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| Introduction | |
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| For the reader's comfort | |
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| The beginning of modern mathematics | |
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| Are mathematicians human? Witless parodies | |
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| Illimitable scope of mathematical evolution | |
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| Pioneers and scouts | |
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| A clue through the maze | |
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| Continuity and discreteness | |
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| Remarkable rarity of common sense | |
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| Vivid mathematics or vague mysticism? Four great ages of mathematics | |
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| Our own the Golden Age | |
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| Modern Minds in Ancient Bodies | |
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| Zeno (fifth century B.C.), Eudoxus (408-355 B.C.), Archimedes (287?-212 B.C.) | |
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| Modern ancients and ancient moderns | |
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| Pythagoras, great mystic, greater mathematician | |
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| Proof or intuition? The taproot of modern analysis | |
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| A bumpkin upsets the philosophers | |
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| Zeno's unresolved riddles | |
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| Plato's needy young friend | |
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| Inexhaustible exhaustion | |
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| The useful conics | |
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| Archimedes, aristocrat, greatest scientist of antiquity | |
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| Legends of his life and personality | |
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| His discoveries and claim to modernity | |
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| A sturdy Roman | |
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| Defeat of Archimedes and triumph of Rome | |
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| Gentleman, Soldier, and Mathematician | |
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| Descartes (1596-1650)The good old days | |
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| A child philosopher but no prig | |
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| Inestimable advantages of lying in bed | |
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| Invigorating doubts | |
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| Peace in war | |
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| Converted by a nightmare | |
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| Revelation of analytic geometry | |
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| More butchering | |
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| Circuses, professional jealousy, swashbuckling, accommodating lady friends | |
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| Distaste for hell-fire and respect for the Church | |
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| Saved by a brace of cardinals | |
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| A Pope brains himself | |
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| Twenty years a recluse | |
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| The Method | |
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| Betrayed by fame | |
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| Doting Elisabeth | |
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| What Descartes really thought of her | |
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| Conceited Christine | |
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| What she did to Descartes | |
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| Creative simplicity of Ms geometry | |
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| The Prince of Amateurs | |
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| Fermat (1601-1665)Greatest mathematician of the seventeenth century | |
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| Fermat's busy, practical life | |
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| Mathematics his hobby | |
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| His flick to the calculus | |
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| His profound physical principle | |
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| Analytic geometry again | |
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| Arithmetica and logistica | |
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| Fermat's supremacy in arithmetic | |
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| An unsolved problem on primes | |
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| Why are some theorems "important"? An intelligence test | |
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| "Infinite descent." Fermat's unanswered challenge to posterity | |
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| "Greatness and Misery of Man | |
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| "Pascal (1625-1662)An infant prodigy buries his talent | |
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| At seventeen a great geometer | |
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| Pascal's wonderful theorem | |
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| Vile health and religious inebriety | |
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| The first calculating Frankenstein | |
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| Pascal's brilliance in physics | |
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| Holy sister Jacqueline, soul-saver | |
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| Wine and women? "Get thee to a nunnery.!" Converted on a spree | |
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| Literature prostituted to bigotry | |
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| The Helen of Geometry | |
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| A celestial toothache | |
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| What the post-mortem revealed | |
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| A gambler makes mathematical history | |
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| Scope of the theory of probability | |
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| Pascal creates the theory with Fermat | |
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| Folly of betting against God or the Devil | |
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| On the Seashore | |
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| Newton (1642-1727)Newton's estimate of himself | |
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| An uncertified youthful genius | |
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| Chaos of his times | |
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| On the shoulders of giants | |
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| His one attachment | |
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| Cambridge days | |
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| Young Newton masters futility of suffering fools gladly | |
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| The Great Plague a greater blessing | |
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| Immortal at twenty four (or less) | |
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| The calculus | |
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| Newton unsurpassed in pure mathematics, supreme in natural philosophy | |
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| Gnats, hornets, and exasperation | |
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| The Principia | |
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| Samuel Pepys and other fussers | |
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| The flattest anticlimax in history | |
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| Controversy, theology, chronology, alchemy, public office, death | |
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| Master of All Trades | |
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| Leibniz (1646-1716) | |
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| Two superb contributions | |
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| A politician's offspring | |
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| Genius at fifteen | |
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| Seduced by the law | |
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| The "universal characteristic." Symbolic reasoning | |
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| Sold out to ambition | |
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| A master diplomat | |
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| Diplomacy being what it is, the diplomatic exploits of the master are left to the historians | |
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| Fox into historian, statesman into mathematician | |
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| Applied ethics | |
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| Existence of God | |
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| Optimism | |
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| Forty years of futility | |
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| Discarded like a dirty rag | |
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| Nature or Nurture? | |
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| The Bernoullis (seventeenth-and eighteenth centuries) | |
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| Eight mathematicians in three generations | |
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| Clinical evidence for her | |