Unknown quantity : a real and imaginary history of algebra
/ John Derbyshire
- Washington, D.C. : Joseph Henry Press , c2006.
- viii, 374 p., [8] p. of plates : ill., ports. ; 24 cm.
Includes bibliographical references and index.
Math Primer: Numbers and Polynomials -- The Unknown Quantity -- Four Thousand Years Ago -- The Father of Algebra -- Completion and Reduction -- Math Primer: Cubic and Quartic Equations -- Commerce and Competition -- Relief for the Imagination -- Universal Arithmetic -- The Lions Claw -- Math Primer: Roots of Unity -- The Assault on the Quintic -- Math Primer: Vector Spaces and Algebras -- The Leap into the Fourth Dimension -- An Oblong Arrangement of Terms -- Victoria's Brumous Isles -- Levels of Abstraction Math Primer: Field Theory -- Pistols at Dawn -- Lady of the Rings -- Math Primer: Algebraic Geometry -- Geometry Makes a Comeback -- Algebraic This, Algebraic That -- From Universal Arithmetic to Universal Algebra.
Algebra emerged early in recorded history, stepping aside from the declarative to create the interrogative, a process that has led to fascination and even obsession. Derbyshire, a mathematician and linguist by education and systems analyst by profession, starts with the algebra of about 4,000 years ago and works up to Diophantus, whose place as the father of algebra may be disputed but whose contributions nevertheless are universally admired, then through Hypatia, Cardano, Descartes, Newton, von Leibniz, Lagrange, Cauchy, Abel, Galois, Riemann, Lie, Poincaré, Hilbert, NoetherLefschetz, Zariski, MacLane and Grothendieck, along with a host of other luminaries, giving readers accessible descriptions of their discoveries and even providing non-specialists with extra help on basics such as vector spaces, field theory and algebraic geometry. The result is concise, readable, and enjoyable.