Unknown Quantity: A Real and Imaginary History of Algebra

For curious nonmathematicians and armchair algebra buffs, John Derbyshire discovers the story behind the formulae, roots, and radicals. As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from "this plus this equals this" to "this plus what equals this?" gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging journey through the development of abstract mathematical thought.

American Scientist

A reader who wants to learn some theory of equations and modern algebra in a relatively painless way will find this book attractive. The explanations of many algebraic topics are accessible and clear, especially those of the following: how Vieta's new general symbolic notation demonstrates the relations between roots and coefficients of polynomials; symmetric polynomials and solvability; the roots of unity; how Paolo Ruffini's proof of the unsolvability of the quintic worked; how studying permutations of roots of polynomial equations gave rise to group theory; how linear transformations and matrices are related; the nature of quaternions and octonions; what an invariant is; an introduction to algebraic geometry; what a vector space is; and what the differences are between groups, division rings and fields. Those explanations also make clear why mathematicians cared about these problems and how these concepts were used. The anecdotes...certainly make the book fun to read. -- Judith V. Grabiner

John Derbyshire is a mathematician and linguist by education, a systems analyist by profession, and the celebrated author of Prime Obsession, a mathematical biography of Bernhard Riemann, and the highly acclaimed novel Seeing Calvin Coolidge in a Dream. His work appears frequently in National Review and The New Criterion.