Hungarian-born Erdős believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century's leading number theorist and the most prolific mathematician who ever lived. Erdős's important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers. Witty and filled with the sort of mathematical puzzles that intrigued Erdős and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.

    In this book, one of the world's preeminent philosophers takes issue with an idea that has found an all-too-prominent place in popular culture and philosophical thought: the idea that while factual claims can be rationally established or refuted, claims about value are wholly subjective, not capable of being rationally argued for or against. Although it is on occasion important and useful to distinguish between factual claims and value judgments, the distinction becomes, Hilary Putnam argues, positively harmful when identified with a dichotomy between the objective and the purely subjective.Putnam explores the arguments that led so much of the analytic philosophy of language, metaphysics, and epistemology to become openly hostile to the idea that talk of value and human flourishing can be right or wrong, rational or irrational; and by which, following philosophy, social sciences such as economics have fallen victim to the bankrupt metaphysics of Logical Positivism. Tracing the problem back to Hume's conception of a matter of fact as well as to Kant's distinction between analytic and synthetic judgments, Putnam identifies a path forward in the work of Amartya Sen. Lively, concise, and wise, his book prepares the way for a renewed mutual fruition of philosophy and the social sciences.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    In addition, the wide range of Leibniz's work--letters, published papers, and fragments on a variety of philosophical, religious, mathematical, and scientific questions over a fifty-year period--heightens the challenge of preparing an edition of his writings in English translation from the French and Latin.

    He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass.In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener.And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.

    It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible style. Includes three new chapters on prediction in chaotic systems, control of chaotic systems, and on the concept of chaos. Provides a discussion of complexity theory.

    In recent years, however, the concept of information has gained importance. Why? In this book, eminent scientists, philosophers and theologians chart various aspects of information, from quantum information to biological and digital information, in order to understand how nature works. Beginning with a historical treatment of the topic, the book also examines physical and biological approaches to information, and its philosophical, theological and ethical implications.

    Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

    Escher -- goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. Come along as Pickover traces the origins of the Mobius strip from the mid-1800s, when the visionary scientist Dr. August Mobius became the first to describe the properties of one-sided surfaces, to the present, where it is an integral part of mathematics, magic, science, art, engineering, literature, and music. It has become a metaphor for change, strangeness, looping, and rejuvenation. Touching on everything from molecules and metal sculptures to postage stamps, architectural structures, and models of our entire universe, The Mobius Strip is lavishly illustrated and gives readers a glimpse into other worlds and new ways of thinking as Pickover reaches across cultures and dimensions.

    Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

    One likely reason why the first edition was ignored is that it contained many untranslated quotations from French and German authors. For this new edition these passages have all been translated into English. Perhaps the main reason why it was denounced is that Cartesian Linguistics contains, implicitly if not explicitly, trenchant criticisms of empiricist theories about linguistics and the mind. Due largely to Chomsky's efforts, these are not so dominant now as they were when the first edition appeared in 1966, although they still command the attention of researchers and the public imagination. In his introduction Professor McGilvray focuses on the contrast between rationalist and empiricist approaches to language and the mind. He discusses at length the two most distinctive features of what he calls Chomsky's "rationalist-romantic" approach: its emphasis on linguistic creativity and its insistence that this creativity can be explained only by assuming that humans are endowed with innate concepts and mental faculties. In the course of the discussion he connects Chomsky's early treatment of these themes with his later development of them, and with Chomsky's well-known views on politics and education.

    It describes how the laws and discoveries of information theory now support controversial revisions to Darwinian evolution, begin to unravel the mysteries of language, memory and dreams, and stimulate provocative ideas in psychology, philosophy, art, music, computers and even the structure of society. Perhaps its most fascinating and unexpected surprise is the suggestion the order and complexity may be as natural as disorder and disorganization. Contrary to the entropy principle, which implies that order is the exception and confusion the rule, information theory asserts that order and sense can indeed prevail against disorder and nonsense. From the simplest forms of organic life to the words used to express our most complex ideas, from our genes to our dreams, from microcomputers to telecommunications, virtually everything around us follows simple rules of information. Life and the material world, like language, remain "grammatical." Grammatical man inhabits a grammatical universe.

    It’s a book about making it stop.What if I told you that a lot of what keeps you unbelievably busy is not only pointless, but avoidable, nonsensical and entirely driven by your own fears, insecurities and ego? You’d probably want to slap me, if you could find the time, right?Don’t worry, I was once just like you: exhausted, harried, overcommitted and flummoxed as to what to cut back on. I’m not completely cured, but for the first time in years I have room to breathe and to think about what kind of life I really want to live. And I have Buddhism to thank for this.In this book I’ve compiled the teachings, ideas and practices that got me to this point. Buddhism helped me dig deep to discover why I was determined to do so much, and why I was so afraid to stand still and be alone with myself. It’s not hippy-trippy stuff, believe me. Buddhism is just as relevant and practical in our modern world as it’s ever been.As crazy as it sounds, I’m asking you to add one more thing to your list today: read this book, and let it help you free yourself from the grind of your unbelievable busyness. Live the peaceful life you know you deserve and be the person you want to be.

    Mathematics: The Loss of Certainty refutes that myth.

    In this autobiography the author provides an honest and sincere account of his childhood memories, his life as a school-goer with a batch of cousins and relatives in Cuttack, his formative years of intellectual development as a promising student of Presidency College in Calcutta, his quest for spiritual enlightenment and his experiences as a student at the prestigious Cambridge University. The autobiography also throws much light on Bose’s indomitable spirit in the freedom movement of India.