Tim's Reviews > e: the Story of a Number

e by Eli Maor
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's review
Feb 25, 2009

really liked it
Read in January, 2009

Maor's account of the place of e, the base of the natural logarithms, in the history of mathematics provides a peek inside a mathematician's brain. More connected by mathematical ideas than by chronology or the usual social, cultural, economic, or political themes taken up by historians, Maor's book opened vistas in the calculus I did not see when I first ploddingly confronted derivatives and integrals some decades ago. He thoroughly covers the differing views of Newton and Leibniz as they developed the calculus. He discusses some of the special characteristics of e revealed in the fact that the exponential function is its own derivative. He shows how e appeared in nature and the arts - musical scales, the spiral mirablis, a hanging chain, the parabolic arc of a projectile, the Gateway Arch. More than other of recent books focused on a particular number, Maor explores the mathematics of e with a mathematician's interest. But metaphysics creeps in as it seems to in discursive accounts of mathematical developments and achievements. Numbers - in particular special numbers like e - have been imbued with mystical connections to larger or hidden things. This account of e raises the questions again, "What is this language of numbers that humans have developed and how is this language linked to the world 'out there'?" In one sense, the number e, like its more famous companion pi, turns out to be not only an irrational number but also non-algebraic - not a solution (root) of a polynomial equation. Such numbers are called transcendental, meaning merely 'beyond algebraic'. In the end, Maor's story of e is an account of human activity in a world of patterns. And it is an excellent companion to a course in calculus.
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