Stewart (Mathematics Emeritus/Warwick Univ.; The Mathematics of Life, 2011, etc.) unravels the secret history of equations that “have been pulling the strings of society, [t]ucked away behind the scenes.”
The author shows how mathematics has played a crucial role in the “ascent of humanity,” but were merely steps in the technological advances that followed. He begins with Pythagoras' Theorem, the essence of which was discovered thousands of years before and laid the basis for navigation and astronomy. He ends with the Black-Scholes Equation, the mathematical formula that created the possibility for computerized derivatives trading and arguably the recent economic meltdown, and urges the need for more regulation of financial markets. Stewart provides clear, cogent explanations of how the equations work without burdening the reader with cumbersome derivations. Instead, he uses them to elaborate his thesis that mathematics, despite its pivotal influence, does not in itself change the world. He gives a fascinating explanation of how Newton's laws, when extended to three-body problems, are still used by NASA to calculate the best route from Earth to Mars and have laid the basis for chaos theory. Throughout, Stewart's style is felicitous and mostly accessible. While the early chapters of the book, which cover trigonometry, calculus and statistics, offer an excellent introduction, the late chapters, which cover quantum, information and chaos theory, require more scientific background to be fully understood.
A readable but not simple mathematical guidebook to the labyrinth of mathematics.