Unknown Quantity: A Real and Imaginary History of Algebra

Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages -- and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics -- it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

• Front Matter
• Introduction
• Part 1 The Unknown Quantity -1 Four Thousand Years Ago
• 2 The Father of Algebra
• 3 Completion and Reduction
• Math Primer: Cubic and Quartic Equations
• 4 Commerce and Competition
• 5 Relief for the Imagination
• Part 2 Universal Arithmetic - 6 The Lion\'s Claw
• Math Primer: Roots of Unity
• 7 The Assault on the Quintic
• Math Primer: Vector Spaces and Algebras
• 8 The Leap into the Fourth Dimension
• 9 An Oblong Arrangement of Terms
• 10 Victoria\'s Brumous Isles
• Part 3 Levels of Abstraction - Math Primer: Field Theory
• 11 Pistols at Dawn
• 12 Lady of the Rings
• Math Primer: Algebraic Geometry
• 13 Geometry Makes a Comeback
• 14 Algebraic This, Algebraic That
• 15 From Universal Arithmetic to Universal Algebra
• Endnotes
• Picture Credits
• Index
• Photos, Illustrations, and Drawings