Introduction 10
c. 150 Million B.C. Ant Odometer 18
c. 30 Million B.C. Primates Count 20
c. 1 Million B.C. Cicada-Generated Prime Numbers 22
c. 100,000 B.C. Knots 24
c. 18,000 B.C. Ishango Bone 26
c. 3000 B.C. Quipu 28
c. 3000 B.C.Dice 30
c. 2200 B.C. Magic Squares 32
c. 1800 B.C. Plimpton 322 34
c. 1650 B.C. Rhind Papyrus 36
c. 1300 B.C. Tic Tac Toe 38
c. 600 B.C. Pythagorean Theorem and Triangles 40
548 B.C. Go 42
c. 530 B.C. Pythagoras Founds Mathematical Brotherhood 44
c. 445 B.C. Zeno's Paradoxes 46
c. 440B.C. Quadrature of the Lune 48
c. 350 B.C. Platonic Solids 50
c. 350 B.C. Aristotle's Organon 52
c. 320 B.C. Aristotle's Wheel Paradox 54
300 B.C. Euclid's Elements 56
c. 250 B.C. Archimedes: Sand, Cattle & Stomachion 58
c. 250 B.C. π 60
c. 240 B.C. Sieve of Eratosthenes 62
c. 240 B.C. Archimedean Semi-Regular Polyhedra 64
225 B.C. Archimedes' Spiral 66
c. 180 B.C. Cissoid of Diocles 68
c. 150 B.C. Ptolemy's Almagest 70
250 Diophantus's Arithmetica 72
c. 340 B.C. Pappus's Hexagon Theorem 74
c. 350 B.C. Bakhshali Manuscript 76
415 The Death of Hypatia 78
c.650 Zero 80
c. 800 Alcuin's Propositiones ad Acuendos Juvenes 82
830 Al-Khwarizmi's Algebra 84
834 Borromean Rings 86
850 Ganita Sara Samgraha 88
c. 850 Thabit Formula for Amicable Numbers 90
c. 953 Chapters in Indian Mathematics 92
1070 Omar Khayyam's Treatise 94
c. 1150 Al-Samawal's The Dazzling 96
c. 1200 Abacus 98
1202 Fibonacci's Liber Abaci 100
1256 Wheat on a Chessboard 102
c. 1350 Harmonic Series Diverges 104
c. 1427 Law of Cosines 106
1478 Treviso Arithmetic 108
c. 1500 Discovery of Series Formula for π 110
1509 Golden Ratio 112
1518 Polygraphiae Libri Sex 114
1537 Loxodrome 116
1545 Cardano's Ars Magna 118
1556 Sumario Compendioso 120
1569 Mercator Projection 122
1572 Imaginary Numbers 124
1611 Kepler Conjecture 126
1614 Logarithms 128
1621 Slide Rule 130
1636 Fermat's Spiral 132
1637 Fermat's Last Theorem 134
1637 Descartes' La Geometrie 136
1637 Cardioid 138
1638 Logarithmic Spiral 140
1639 Projective Geometry 142
1641 Torricelli's Trumpet 144
1654 Pascal's Triangle 146
1657 The Length of Neile's Semicubical Parabola 148
1659 Viviani's Theorem 150
c. 1665 Discovery of Calculus 152
1669 Newton's Method 154
1673 Tautochrone Problem 156
1674 Astroid 158
1696 L'Hopital's Analysis of the Infinitely Small 160
1702 Rope around the Earth Puzzle 162
1713 Law of Large Numbers 164
1727 Euler's Number, e 166
1730 Stirling's Formula 168
1733 Normal Distribution Curve 170
1735 Euler-Mascheroni Constant 172
1736 Konigsberg Bridges 174
1738 St. Petersburg Paradox 176
1742 Goldbach Conjecture 178
1748 Agnesi's Instituzioni Analitiche 180
1751 Euler's Formula for Polyhedra 182
1751 Euler's Polygon Division Problem 184
1759 Knight's Tours 186
1761 Bayes' Theorem 188
1769 Franklin Magic Square 190
1774 Minimal Surface 192
1777 Buffon's Needle 194
1779 Thirty-Six Officers Problem 196
c. 1789 Sangaku Geometry 198
1795 Least Squares 200
1796 Constructing a Regular Heptadecagon 202
1797 Fundamental Theorem of Algebra 204
1801 Gauss's Disquisitiones Arithmeticae 206
1801 Three-Armed Protractor 208
1807 Fourier Series 210
1812 Laplace's Theorie Analytique des Probabilites 212
1816 Prince Rupert's Problem 214
1817 Bessel Functions 216
1822 Babbage Mechanical Computer 218
1823 Cauchy's Le Calcul Infinitesimal 220
1827 Barycentric Calculus 222
1829 Non-Euclidean Geometry 224
1831 Mobius Function 226
1832 Group Theory 228
1834 Pigeonhole Principle 230
1843 Quaternions 232
1844 Transcendental Numbers 234
1844 Catalan Conjecture 236
1850 The Matrices of Sylvester 238
1852 Four-Color Theorem 240
1854 Boolean Algebra 242
1857 Icosian Game 244
1857 Harmonograph 246
1858 The Möbius Strip 248
1858 Holditch's Theorem 250
1859 Riemann Hypothesis 252
1868 Beltrami's Pseudosphere 254
1872 Weierstrass Function 256
1872 Gros's Theorie du Baguenodier 258
1874 The Doctorate of Kovalevskaya 260
1874 Fifteen Puzzle 262
1874 Cantor's Transfinite Numbers 264
1875 Reuleaux Triangle 266
1876 Harmonic Analyzer 268
1879 Ritty Model I Cash Register 270
1880 Venn Diagrams 272
1881 Benford's Law 274
1882 Klein Bottle 276
1883 Tower of Hanoi 278
1884 Flatland 280
1888 Tesseract 282
1889 Peano Axioms 284
1890 Peano Curve 286
1891 Wallpaper Groups 288
1893 Sylvester's Line Problem 290
1896 Proof of the Prime Number Theorem 292
1899 Pick's Theorem 294
1899 Morley's Trisector Theorem 296
1900 Hilbert's 23 Problems 298
1900 Chi-Square 300
1901 Boy's Surface 302
1901 Barber Paradox 304
1901 Jung's Theorem 306
1904 Poincare Conjecture 308
1904 Koch Snowflake 310
1904 Zermelo's Axiom of Choice 312
1905 Jordan Curve Theorem 314
1906 Thue-Morse Sequence 316
1909 Brouwer Fixed-Point Theorem 318
1909 Normal Number 320
1909 Boole's Philosophy and Fun of Algebra 322
1910-1913 Principia Mathematica 324
1912 Hairy Ball Theorem 326
1913 Infinite Monkey Theorem 328
1916 Bieberbach Conjecture 330
1916 Johnson's Theorem 332
1918 Hausdorff Dimension 334
1919 Brun's Constant 336
c. 1920 Googol 338
1920 Antoine's Necklace 340
1921 Noether's Idealtheorie 342
1921 Lost in Hyperspace 344
1922 Geodesic Dome 346
1924 Alexander's Horned Sphere 348
1924 Banach-Tarski Paradox 350
1925 Squaring a Rectangle 352
1925 Hilbert's Grand Hotel 354
1926 Menger Sponge 356
1927 Differential Analyzer 358
1928 Ramsey Theory 360
1931 Godel's Theorem 362
1933 Champernowne's Number 364
1935 Bourbaki: Secret Society 366
1936 Fields Medal 368
1936 Turing Machines 370
1936 Voderberg Tilings 372
1937 Collatz Conjecture 374
1938 Ford Circles 376
1938 The Rise of Randomizing Machines 378
1939 Birthday Paradox 380
c. 1940 Polygon Circumscribing 382
1942 Hex 384
1945 Pig Game Strategy 386
1946 ENIAC 388
1946 Von Neumann's Middle-Square Randomizer 390
1947 Gray Code 392
1948 Information Theory 394
1948 Curta Calculator 396
1949 Csaszar Polyhedron 398
1950 Nash Equilibrium 400
c. 1950 Coastline Paradox 402
1950 Prisoner's Dilemma 404
1952 Cellular Automata 406
1957 Martin Gardner's Mathematical Recreations 408
1958 Gilbreath's Conjecture 410
1958 Turning a Sphere Inside Out 412
1958 Platonic Billiards 414
1959 Outer Billiards 416
1960 Newcomb's Paradox 418
1960 Sierpinski Numbers 420
1963 Chaos and the Butterfly Effect 422
1963 Ulam Spiral 424
1963 Continuum Hypothesis Undecidability 426
c. 1965 Superegg 428
1965 Fuzzy Logic 430
1966 Instant Insanity 432
1967 Langlands Program 434
1967 Sprouts 436
1968 Catastrophe Theory 438
1969 Tokarsky's Unilluminable Room 440
1970 Donald Knuth and Mastermind 442
1971 Erdos and Extreme Collaboration 444
1972 HP-35: First Scientific Pocket Calculator 446
1973 Penrose Tiles 448
1973 Art Gallery Theorem 450
1974 Rubik's Cube 452
1974 Chaitin's Omega 454
1974 Surreal Numbers 456
1974 Perko Knots 458
1975 Fractals 460
1975 Feigenbaum Constant 462
1977 Public-Key Cryptography 464
1977 Szilassi Polyhedron 466
1979 Ikeda Attractor 468
1979 Spidrons 470
1980 Mandelbrot Set 472
1981 Monster Group 474
1982 Ball Triangle Picking 476
1984 Jones Polynomial 478
1985 Weeks Manifold 480
1985 Andrica's Conjecture 482
1985 The ABC Conjecture 484
1986 Audioactive Sequence 486
1988 Mathematica 488
1988 Murphy's Law and Knots 490
1989 Butterfly Curve 492
1996 The On-Line Encyclopedia of Integer Sequences 494
1999 Eternity Puzzle 496
1999 Perfect Magic Tesseract 498
1999 Parrondo's Paradox 500
1999 Solving of the Holyhedron 502
2001 Bed Sheet Problem 504
2002 Solving the Game of Awari 506
2002 Tetris Is NP-Complete 508
2005 NUMB3RS 510
2007 Checkers Is Solved 512
2007 The Quest for Lie Group E8 514
2007 Mathematical Universe Hypothesis 516
Notes and Further Reading 518
Index 526
Photo Credits 528