With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

    In his delightfully down-to-earth style, he explores & explains a mind-boggling future of intelligent robots, extraterrestrial life & its consquences, & other provocative, fascinating quandries of the future we want to see today.

    Readers will find an enlightening history of the vacuum: how the efforts to make a better vacuum led to the discovery of the electron; the ideas of Newton, Mach, and Einstein on the nature of space and time; the mysterious aether and how Einstein did away with it; and the latest ideas that the vacuum is filled with the Higgs field. The story ranges from the absolute zero of temperature and the seething vacuum of virtual particles and anti-particles that fills space, to the extreme heat and energy of the early universe. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    But that doesn’t mean that mathematics isn’t a crucial tool for understanding love. Love, like most things in life, is full of patterns. And mathematics is ultimately the study of patterns—from predicting the weather to the fluctuations of the stock market, the movement of planets or the growth of cities. These patterns twist and turn and warp and evolve just as the rituals of love do. In The Mathematics of Love, Dr. Hannah Fry takes the reader on a fascinating journey through the patterns that define our love lives, applying mathematical formulas to the most common yet complex questions pertaining to love: What’s the chance of finding love? What’s the probability that it will last? How do online dating algorithms work, exactly? Can game theory help us decide who to approach in a bar? At what point in your dating life should you settle down? From evaluating the best strategies for online dating to defining the nebulous concept of beauty, Dr. Fry proves—with great insight, wit, and fun—that math is a surprisingly useful tool to negotiate the complicated, often baffling, sometimes infuriating, always interesting, mysteries of love.

    Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review

    In that spirit, Edge.org publisher and author of Know This, John Brockman, asks 206 of the world’s most brilliant minds the 2017 Edge Question: What scientific term or concept ought to be more widely known?Contributors include: author of The God Delusion RICHARD DAWKINS on using animals’ “Genetic Book of the Dead” to reconstruct ecological history; MacArthur Fellow REBECCA NEWBERGER GOLDSTEIN on “scientific realism,” the idea that scientific theories explain phenomena beyond what we can see and touch; author of Seven Brief Lessons on Physics CARLO ROVELLI on “relative information,” which governs the physical world around us; theoretical physicist LAWRENCE M. KRAUSS on the hidden blessings of “uncertainty”; cognitive scientist and author of The Language Instinct STEVEN PINKER on “The Second Law of Thermodynamics”; biogerontologist AUBREY DE GREY on why “maladaptive traits” have been conserved evolutionarily; musician BRIAN ENO on “confirmation bias” in the internet age; Man Booker-winning author of Atonement IAN MCEWAN on the “Navier-Stokes Equations,” which govern everything from weather prediction to aircraft design and blood flow; plus pieces from RICHARD THALER, JARED DIAMOND, NICHOLAS CARR, JANNA LEVIN, LISA RANDALL, KEVIN KELLY, DANIEL COLEMAN, FRANK WILCZEK, RORY SUTHERLAND, NINA JABLONSKI, MARTIN REES, ALISON GOPNIK, and many, many others.

    Learn to think like the greatest creative minds of our era—to question, challenge, and create new rules for your ideas of love, education, spirituality, work, happiness, and meaning. The Code of the Extraordinary Mind is a blueprint for retraining our minds to hack everything—how we work, love, parent, and heal—and learn to succeed on our own terms. No matter where you’re starting from, you can build a life that’s truly extraordinary and make a dent in the universe. In this book, you will learn to bend reality, question the brules, transcend the culturescape, embrace your quest, practice consciousness engineering, live in blissipline, and push humanity forward. You will question your limits and realize that there are none. Your understanding of the world around you and your place in it will change, and you will find yourself operating at a new, extraordinary level in every way—with happiness, purpose, fulfillment, and love.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    An invaluable resource for any manager or professional, this book offers a collection of proven, practical methods for simplifying any problem and making faster, better decisions every time.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.

    Now, two of the world's most eminent thinkers -- University of London physicists David Bohm, a former protege of Einstein's and one of the world's most respected quantum physicists, and Stanford neurophysiologist Karl Pribram, one of the architects of our modern understanding of the brain -- believe that the universe itself may be a giant hologram, quite literally a kind of image or construct created, at least in part, by the human mind. This remarkable new way of looking at the universe explains not only many of the unsolved puzzles of physics, but also such mysterious occurrences as telepathy, out-of-body and near death experiences, "lucid" dreams, and even religious and mystical experiences such as feelings of cosmic unity and miraculous healings.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.