Sudhrut (Before 600 BC) 74
Anaximenes of Miletus (Around 585–525 BC) 75
Pythagoras (Around 582–481 BC) 75
Theano of Crotona (About 546 BC) 81
Pingala (About 500 BC) 81
Hippasus of Metapontum (About 500 BC) 82
Anaxagoras of Clazomanae (500–428 BC) 82
Zeno of Elea (Around 495–435 BC) 83
Protagoras of Abdera (Around 484–414 BC) 84
Antiphon of Rhamnos (Around 480–411 BC) 85
Philolaus of Croton (Around 480–405 BC) 85
Hippocrates of Chios (About 470 BC) 86
Hippias of Elis (About 460 BC) 87
Democritus of Abdera (Around 460–362 BC) 87
Bryson of Heraclea (About 450 BC) 89
Theodorus of Cyrene (Now Shabhat, Libya) (About 431 BC) 89
Archytas of Tarentum (Around 428–347 BC) 89
Plato of Athens (Around 427–347 BC) 89
Eudoxus of Cnidus (Around 400–347 BC) 91
Xenocrates of Chalcedon (Around 396–314 BC) 93
Aristotle (Around 384–322 BC) 93
Menaechmus of Proconnesus (or Alopeconnesus) (Around 375–325 BC) 94
Aristaeus the Elder (Around 370–300 BC) 95
Callippus of Cyzicus (Around 370–300 BC) 95
Dicaearchus of Messana (Sicily) (Around 350–285 BC) 95
Euclid of Alexandria (Around 325–265 BC) 96
Aristarchus of Samos (310–250 BC) 98
Archimedes of Syracuse (287–212 BC) 99
Ctesibius of Alexandria (Working 285–222 BC) 102
Eratosthenes of Rhodes (Around 276–194 BC) 102
Apollonius of Perga (Around 262–200 BC) 104
Diocles (Around 240–180 BC) 105
Bakhshali Manuscript (About 200 BC) 105
Hipparchus (Around 190–120 BC) 105
Posidonius of Apamea (135–51 BC) 106
Bhaskara I (Before 123 BC) 107
Daivajna Varahamihira (Working 123 BC) 107
Thrasyllus of Mendes (Around 50 BC–36 AD) 108
Brahmagupta (Born 30 BC) 109
Geminus of Rhodes (Around 10 BC–60 AD) 110
Nicomachus of Gerasa (Around 60–120 AD) 110
Menelaus of Alexandria (Around 70–140 AD) 111
Heron of Alexandria (About 75 AD) 111
Zhang Heng (78–139 AD) 112
Alexandrian Claudius Ptolemaeus (Around 90–168 AD) 113
Liu Hui (Around 220–280) 114
Sporus of Nicaea (Around 240–300) 115
Iamblichus (Around 245–325) 115
Diophantus of Alexandria (About 250) 116
Pappus of Alexandria (Around 290–350) 117
Hypatia of Alexandria (370–415) 118
Sun Tsu (About 400) 119
Tsu Ch'ung Chih (Zu Chongzhi) (429–500) 119
Anthemius of Tralles (Around 474–558) 120
Anicius Manlius Severinus Boethius (Around 475–526) 120
Sridhara (Before 486) 121
Bhaskara II or Bhaskaracharya (Working 486) 121
Flavius Magnus Aurelius Cassiodorus Senator (490–585) 123
Isidorus of Miletus (About 540) 123
Isidore of Seville (560–636) 124
Virahanka (About 600 AD) 124
Anania Shirakatsi (610–685) 124
Venerable Bedé (673–735) 125
Lalla (Around 720–790) 125
Alcuin of York (Around 735–804) 125
Masha'allah ibn Athari (740–815) 126
Abu Jafar Mohammed Ibn Musa al-Khwarizmi (Around 780–850) 126
Ja'far ibn Muhammad Abu Ma'shar al-Balkhi (787–886) 128
Govindasv?mi (or Govindasv?min or Govindaswami) (Around 800–860) 129
Ab?-Y?suf Ya'q?b ibn Ish?q al-Sabbah al-Kind? (Around 801–873) 129
Mahavira (817–875) 130
Thabit ibn Qurra (826–901) 132
Ab? K?mil, Shuj?' ibn Aslam ibn Muh?ammad Ibn Shuj?' (850–930) 133
Abu Abdallah Muhammad ibn Jabir ibn Sinan ar-Raqqi al-Harrani as-Sabi al-Battani (858–929) 133
Aboul Wéfá (940–997) 134
Vijayanandi (Around 940–1010) 134
Gerbert d'Aurillac, Pope Sylvester II (945–1003) 135
al-Karkhi of Baghdad (953–1029) 135
Abu-Ali al-Hassan ibn al-Hasan ibn al-Haitham (965–1039) 136
Abu Arrayhan Muhammad ibn Ahmad al-Biruni (973–1048) 136
Sripati (Around 1019–1066) 137
Omar Khayyám (1048–1131) 137
Rabbi Abraham Bar Hiyya ha-Nasi (1070–1136) 138
Rabbi Abraham ben Meir ibn Ezra (Around 1090–1167) 139
Fibonacci (Leonardo of Pisa) (Around 1170–1250) 139
Vincent of Beauvais (Around 1190–1264) 141
Li Chih (1192–1279) 141
Albertus Magnus (Around 1193–1280) 141
Nasir-al-Din al-Tusi (1201–1274) 142
Ch'in Chiu-Shao (Around 1202–1261) 142
William of Moerbeke (1215–1286) 143
Campanus of Novara (Around 1220–1296) 143
Jordanus Nemorarius (1225–1260) 144
Jacob ben Machir ibn Tibbon (Around 1236–1304) 144
Yang Hui (1238–1298) 144
Maximus Planudes (1260–1330) 145
Richard of Wallingford (1292–1336) 145
Chu Shih-Chieh (about 1300) 145
Ala al-Din Abu'l-Hasan Ali Ibn Ibrahim Ibn al-Shatir (1304–1375) 146
Nicole Oresme (1320–1382) 146
Narayanan Pandit (1340–1400) 147
Madhava of Sangamagramma (1340–1425) 147
Parameshvara Namboodri (Around 1370–1460) 149
Jemshid al-Kashi (Around 1380–1429) 149
Nicholas of Cusa (1401–1464) 150
George Pürbach (1423–1461) 151
Johann Regiomontanus (1436–1476) 151
Nilakanthan Somayaji (Around 1444–1544) 152
Nicolas Chuquet (Around 1445–1488) 152
Jacques Lefévre (1455–1536) 153
Scipione del Ferro (1465–1526) 153
Nicolaus Copernicus (1473–1543) 154
Michael Stifel (1486–1567) 155
Oronce Finé (1494–1555) 155
Francesco Maurolico (1494–1575) 156
Niccoló Fontana (Tartaglia) (1500–1557) 156
Jyesthadevan (Around 1500–1600) 157
Sankara Variar (Around 1500–1600) 158
Girolamo Cardano (1501–1576) 158
Robert Recorde (Around 1510–1558) 161
Gerhardus Mercator (1512–1594) 162
Pierre de la Ramée (1515–1572) 163
Jacques Pelletier (Peletier) du Mans (1517–1582) 163
Ludovico Ferrari (1522–1565) 163
Rafael Bombelli (1526–1573) 164
Chitrabhanu (About 1530) 165
Zuanne de Tonini da Coi (About 1530) 165
Guillaume Gosselin (1536–1600) 165
Christopher Clavius (1537–1612) 166
Ludolph van Ceulen (1539–1610) 166
Francois Viéte (1540–1603) 166
Tycho Brahe (1546–1601), the Eldest Son of Otto Brahe (1518–1571) 168
Simon Stevin (1548–1620) 168
John Napier (1550–1617) 169
Thrikkandiyoor Achyuta Pisharati (1550–1621) 170
Pietro Antonio Cataldi (1552–1626) 170
Jobst Bürgi (1552–1632) 171
Melpathur Narayana Bhattathiri (1559–1632) 171
Thomas Harriot (1560–1621) 171
Edward Wright (1561–1615) 172
Galileo Galilei (1564–1642) 172
Johannes Kepler (1571–1630) 176
William Oughtred (1575–1660) 178
Willebrord Snell (1580–1626) 178
Johann Faulhaber (1580–1635) 179
Edmund Gunter (1581–1626) 179
Claude Gaspard Bachet de Méziriac (1581–1638) 179
Pére Marin Mersenne (1588–1648) 180
Gerard Desargues (1591–1661) 181
Albert Girard (1595–1632) 181
René Descartes (1596–1650) 182
Edmund Wingate (1596–1656) 185
Bonaventura Francesco Cavalieri (1598–1647) 185
Antoine de Lalouvére (1600–1664) 186
Puthumana Somayaji (Around 1600–1740) 186
Pierre de Fermat (1601–1665) 186
Evangelista Torricelli (1608–1647) 189
Frans van Schooten (1615–1660) 189
John Wallis (1616–1703) 190
John Graunt (1620–1674) 191
William Viscount Brouncker (1620–1684) 192
Nicolaus Mercator (Kauffmann) (1620–1687) 192
Blaise Pascal (1623–1662) 192
Christiaan Huygens (1629–1695) 194
Johann van Waveren Hudde (1629–1704) 195
Isaac Barrow (1630–1677) 196
Robert Hooke (1635–1703) 197
James Gregory (1638–1675) 198
Philippe De la Hire (1640–1719) 200
Seki Kowa (1642–1708) 201
Sir Isaac Newton (1642–1727) 201
Gottfried Wilhelm von Leibniz (1646–1716) 206
John Flamsteed (1646–1719) 208
Joseph Raphson (1648–1715) 208
Ehrenfried Walter von Tschirnhaus (1651–1708) 209
Michel Rolle (1652–1719) 209
Jacob Bernoulli (1654–1705) 210
Pierre Varignon (1654–1722) 210
Edmund Halley (1656–1742) 211
Guillaume Francois Antoine de L'Hôpital (1661–1704) 213
John Craig (1663–1731) 214
Johann Bernoulli (1667–1748) 214
William Whiston (1667–1752) 215
Abraham De Moivre (1667–1754) 215
Luigi Guido Grandi (1671–1742) 216
Count Jacopo Francesco Riccati (1676–1754) 217
Jacques Cassini (1677–1756) 217
Jacob Hermann (1678–1733) 218
Roger Cotes (1682–1716) 218
Brook Taylor (1685–1731) 219
Gabriel Daniel Fahrenheit (1686–1736) 219
Christian Goldbach (1690–1764) 220
James Stirling (1692–1770) 220
Colin Maclaurin (1698–1746) 220
Daniel Bernoulli (1700–1782) 221
Anders Celsius (1701–1744) 222
Gabriel Cramer (1704–1752) 222
Émilie, Marquise du Châtelet–Laumont (1706–1749) 223
Leonhard Euler (Pronounced ``Oiler'') (1707–1783) 224
Thomas Simpson (1710–1761) 226
Rud?er Josip Boškovi? (Roger Joseph Boscovich) (1711–1787) 227
Alexis Claude Clairaut (1713–1765) 228
Jean le Rond d'Alembert (1717–1783) 229
Maria Gaetana Agnesi (1718–1799) 229
Johann Heinrich Lambert (1728–1777) 230
Benjamin Banneker (1731–1806) 231
Alexandre-Théophile Vandermonde (1735–1796) 231
Jean-Sylvain Bailly (1736–1793) 232
Joseph Louis Lagrange (1736–1813) 232
Marquis de Condorcet (1743–1794) 234
Gaspard Monge, Comte de Péluse (1746–1818) 235
John Playfair (1748–1819) 236
Pierre Simon de Laplace (1749–1827) 237
Lorenzo Mascheroni (1750–1800) 239
Adrien–Marie Legendre (1752–1833) 239
Marc-Antoine Parseval des Chénes (1755–1836) 241
Gaspard Clair François Marie Riche de Prony (1755–1839) 241
Sylvestre Francois Lacroix (1765–1843) 241
Thomas Robert Malthus (1766–1834) 242
Jean-Robert Argand (1768–1822) 242
Jean Baptiste Joseph Fourier (1768–1830) 242
Johann Christian Martin Bartels (1769–1836) 244
Robert Woodhouse (1773–1827) 245
Marie-Sophie Germain (1776–1831) 245
Jósef Maria Hoëne Wronski (1776–1853) 246
Karl Friedrich Gauss (1777–1855) 246
Mary Fairfax Somerville (1780–1872) 252
Siméon Denis Poisson (1781–1840) 253
Bernhard Placidus Johann Nepomuk Bolzano (1781–1848) 254
Friedrich Wilhelm Bessel (1784–1846) 255
Charles Jules Brianchon (1785–1864) 255
Jacques Phillipe Marie Binet (1786–1856) 256
Georg Simon Ohm (1789–1854) 256
Jean-Victor Poncelet (1788–1867) 257
Augustin-Louis Cauchy (1789–1857) 258
August Ferdinand Möbius (1790–1868) 260
Charles Babbage (1791–1871) 261
Nicolai Ivanovich Lobachevsky (1792–1856) 262
George Green (1793–1841) 263
Michel Floréal Chasles (1793–1880) 264
Olinde Rodrigues (1794–1851) 264
Gabriel Lamé (1795–1870) 265
Jacob Steiner (1796–1863) 265
Sankaran Varman (1800–1838) 266
Mikhail Vasilevich Ostrogradsky (1801–1862) 266
Julius Plücker (1801–1868) 267
Sir George Biddell Airy (1801–1892) 268
Niels Henrik Abel (1802–1829) 269
Janos Bolyai (1802–1860) 271
Jacques Charles Francois Sturm (1803–1855) 271
Giusto Bellavitis (1803–1880) 272
Pierre Francois Verhulst (1804–1849) 273
Carl Guslov Jacob Jacobi (1804–1851) 273
Victor Jakowlewitsch Buniakovski (1804–1899) 275
Peter Gustav Lejeune Dirichlet (1805–1859) 275
William Rowan Hamilton (1805–1865) 276
Augustus De Morgan (1806–1871) 277
Hermann Günter Grassmann (1809–1877) 278
Joseph Liouville (1809–1882) 279
Ernst Eduard Kummer (1810–1893) 280
Evariste Galöis (1811–1832) 281
Ludwig Otto Hesse (1811–1874) 282
Urbain Jean Joseph Le Verrier (1811–1877) 283
Pierre Wantzel (1814–1848) 283
James Joseph Sylvester (1814–1897) 283
Ada Augusta, Countess of Lovelace (1815–1852) 285
George Boole (1815–1864) 286
Karl Theodor Wilhelm Weierstrass (1815–1897) 286
John Couch Adams (1819–1892) 289
George Gabriel Stokes (1819–1903) 290
George Salmon (1819–1904) 291
Heinrich Edward Heine (1821–1881) 291
Pafnuty Lvovich Chebyshev (1821–1894) 292
Arthur Cayley (1821–1895) 294
Phillip Ludwig von Seidel (1821–1896) 295
Gregor Johann Mendel (1822–1884) 296
Charles Hermite (1822–1901) 296
Francis Galton (1822–1911) 297
Leopold Kronecker (1823–1891) 298
Oskar Xaver Schlömlich (1823–1901) 300
Johann Martin Zacharias Dase (1824–1861) 300
Gustav Robert Kirchhoff (1824–1887) 301
George Friedrich Bernhard Riemann (1826–1866) 302
Henry John Stephen Smith (1826–1883) 304
Elwin Bruno Christoffel (1829–1900) 304
Julius Wilhelm Richard Dedekind (1831–1916) 305
Charles Lutwidge Dodgson (1832–1898) 306
Rudolf Otto Sigismund Lipschitz (1832–1903) 307
Karl Gottfried Neumann (1832–1925) 308
Rudolf Friedrich Alfred Clebsch (1833–1872) 308
Immanuel Lazarus Fuchs (1833–1902) 308
Edmond Nicolas Laguerre (1834–1886) 309
John Venn (1834–1923) 309
Felice Casorati (1835–1890) 309
Paul Gustav Heinrich Bachmann (1837–1920) 310
Thorvald Nicolai Thiele (1838–1910) 310
George William Hill (1838–1914) 311
Marie Ennemond Camille Jordan (1838–1922) 311
Josiah Willard Gibbs (1839–1903) 312
Julius Peter Christian Petersen (1839–1910) 313
Charles Sanders Peirce (1839–1914) 314
Ernst Schröder (1841–1902) 315
François Édouard Anatole Lucas (1842–1891) 315
François Marius Sophus Lie (1842–1899) 316
Wilhelm Jordan (1842–1899) 316
Jean Gaston Darboux (1842–1917) 317
Joseph Valentin Boussinesq (1842–1929) 318
Karl Hermann Amandus Schwarz (1843–1921) 318
William Kingdon Clifford (1845–1879) 319
Georg Cantor (1845–1918) 319
Nicolai Yegorovich Zhukovski (1847–1921) 322
Friedrich Ludwig Gottlob Frege (1848–1925) 322
Alfred Bray Kempe (1849–1922) 323
Felix Christian Klein (1849–1925) 324
Sofia Vasilyevna Kovalevskaya (1850–1891) 325
Jörgen Pederson Gram (1850–1916) 325
Carl Gustav Axel Harnack (1851–1888) 326
Carl Louis Ferdinand von Lindemann (1852–1939) 326
Jules Henri Poincaré (1854–1912) 327
Andrei Andreyevich Markov (1856–1922) 329
Carl David Tolmé Runge (1856–1927) 330
Charles Emile Picard (1856–1941) 330
Alexander Mikhailovich Liapunov (1857–1918) 331
Karl (Carl) Pearson (1857–1936) 332
Charlotte Angas Scott (1858–1931) 333
Guiseppe Peano (1858–1932) 334
Ernesto Cesáro (1859–1906) 335
Otto Ludwig Hölder (1859–1937) 336
Alicia Boole Stott (1860–1940) 336
Vito Volterra (1860–1940) 337
Ivar Otto Bendixson (1861–1935) 337
Alfred North Whitehead (1861–1947) 338
David Hilbert (1862–1943) 339
William Henry Young (1863–1942) 344
Stanislaw Zaremba (1863–1942) 344
Hermann Minkowski (1864–1909) 345
William Fogg Osgood (1864–1943) 346
Charles Proteus Steinmetz (1865–1923) 346
Jacques Salomon Hadamard (1865–1963) 347
Erik Ivar Fredholm (1866–1927) 349
Maxime Bôcher (1867–1918) 350
Martin Wilhelm Kutta (1867–1944) 350
Felix Hausdorff (1868–1942) 351
Élie Joseph Cartan (1869–1951) 351
Alfred Marie Liénard (1869–1958) 352
Ernst Friedrich Ferdinand Zermelo (1871–1953) 352
Félix Édouard Justin Émil Borel (1871–1956) 353
Forest Ray Moulton (1872–1952) 354
Bertrand Arthur William Russell (1872–1970) 354
Constantin Carathéodory (1873–1950) 357
Leonard Eugene Dickson (1874–1954) 357
André-Louis Cholesky (1875–1918) 358
Giuseppe Vitali (1875–1932) 359
Henri Léon Lebesgue (1875–1941) 359
Issai Schur (1875–1941) 360
Ludwig Prandtl (1875–1953) 361
Waldemar Hermann Gerhard Kowalewski (1876–1950) 362
Gilbert Ames Bliss (1876–1951) 362
Edmund Georg Hermann (Yehezkel) Landau (1877–1938) 363
Godfrey Harold Hardy (1877–1947) 364
Louis Pierre Joseph Fatou (1878–1929) 366
Jan Lukasiewicz (1878–1956) 366
Maurice René Fréchet (1878–1973) 367
Albert Einstein (1879–1955) 367
Robert Daniel Carmichael (1879–1967) 371
Alfred James Lotka (1880–1949) 372
Lipót Fejér (1880–1959) 372
Leonard Bairstow (1880–1963) 373
Oskar Perron (1880–1975) 373
Luitzen Egbertus Jan Brouwer (1881–1966) 374
Amalie Emmy Noether (1882–1935) 375
Harry Bateman (1882–1946) 378
Joseph Henry Maclagan Wedderburn (1882–1948) 378
Waclaw Franciszek Sierpi?ski (1882–1969) 379
Robert Lee Moore (1882–1974) 380
Nikolai Nikolaevich Luzin (1883–1950) 381
Richard Edler von Mises (1883–1953) 382
Henry Maurice Sheffer (1883–1964) 383
George David Birkhoff (1884–1944) 383
Tobias Dantzig (1884–1956) 384
Bharati Krishna Tirthaji Maharaja (1884–1960) 385
Hermann Klaus Hugo Weyl (1885–1955) 386
Herbert Westren Turnbull (1885–1961) 387
Niels Henrik David Bohr (1885–1962) 388
Srinivasa Ramanujan (1887–1920) 389
Erwin Schrödinger (1887–1961) 392
Hugo Dyonizy Steinhaus (1887–1972) 393
George Polya (1887–1985) 393
Zygmunt Janiszewski (1888–1920) 395
Stefan Mazurkiewicz (1888–1945) 396
Chandrasekhara Venkata Raman (1888–1970) 397
Richard Courant (1888–1972) 400
Balthasar van der Pol (1889–1959) 401
Sir Ronald Aylmer Fisher (1890–1962) 401
Ivan Matveevich Vinogradov (1891–1983) 402
Stefan Banach (1892–1945) 403
Gaston Maurice Julia (1893–1978) 404
Norbert Wiener (1894–1964) 405
Satyendra Nath Bose (1894–1974) 406
Warren Weaver (1894–1978) 408
Tadeusz Wa?ewski (1896–1972) 409
Kazimierz Kuratowski (1896–1980) 409
Helmut Hasse (1898–1979) 410
Werner Karl Heisenberg (1901–1976) 411
Alfred Tarski (1902–1983) 414
Paul Adrien Maurice Dirac (1902–1984) 415
Frank Plumpton Ramsey (1903–1930) 417
John Louis von Neumann (1903–1957) 417
Andrey Nikolaevich Kolmogorov (1903–1987) 420
Alonzo Church (1903–1995) 422
Witold Hurewicz (1904–1956) 422
Alston Scott Householder (1904–1993) 423
Henri Cartan (1904–2008) 423
Lev Genrikhovich Schnirelmann (1905–1938) 424
Rózsa Péter (1905–1977) 424
Aleksander Osipovich Gelfond (1906–1968) 425
Kurt Friedrich Gödel (1906–1978) 425
Rear Admiral Grace Murray Hopper (1906–1992) 428
Olga Taussky Todd (1906–1995) 429
André Weil (1906–1998) 430
Sir Edward Maitland Wright (1906–2005) 431
Lev Davidovich Landau (1908–1968) 432
Lev Semenovich Pontryagin (1908–1988) 433
Morris Kline (1908–1992) 434
Willard Van Orman Quine (1908–2000) 435
Stephen Cole Kleene (1909–1994) 435
Subramanyan Chandrasekhar (1910–1995) 436
Alan Mathison Turing (1912–1954) 437
Prabhu Lal Bhatnagar (1912–1976) 438
Andrzej Mostowski (1913–1975) 439
Paul Erdös (1913–1996) 440
Samuel Eilenberg (1913–1998) 441
Israel Moiseevich Gelfand (1913–2009) 442
Richard Wesley Hamming (1915–1998) 443
John Wilder Tukey (1915–2000) 444
Laurent Moïse Schwartz (1915–2002) 445
Claude Elwood Shannon (1916–2001) 446
Edward Norton Lorenz (1917–2008) 446
Julia Hall Bowman Robinson (1919–1985) 447
Raymond Merrill Smullyan (Born 1919) 448
Calyampudi Radhakrishna Rao (Born 1920) 449
Olga Alexandrovna Ladyzhenskaya (1922–2004) 450
Harish Chandra Mehrotra (1923–1983) 451
John Warner Backus (1924–2007) 453
Benoit Mandelbrot (1924–2010) 453
Maurice Karnaugh (Born 1924) 454
John Torrence Tate Jr. (Born 1925) 454
Peter David Lax (Born 1926) 455
Jean-Pierre Serre (Born 1926) 455
John McCarthy (1927–2011) 456
Peter Naur (Born 1928) 457
Sir Michael Francis Atiyah (Born 1929) 457
Edsger Wybe Dijkstra (1930–2002) 458
Jacob Theodore Schwartz (1930–2009) 458
Stephen Smale (Born 1930) 459
Chen Jing-Run (1933–1996) 460
Paul Joseph Cohen (1934–2007) 461
Edayathumangalam Venkatarama Krishnamurthy (1934–2012) 461
Charles Antony Richard Hoare (Born 1934) 462
Donald Ervin Knuth (Born 1938) 462
Neil James Alexander Sloane (Born 1939) 463
Nicolas Bourbaki (Born 1939) 464
Enrico Bombieri (Born 1940) 465
Sathamangalam Ranga Iyengar Srinivasa Varadhan (Born 1940) 465
Mikhail Leonidovich Gromov (Born 1943) 466
Mitchell Jay Feigenbaum (Born 1944) 467
Leonard Max Adleman (Born 1945) 467
Ronald Linn Rivest (Born 1947) 468
Shing-Tung Yau (Born 1949) 468
Adi Shamir (Born 1952) 469
Narendra Karmarkar (Born 1957) 470
Manindra Agrawal (Born 1966) 470
Terence Chi-Shen Tao (Born 1975) 471
Bibliography 473
Name Index 481
Subject Index 498