Review: A Tour of the Calculus

A Tour of the Calculus
A Tour of the Calculus
David Berlinski
New York: Vintage Books, 1995

Review Copyright — 2002 Garret Wilson — 24 March 2002 11:00am

Rolle's slow-eyed mistress, her black hair spread over the muslin of their single pillow, has long since fallen asleep, a childish bubble forming on her full red lips; and as the moments pass in the seventeenth century and again in the twentieth, one though engenders another, the movement of thoughts expressing the inferential chain so natural as to appear unforced, as breathing itself. The curve rises and then falls. At the point where the curve changes its direction, a line tangent to the curve must be parallel to the coordinate axis... (193)


Perhaps the only explanation for this is that Davird Berlinski, as he gives A Tour of the Calculus, begins to think (or already thought) that he is Salman Rushdie.

Berlinski's story meanders, it swoops up, takes a few lofty twirls around some obscure corner of the universe of mathematical history, then plummets down to pounce upon a cogent treatise of the calculus as it scampers through the field of real numbers. In this instance, he is explaining how Michel Rolle (1652-1719) contributed to the development of the Mean Value Theorem.

The descriptions at times become torrents of exuberant proclamations, effusive odes to the very act of telling. In the end, the readers find themselves suddenly swept upon a forested island, a protected landing that gives a surprisingly good view of the rolling tide of calculus terms and concepts that before seemed dark and foreboding.

As a safe (symbols are only used when they are absolutely necessary) but surprisingly thorough introduction, or merely a sweeping review, A Tour of the Calculus somehow succeeds, leaving  readers with a grasp not only of the terms but also of the concepts and a bit of history of the calculus. Heads spinning, through, they might not be absolutely sure of how they arrived there.