Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    Delving into an immense range of topics, from philosophy and literature to social criticism to mathematics and science, with essays that date from 1930s to the 1990s, Martin Gardner has astounded readers with his insight and erudition. The Night Is Large is the crowning achievement of his extraordinary career.

    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.

    This Harriman House edition includes Charles Mackay's account of the three infamous financial manias - John Law's Mississipi Scheme, the South Sea Bubble, and Tulipomania.Between the three of them, these historic episodes confirm that greed and fear have always been the driving forces of financial markets, and, furthermore, that being sensible and clever is no defence against the mesmeric allure of a popular craze with the wind behind it.In writing the history of the great financial manias, Charles Mackay proved himself a master chronicler of social as well as financial history. Blessed with a cast of characters that covered all the vices, gifted a passage of events which was inevitably heading for disaster, and with the benefit of hindsight, he produced a record that is at once a riveting thriller and absorbing historical document. A century and a half later, it is as vibrant and lurid as the day it was written.For modern-day investors, still reeling from the dotcom crash, the moral of the popular manias scarcely needs spelling out. When the next stock market bubble comes along, as it surely will, you are advised to recall the plight of some of the unfortunates on these pages, and avoid getting dragged under the wheels of the careering bandwagon yourself.

    It's the art of anticipating your opponent's next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintuitive, and it can only be mastered by developing a new way of seeing the world. Using a diverse array of rich case studies—from pop culture, TV, movies, sports, politics, and history—the authors show how nearly every business and personal interaction has a game-theory component to it. Are the winners of reality-TV contests instinctive game theorists? Do big-time investors see things that most people miss? What do great poker players know that you don't? Mastering game theory will make you more successful in business and life, and this lively book is the key to that mastery.

    He maintains at the outset that the importance of a physical law isn't "how clever we are to have found it out, but...how clever nature is to pay attention to it" & tends his discussions toward a final exposition of the elegance & simplicity of all scientific laws. Rather than an essay on the most significant achievements in modern science, The Character of Physical Law is a statement of what is most remarkable in nature. His enlightened approach, wit & enthusiasm make this a memorable exposition of the scientist's craft. The Law of Gravitation is the principal example. Relating the details of its discovery & stressing its mathematical character, he uses it to demonstrate the essential interaction of mathematics & physics. He views mathematics as the key to any system of scientific laws, suggesting that if it were possible to fill out the structure of scientific theory completely, the result would be an integrated set of axioms. The principles of conservation, symmetry & time-irreversibility are then considered in relation to developments in classical & modern physics. In his final lecture he develops his own analysis of the process & future of scientific discovery. Like any set of oral reflections, The Character of Physical Law has value as a demonstration of a mind in action. The reader is particularly lucky in Feynman. One of the most eminent & imaginative modern physicists, he was Professor of Theoretical Physics at the California Institute of Technology until his death in 1988. He's best known for work on the quantum theory of the electromagnetic field, as well as for later research in the field of low-temperature physics. In 1954 he received the Albert Einstein Award for an "outstanding contribution to knowledge in mathematical & physical sciences"; in 1965 he was appointed to Foreign Membership in the Royal Society & was awarded the Nobel Prize.

    Now, in What the Dog Saw, he brings together, for the first time, the best of his writing from The New Yorker over the same period. Here you'll find the bittersweet tale of the inventor of the birth control pill, and the dazzling creations of pasta sauce pioneer Howard Moscowitz. Gladwell sits with Ron Popeil, the king of the American kitchen, as he sells rotisserie ovens, and divines the secrets of Cesar Millan, the "dog whisperer" who can calm savage animals with the touch of his hand. He explores intelligence tests and ethnic profiling and why it was that employers in Silicon Valley once tripped over themselves to hire the same college graduate.

    When Dr Ben Goldacre saw someone on daytime TV dipping her feet in an 'Aqua Detox' footbath, releasing her toxins into the water, turning it brown, he thought he'd try the same at home. 'Like some kind of Johnny Ball cum Witchfinder General', using his girlfriend's Barbie doll, he gently passed an electrical current through the warm salt water. It turned brown. In his words: 'before my very eyes, the world's first Detox Barbie was sat, with her feet in a pool of brown sludge, purged of a weekend's immorality.' Dr Ben Goldacre is the author of the Bad Science column in the Guardian. His book is about all the 'bad science' we are constantly bombarded with in the media and in advertising. At a time when science is used to prove everything and nothing, everyone has their own 'bad science' moments from the useless pie-chart on the back of cereal packets to the use of the word 'visibly' in cosmetics ads.

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

    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.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.