# In Pursuit of the Unknown

## 17 Equations That Changed the World

Book - 2012Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents--from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity--within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.

An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

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#### Summary

Add a SummaryIan Stewart, an emeritus professor of mathematics at Warwick University in England, discusses equations and an inequality that he feels have had a significant impact on human history. They include equations from pure mathematics, mathematical physics, information theory, and finance. In each case, Stewart discusses how the equation was discovered, its original purpose, and how its use led to practical discoveries that were sometimes far afield from the original purpose of the equation. The equations under discussion include the Pythagorean Theorem, the definition of i, the definition of the derivative, a property of logarithms, Euler's formula for polyhedra, the normal curve, the wave equation, the heat equation, Newton's Law of Gravity, Maxwell's equations for electricity and magnetism, the Navier-Stokes equation for fluid dynamics, the Fourier transform, Einstein's equation relating mass and energy, Schrodinger's equation in quantum mechanics, an iterative equation that produces chaotic dynamics, a theorem from information theory, and the Black-Scholes equation for the value of financial derivatives. The inequality is a form of the Second Law of Thermodynamics. The intended audience is the numerate, intellectually curious lay reader, so much of the mathematics is confined to an appendix.

## Comment

Add a CommentA very clearly written, well-organized, and enjoyable book. My favourite part was the discussion of 'tubes' though the solar system in the discussion of Newton's law of gravity: I literally had no notion of it; its great to learn interesting things in unexpected places.

Ian Stewart, an emeritus professor of mathematics at the University of Warwick, discusses equations and an inequality that he feels have had a significant impact on human history. The equations are drawn from pure mathematics, mathematical physics, information theory, and finance. The inequality is a formulation of the Second Law of Thermodynamics (entropy always increases). In each case, Stewart discusses the discovery of the equation (or inequality), its original purpose, and the discoveries to which it led. Among the salient points that Stewart raises is that mathematicians begin with a simplified model of a physical problem, then modify that model to account for observed data. He also points out that the original purpose of an equation was sometimes quite different from the way it is used today and that the discoveries to which an equation led may have been inconceivable to the person who discovered the equation. Since Stewart writes for a lay audience, the mathematics is largely confined to an appendix. However, some familiarity with mathematics and physics will increase your appreciation of Stewart's lucid explanations of the importance of the equations and inequality and how their use has shaped human development.