From Impractical to Irreplaceable

From Impractical to Irreplaceable

By Bruce D. Rhodewalt

The book covers a generous range of mathematics, including information theory, chaos theory, economics, quantum mechanics, and relativity. Although the average Instagram addict may have a vague feeling that math is somehow involved in digital photography, the curious reader will appreciate Stewart’s chapter on the Fourier transform, effortlessly evolving into a clear lesson on data compression, a technology that makes digital photography practical. A technically inclined adolescent might be prodded in any number of life-changing directions by reading this.

Review of In Pursuit of the Unknown: 17 Equations That Changed the World  by Ian Stewart (Basic Books, 2012)

Excerpts

In Pursuit of the Unknown repeatedly tells one story, which occurs over and over again in different centuries and in different branches of mathematics. This is the story of an abstract, seemingly pointless (from a practical point of view) mathematical discovery becoming necessary many years later in some technological leap forward. An early example is i (the square root of -1), discovered in the sixteenth century and derided for many years by laymen and mathematicians themselves, only to emerge as a necessary ingredient in quantum mechanics, itself fundamental to understanding interactions on the smallest scale. Without it we might not have lasers, transistors, diodes, and the machines that depend on these. Indeed a discovery, if not quite an equation, that changed the world.

Extraordinary Mathematics Step by Step

Each chapter begins with an equation, labeled in detail, and three questions—What does it tell us? Why is that important? What did it lead to?—along with their respective answers. Each equation serves as an introduction to a branch or topic of mathematics or science. Chapter 6, called “Much ado about knotting (Euler’s Formula for Polyhedra),” leads to an entire chapter on topology, including knots. Chapter 8—“Good vibrations (Wave Equation)”—discusses waves and leads in some predictable directions, such as the physics of music, and in some surprising directions, such as waves in the Earth (whose study makes possible the geology that allows oil drilling and hence the internal-combustion engine).

For pdf of the review: From Impractical to Irreplaceable