| 0.09 | | Preface |
| 0.11 | | Introduction |
| 3 | Chapter One: | Leibniz's Dream |
| | | Leibniz's Wonderful Idea |
| | | Paris |
| | | Hanover |
| | | The Universal Characteristic |
| 21 | Chapter Two: | Boole Turns Logic into Algebra |
| | | George Boolle's Hard Life |
| | | George Boole's Algebra of Logic |
| | | Boole and Leibniz's Dream |
| 41 | Chapter Three: | Frege: From Breakthrough to Despair |
| | | Frege's Begriffsschrift |
| | | Frege Invents Formal Syntax |
| | | Why Bertrand Russell's Letter Was So Devastating |
| | | Frege and the Philosophy of Language |
| | | Frege and Leibniz's Dream |
| 59 | Chapter Four: | Cantor: Detour through Infinity |
| | | Engineer or Mathematician |
| | | Infinite Sets Come in Different Sizes |
| | | Cantor's Quest for Infinite Numbers |
| | | The Diagonal Method |
| | | Depression and Tragedy |
| | | A Decisive Battle? |
| 83 | Chapter Five: | Hilbert to the Rescue |
| | | Hilbert's Early Triumphs |
| | | Toward a New Century |
| | | Kronecker's Ghost |
| | | Metamathematics |
| | | Catastrophe |
| 107 | Chapter Six: | Gödel Upsets the Applecart |
| | | The Return of Kronecker's Ghost |
| | | Undecidable Propositions |
| | | Kurt Gödel, Computer Programmer |
| | | The Conference aat Königsberg |
| | | Love and Hate |
| | | Hilbert's Dictum |
| | | A Strange Man and a Sad End |
| 139 | Chapter Seven: | Turing Conceives of thee All-Purpose Computer |
| | | A Child of the Empire |
| | | Hilbert's Entscheidungsproblem |
| | | Turing's Analysis of the Computation Process |
| | | Turing Machines in Action |
| | | Turing Applies Cantor's Diagonal Method |
| | | Unsolvable Problems |
| | | Turing's Universal Machine |
| | | Alan Turing in Princeton |
| | | Alan Turing's War |
| 177 | Chapter Eight: | Making the First Universal Computers |
| | | Who Invented the Computer? |
| | | Joseph-Marie Jacquard (1752-1834) |
| | | Charles Babbage (1791-1871) |
| | | Ada Lovelace (1815-1852) |
| | | Claude Shannon (1916-[2001 - ndc]) |
| | | Howard Aiken (1900-1973) |
| | | John Atanasoff (1903-1995) |
| | | John Mauchly (1907-1980) |
| | | J. Presper Eckert Jr. (1919-1995) |
| | | Herman Goldstine (1913-[2004 - ndc]) |
| | | Earl R. Larson (1911-[2001-ndc]) |
| | | John Von Neumann and the More School |
| | | Alan Turing's Ace |
| | | Eckert, Von Neumann, and Turing |
| | | A Grateful Nation Rewards Its Hero |
| 199 | Chapter Nine: | Beyond Leibniz's Dream |
| | | Computers, Brains, and Minds |
| 209 | | Epilogue |
| 211 | | Notes |
| 239 | | References |
| 249 | | Index |
| 257 | | _ |
