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"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 1s just as fascinating and important as its scientific side as it, too, has changed the world. "Central to the story 1s 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 Zeno’s had two millennia earlier. These conundrums were resolved over the next century by the mathematicians who called themselves 'analysts.' The name was apt. They put calculus on the couch, and probed it, trying to root out every last trace of pathology. They succeeded for calculus, but not for infinity itself. There the pathology ran deeper. The riddles of infinity are still challenging logicians, mathematicians, and philosophers today." STEVEN STROGATZ is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He is the bestselling author of The Joy Of X, The Calculus Of Friendship, and Sync. His research has been featured in Nature, Science, Scientific American, the New York Times, the New Yorker, and broadcast on BBC Radio, National Public Radio, CBS News, among others. In 2010, he wrote a 15-part series about the elements of math for the New York Times, and a second series, Me, Myself and Math, appeared in 2012. Strogatz has spoken at TED and the Aspen Ideas Festival and has been a frequent guest on Radiolab and Science Friday. He has received numerous awards for his research, teaching, and public communication, including, most recently, the Lewis Thomas Prize for Writing about Science (2015). -0 THE POWER OF HUMAN By Adam Waytz [US — W.W. Norton; Proposal; 70,000 words; Delivery: February 2018] Adam Waytz is a rising star in the Kellogg School of Management at Northwestern University, whose research uses methods from social psychology and cognitive neuroscience to study how people think about minds. Waytz is the first person to receive twice the Theoretical Innovation Prize from the Society for Personality and Social Psychology. He is also the winner of the SAGE Young Scholar Award and the International Social Cognition Network's Early Career Award. Waytz writes: "Everyday life is increasingly human-free. Robotic technology has begun replacing human jobs and will replace millions more over the next five years. In domains such as manufacturing and agriculture, robotic employees are already a reality. Tasks like getting directions from another human or consulting with a bank teller to deposit money have become obsolete. These advances contribute to well-documented declines in social interaction. Not only has interaction with human beings diminished, but existing human interaction has Brockman, Inc. Frankfurt 2016 Hotlist -13- HOUSE_OVERSIGHT_025159