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.

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    It has been inspired by the scientific ferment that swept through Britain at the end of the 18th century, and which Holmes now radically redefines as 'the revolution of Romantic Science'.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    The planet most like ours, it has still been thought impossible to reach, let alone explore and inhabit.Now with the advent of a revolutionary new plan, all this has changed. leading space exploration authority Robert Zubrin has crafted a daring new blueprint, Mars Direct, presented here with illustrations, photographs, and engaging anecdotes.The Case for Mars is not a vision for the far future or one that will cost us impossible billions. It explains step-by-step how we can use present-day technology to send humans to Mars within ten years; actually produce fuel and oxygen on the planet's surface with Martian natural resources; how we can build bases and settlements; and how we can one day "terraform" Mars--a process that can alter the atmosphere of planets and pave the way for sustainable life.

    Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide.With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity—his eccentricities, his brilliance, his fatal candor—and elegantly explains his work and its implications.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    This staggering amount of information—unprecedented in history—can tell us a great deal about who we are—the fears, desires, and behaviors that drive us, and the conscious and unconscious decisions we make. From the profound to the mundane, we can gain astonishing knowledge about the human psyche that less than twenty years ago, seemed unfathomable.Everybody Lies offers fascinating, surprising, and sometimes laugh-out-loud insights into everything from economics to ethics to sports to race to sex, gender and more, all drawn from the world of big data. What percentage of white voters didn’t vote for Barack Obama because he’s black? Does where you go to school effect how successful you are in life? Do parents secretly favor boy children over girls? Do violent films affect the crime rate? Can you beat the stock market? How regularly do we lie about our sex lives and who’s more self-conscious about sex, men or women?Investigating these questions and a host of others, Seth Stephens-Davidowitz offers revelations that can help us understand ourselves and our lives better. Drawing on studies and experiments on how we really live and think, he demonstrates in fascinating and often funny ways the extent to which all the world is indeed a lab. With conclusions ranging from strange-but-true to thought-provoking to disturbing, he explores the power of this digital truth serum and its deeper potential—revealing biases deeply embedded within us, information we can use to change our culture, and the questions we’re afraid to ask that might be essential to our health—both emotional and physical. All of us are touched by big data everyday, and its influence is multiplying. Everybody Lies challenges us to think differently about how we see it and the world.

    In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    So wrong that a chimpanzee choosing answers at random will consistently outguess teachers, journalists, Nobel laureates, and investment bankers.In Factfulness, Professor of International Health and global TED phenomenon Hans Rosling, together with his two long-time collaborators, Anna and Ola, offers a radical new explanation of why this happens. They reveal the ten instincts that distort our perspective—from our tendency to divide the world into two camps (usually some version of us and them) to the way we consume media (where fear rules) to how we perceive progress (believing that most things are getting worse).Our problem is that we don’t know what we don’t know, and even our guesses are informed by unconscious and predictable biases.It turns out that the world, for all its imperfections, is in a much better state than we might think. That doesn’t mean there aren’t real concerns. But when we worry about everything all the time instead of embracing a worldview based on facts, we can lose our ability to focus on the things that threaten us most.Inspiring and revelatory, filled with lively anecdotes and moving stories, Factfulness is an urgent and essential book that will change the way you see the world and empower you to respond to the crises and opportunities of the future.

    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

    One hundred crystal-clear articles explore the Law Code of Hammurabi, the Renaissance, the American Revolution, World War II, and much, much more, bringing the events and people of history to life.As part of DK's award-winning Big Ideas Simply Explained series, The History Book uses infographics and images to explain key ideas and themes. Biographies of key leaders, thinkers, and warriors, from Julius Caesar to Barack Obama, offer insight into their lives and further historical insight into these world-changing episodes.The History Book makes the past 4,000 years of history accessible and provides enlightenment on the forces that shaped the world as we know it today, for students and history buffs alike.Series Overview: Big Ideas Simply Explained series uses creative design and innovative graphics, along with straightforward and engaging writing, to make complex subjects easier to understand. These award-winning books provide just the information needed for students, families, or anyone interested in concise, thought-provoking refreshers on a single subject.Reviews:"[The Big Ideas Simply Explained books] are beautifully illustrated with shadow-like cartoons that break down even the most difficult concepts so they are easier to grasp. These step-by-step diagrams are an incredibly clever learning device to include, especially for visual learners." - Examiner.com"The visual layout promotes browsing with illustrations, pull quotes, and simple mind maps to explain concepts quickly." - Library Journal"Accessible guide to the great thinkers." - School Library Journal"Clever and engaging." - Booklist

    In Dataclysm, Christian Rudder uses it to show us who we truly are.   For centuries, we’ve relied on polling or small-scale lab experiments to study human behavior. Today, a new approach is possible. As we live more of our lives online, researchers can finally observe us directly, in vast numbers, and without filters. Data scientists have become the new demographers.   In this daring and original book, Rudder explains how Facebook "likes" can predict, with surprising accuracy, a person’s sexual orientation and even intelligence; how attractive women receive exponentially more interview requests; and why you must have haters to be hot. He charts the rise and fall of America’s most reviled word through Google Search and examines the new dynamics of collaborative rage on Twitter. He shows how people express themselves, both privately and publicly. What is the least Asian thing you can say? Do people bathe more in Vermont or New Jersey? What do black women think about Simon & Garfunkel? (Hint: they don’t think about Simon & Garfunkel.) Rudder also traces human migration over time, showing how groups of people move from certain small towns to the same big cities across the globe. And he grapples with the challenge of maintaining privacy in a world where these explorations are possible.   Visually arresting and full of wit and insight, Dataclysm is a new way of seeing ourselves—a brilliant alchemy, in which math is made human and numbers become the narrative of our time.

    In Ten Arguments For Deleting Your Social Media Accounts Right Now Jaron Lanier draws on his insider's expertise to explain precisely how social media works and why its cruel and dangerous effects are at the heart of its current business model and design. As well as offering ten simple arguments for liberating yourself from its addictive hold, his witty and urgent manifesto outlines a vision for an alternative that provides all the benefits of social media without the harm. nicer person in the process.