HOUSE OVERSIGHT 025159 "Calculus is one of the greatest ideas that anyone has ever had and certainly the greatest idea in all of mathematics. The scientific and technological importance of calculus is one reason why we require all budding scientists and engineers to learn the subject. Taming Infinity is the human side of calculus: the gripping story of how it was discovered, and lost, and then rediscovered a thousand years later, or how it perplexed many of the geniuses who struggled to invent it, and in a few tragic cases, drove them insane. In a very real sense, this humanistic side of calculus is just as fascinating and important as its scientific side as it, too, has changed the world. "Central to the story is the mathematicians' quest to tame infinity, which begins with the philosopher Zeno of Elea (about 450 BC, before Socrates) who raised paradoxes about infinity, continuity, time, space, and motion that confounded his contemporaries and provoked no less than Aristotle to banish infinity from Greek philosophy and mathematics from then on. Fast-forward more than 2,500 years, and we're still wrestling with infinity and the paradoxes it raises. In between, the inventors of calculus, starting with Archimedes around 250 BC and culminating with Newton and Leibniz in the mid-1600s, tried to domesticate infinity to make what we now regard as integral and differential calculus. And to a large extent, they succeeded. The carefully controlled use of infinity is the secret to calculus, the source of its enormous predictive power. "But like Frankenstein's monster or the golem in Jewish folklore, infinity was never quite under control. As in any tale of hubris, the monster inevitably turned on its creator. Soon after the work of Newton and Leibniz, disturbing paradoxes emerged in the 1700s and early 1800s. Calculations came out wrong. Calculus seemed unreliable. These difficulties provoked another wave of philosophical and logical handwringing, much as Z