INFINITESIMAL

In the mid-17th century, debate raged over a mathematical concept of the infinitely small—and nothing less than modernity as we know it was at stake.

At its core, the public argument over the infinitesimal—the idea that a line is composed of an endless number of immeasurably small component parts—is rooted in the ideological scope of post-Reformation Europe. The church, struggling to maintain autonomy over an increasingly disparate populace, fought to bar the infinitesimal from mathematical doctrine due to its implication that nature itself is not orderly, logical and completely subject to deductive reasoning. At the same time, leading intellectuals like Thomas Hobbes and John Wallis insisted that embracing the idea of the infinite in mathematics would open up a remarkable new opportunity to experimentally explore the world around us. Alexander (History/UCLA; Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, 2010, etc.) tells this story of intellectual strife with the high drama and thrilling tension it deserves, weaving a history of mathematics through the social and religious upheavals that marked much of the era. For the people of Europe, more than just academic success was on the line: The struggle for civil liberties and rebellion against the rigid doctrines of the establishment were entrenched in the conceptual war over the infinitesimal. The fact that progressive mathematics prevailed was unquestionably momentous, as the addition of the concept of the infinitesimal eventually led to calculus, physics and many of the technological advances that are the bedrock of modern science and society. The author navigates even the most abstract mathematical concepts as deftly as he does the layered social history, and the result is a book about math that is actually fun to read.

A fast-paced history of the singular idea that shaped a multitude of modern achievements.