# In Pursuit of the Unknown

## 17 Equations That Changed the World

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## Opinion

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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.