But by knowing what they are and how to spot them, we can avoid them and make better choices-whether dealing with a personal problem or a business negotiation; trying to save money or make money; working out what we do or don't want in life: and how best to get it.Simple, clear and always surprising, this indispensable book will change the way you think and transform your decision-making-work, at home, every day. It reveals, in 99 short chapters, the most common errors of judgment, and how to avoid them.

    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    In The Invisible Gorilla, Christopher Chabris and Daniel Simons, creators of one of psychology’s most famous experiments, use remarkable stories and counterintuitive scientific findings to demonstrate an important truth: Our minds don’t work the way we think they do. We think we see ourselves and the world as they really are, but we’re actually missing a whole lot.Again and again, we think we experience and understand the world as it is, but our thoughts are beset by everyday illusions. We write traffic laws and build criminal cases on the assumption that people will notice when something unusual happens right in front of them. We’re sure we know where we were on 9/11, falsely believing that vivid memories are seared into our minds with perfect fidelity. And as a society, we spend billions on devices to train our brains because we’re continually tempted by the lure of quick fixes and effortless self-improvement.  The Invisible Gorilla reveals the myriad ways that our intuitions can deceive us, but it’s much more than a catalog of human failings. Chabris and Simons explain why we succumb to these everyday illusions and what we can do to inoculate ourselves against their effects. Ultimately, the book provides a kind of x-ray vision into our own minds, making it possible to pierce the veil of illusions that clouds our thoughts and to think clearly for perhaps the first time.

    As a celebrated cultural critic and a writer for national publications like The Atlantic and Harper's, Alan Jacobs has spent his adult life belonging to communities that often clash in America's culture wars. And in his years of confronting the big issues that divide us--political, social, religious--Jacobs has learned that many of our fiercest disputes occur not because we're doomed to be divided, but because the people involved simply aren't thinking.Most of us don't want to think, Jacobs writes. Thinking is trouble. Thinking can force us out of familiar, comforting habits, and it can complicate our relationships with like-minded friends. Finally, thinking is slow, and that's a problem when our habits of consuming information (mostly online) leave us lost in the spin cycle of social media, partisan bickering, and confirmation bias.In this smart, endlessly entertaining book, Jacobs diagnoses the many forces that act on us to prevent thinking--forces that have only worsened in the age of Twitter, "alternative facts," and information overload--and he also dispels the many myths we hold about what it means to think well. (For example: It's impossible to "think for yourself.")Drawing on sources as far-flung as novelist Marilynne Robinson, basketball legend Wilt Chamberlain, British philosopher John Stuart Mill, and Christian theologian C.S. Lewis, Jacobs digs into the nuts and bolts of the cognitive process, offering hope that each of us can reclaim our mental lives from the impediments that plague us all. Because if we can learn to think together, maybe we can learn to live together, too.

    It proposes enlightening similarities between, for instance, maneuvering in limited war and in a traffic jam; deterring the Russians and one's own children; the modern strategy of terror and the ancient institution of hostages.

    Mirroring his theory, Minsky boldly casts The Society of Mind as an intellectual puzzle whose pieces are assembled along the way. Each chapter -- on a self-contained page -- corresponds to a piece in the puzzle. As the pages turn, a unified theory of the mind emerges, like a mosaic. Ingenious, amusing, and easy to read, The Society of Mind is an adventure in imagination.

    Human beings have long been both fascinated and appalled by randomness. On the one hand, we love the thrill of a surprise party, the unpredictability of a budding romance, or the freedom of not knowing what tomorrow will bring. We are inexplicably delighted by strange coincidences and striking similarities. But we also hate uncertainty's dark side. From cancer to SARS, diseases strike with no apparent pattern. Terrorists attack, airplanes crash, bridges collapse, and we never know if we'll be that one in a million statistic. We are all constantly faced with situations and choices that involve randomness and uncertainty. A basic understanding of the rules of probability theory, applied to real-life circumstances, can help us to make sense of these situations, to avoid unnecessary fear, to seize the opportunities that randomness presents to us, and to actually enjoy the uncertainties we face. The reality is that when it comes to randomness, you can run, but you can't hide. So many aspects of our lives are governed by events that are simply not in our control. In this entertaining yet sophisticated look at the world of probabilities, author Jeffrey Rosenthal--an improbably talented math professor--explains the mechanics of randomness and teaches us how to develop an informed perspective on probability.

    'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.

    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.

    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

    Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances." Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening. Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world. --Gregory McNamee

    Equal parts personal, practical, and profound, Applied Minds charts a path to a future where we borrow strategies from engineering to find inspired solutions to our most pressing challenges.

    Even as technology exerts new pressures to speed up our lives, it turns out that the choices we make--unconsciously and consciously, in time frames varying from milliseconds to years--benefit profoundly from delay. As this winning and provocative book reveals, taking control of time and slowing down our responses yields better results in almost every arena of life ... even when time seems to be of the essence.The procrastinator in all of us will delight in Partnoy's accounts of celebrity "delay specialists," from Warren Buffett to Chris Evert to Steve Kroft, underscoring the myriad ways in which delaying our reactions to everyday choices--large and small--can improve the quality of our lives.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.