presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.

    And by improving the quality of your thinking, you can improve the quality of your life. It will make you more aware of what you think and why—and how you can change what you think.

    In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself. In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms.

    Digital technologies—with hardware, software, and networks at their core—will in the near future diagnose diseases more accurately than doctors can, apply enormous data sets to transform retailing, and accomplish many tasks once considered uniquely human.In The Second Machine Age MIT’s Erik Brynjolfsson and Andrew McAfee—two thinkers at the forefront of their field—reveal the forces driving the reinvention of our lives and our economy. As the full impact of digital technologies is felt, we will realize immense bounty in the form of dazzling personal technology, advanced infrastructure, and near-boundless access to the cultural items that enrich our lives.Amid this bounty will also be wrenching change. Professions of all kinds—from lawyers to truck drivers—will be forever upended. Companies will be forced to transform or die. Recent economic indicators reflect this shift: fewer people are working, and wages are falling even as productivity and profits soar.Drawing on years of research and up-to-the-minute trends, Brynjolfsson and McAfee identify the best strategies for survival and offer a new path to prosperity. These include revamping education so that it prepares people for the next economy instead of the last one, designing new collaborations that pair brute processing power with human ingenuity, and embracing policies that make sense in a radically transformed landscape.A fundamentally optimistic book, The Second Machine Age alters how we think about issues of technological, societal, and economic progress.

    Continuously in print since 1932, Ortega's vision of Western culture as sinking to its lowest common denominator and drifting toward chaos brought its author international fame and has remained one of the influential books of the 20th century.

    But Plato’s role in shaping philosophy was pivotal. On her way to considering the place of philosophy in our ongoing intellectual life, Goldstein tells a new story of its origin, re-envisioning the extraordinary culture that produced the man who produced philosophy. But it is primarily the fate of philosophy that concerns her. Is the discipline no more than a way of biding our time until the scientists arrive on the scene? Have they already arrived? Does philosophy itself ever make progress? And if it does, why is so ancient a figure as Plato of any continuing relevance? Plato at the Googleplex is Goldstein’s startling investigation of these conundra. She interweaves her narrative with Plato’s own choice for bringing ideas to life—the dialogue. Imagine that Plato came to life in the twenty-first century and embarked on a multicity speaking tour. How would he handle the host of a cable news program who denies there can be morality without religion?  How would he mediate a debate between a Freudian psychoanalyst and a tiger mom on how to raise the perfect child? How would he answer a neuroscientist who, about to scan Plato’s brain, argues that science has definitively answered the questions of free will and moral agency? What would Plato make of Google, and of the idea that knowledge can be crowd-sourced rather than reasoned out by experts? With a philosopher’s depth and a novelist’s imagination and wit, Goldstein probes the deepest issues confronting us by allowing us to eavesdrop on Plato as he takes on the modern world.(With black-and-white photographs throughout.)

    The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order. Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.

    Thing 4: The washing machine has changed the world more than the Internet. Thing 5: Assume the worst about people, and you get the worst. Thing 13: Making rich people richer doesn't make the rest of us richer.If you've wondered how we did not see the economic collapse coming, Ha-Joon Chang knows the answer: We didn't ask what they didn't tell us about capitalism. This is a lighthearted book with a serious purpose: to question the assumptions behind the dogma and sheer hype that the dominant school of neoliberal economists-the apostles of the freemarket-have spun since the Age of Reagan.Chang, the author of the international bestseller Bad Samaritans, is one of the world's most respected economists, a voice of sanity-and wit-in the tradition of John Kenneth Galbraith and Joseph Stiglitz. 23 Things They Don't Tell You About Capitalism equips readers with an understanding of how global capitalism works-and doesn't. In his final chapter, "How to Rebuild the World," Chang offers a vision of how we can shape capitalism to humane ends, instead of becoming slaves of the market.Ha-Joon Chang teaches in the Faculty of Economics at the University of Cambridge. His books include the bestselling Bad Samaritans: The Myth of Free Trade and the Secret History of Capitalism. His Kicking Away the Ladder received the 2003 Myrdal Prize, and, in 2005, Chang was awarded the Leontief Prize for Advancing the Frontiers of Economic Thought.

    In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

    How To is a guide to the third kind of approach. It's full of highly impractical advice for everything from landing a plane to digging a hole.Bestselling author and cartoonist Randall Munroe explains how to predict the weather by analyzing the pixels of your Facebook photos. He teaches you how to tell if you're a baby boomer or a 90's kid by measuring the radioactivity of your teeth. He offers tips for taking a selfie with a telescope, crossing a river by boiling it, and powering your house by destroying the fabric of space-time. And if you want to get rid of the book once you're done with it, he walks you through your options for proper disposal, including dissolving it in the ocean, converting it to a vapor, using tectonic plates to subduct it into the Earth's mantle, or launching it into the Sun.By exploring the most complicated ways to do simple tasks, Munroe doesn't just make things difficult for himself and his readers. As he did so brilliantly in What If?, Munroe invites us to explore the most absurd reaches of the possible. Full of clever infographics and amusing illustrations, How To is a delightfully mind-bending way to better understand the science and technology underlying the things we do every day.

    In his most important work, The General Theory of Employment, Interest, and Money (1936), Keynes critiqued the laissez-faire policies of his day, particularly the proposition that a normally functioning market economy would bring full employment. Keynes's forward-looking work transformed economics from merely a descriptive and analytic discipline into one that is policy oriented. For Keynes, enlightened government intervention in a nation's economic life was essential to curbing what he saw as the inherent inequalities and instabilities of unregulated capitalism.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    Whether you're a beginner, and avid student, or an armchair expert, you'll find plenty to stimulate you within this book.--book jacket

    None of these factors is either definitive or destiny. Otherwise, how to explain why Botswana has become one of the fastest growing countries in the world, while other African nations, such as Zimbabwe, the Congo, and Sierra Leone, are mired in poverty and violence? Daron Acemoglu and James Robinson conclusively show that it is man-made political and economic institutions that underlie economic success (or lack of it). Korea, to take just one of their fascinating examples, is a remarkably homogeneous nation, yet the people of North Korea are among the poorest on earth while their brothers and sisters in South Korea are among the richest. The south forged a society that created incentives, rewarded innovation, and allowed everyone to participate in economic opportunities. The economic success thus spurred was sustained because the government became accountable and responsive to citizens and the great mass of people. Sadly, the people of the north have endured decades of famine, political repression, and very different economic institutions—with no end in sight. The differences between the Koreas is due to the politics that created these completely different institutional trajectories. Based on fifteen years of original research Acemoglu and Robinson marshall extraordinary historical evidence from the Roman Empire, the Mayan city-states, medieval Venice, the Soviet Union, Latin America, England, Europe, the United States, and Africa to build a new theory of political economy with great relevance for the big questions of today, including:    - China has built an authoritarian growth machine. Will it continue to grow at such high speed and overwhelm the West?    - Are America’s best days behind it? Are we moving from a virtuous circle in which efforts by elites to aggrandize power are resisted to a vicious one that enriches and empowers a small minority?    - What is the most effective way to help move billions of people from the rut of poverty to prosperity? More philanthropy from the wealthy nations of the West? Or learning the hard-won lessons of Acemoglu and Robinson’s breakthrough ideas on the interplay between inclusive political and economic institutions? Why Nations Fail will change the way you look at—and understand—the world.