Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    Mandelbrot, one of the century's most influential mathematicians, is world-famous for making mathematical sense of a fact everybody knows but that geometers from Euclid on down had never assimilated: Clouds are not round, mountains are not cones, coastlines are not smooth. To these classic lines we can now add another example: Markets are not the safe bet your broker may claim. In his first book for a general audience, Mandelbrot, with co-author Richard L. Hudson, shows how the dominant way of thinking about the behavior of markets-a set of mathematical assumptions a century old and still learned by every MBA and financier in the world-simply does not work. As he did for the physical world in his classic The Fractal Geometry of Nature, Mandelbrot here uses fractal geometry to propose a new, more accurate way of describing market behavior. The complex gyrations of IBM's stock price and the dollar-euro exchange rate can now be reduced to straightforward formulae that yield a far better model of how risky they are. With his fractal tools, Mandelbrot has gotten to the bottom of how financial markets really work, and in doing so, he describes the volatile, dangerous (and strangely beautiful) properties that financial experts have never before accounted for. The result is no less than the foundation for a new science of finance.

    But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    Kathryn Schulz, editor of Grist magazine, argues that error is the fundamental human condition and should be celebrated as such. Guiding the reader through the history and psychology of error, from Socrates to Alan Greenspan, Being Wrong will change the way you perceive screw-ups, both of the mammoth and daily variety, forever.

    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.

    Now, two science professors give us the tools to dismantle misinformation and think clearly in a world of fake news and bad data.It's increasingly difficult to know what's true. Misinformation, disinformation, and fake news abound. Our media environment has become hyperpartisan. Science is conducted by press release. Startup culture elevates bullshit to high art. We are fairly well equipped to spot the sort of old-school bullshit that is based in fancy rhetoric and weasel words, but most of us don't feel qualified to challenge the avalanche of new-school bullshit presented in the language of math, science, or statistics. In Calling Bullshit, Professors Carl Bergstrom and Jevin West give us a set of powerful tools to cut through the most intimidating data.You don't need a lot of technical expertise to call out problems with data. Are the numbers or results too good or too dramatic to be true? Is the claim comparing like with like? Is it confirming your personal bias? Drawing on a deep well of expertise in statistics and computational biology, Bergstrom and West exuberantly unpack examples of selection bias and muddled data visualization, distinguish between correlation and causation, and examine the susceptibility of science to modern bullshit.We have always needed people who call bullshit when necessary, whether within a circle of friends, a community of scholars, or the citizenry of a nation. Now that bullshit has evolved, we need to relearn the art of skepticism.

    Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.

    Along the way she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how this little symbol holds the biggest idea of all. "Beyond Infinity is a spirited and friendly guide--appealingly down to earth about math that's extremely far out." --Jordan Ellenberg, author of How Not to Be Wrong "Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board." --Natalie Angier, New York Times

    We all know that the very rich have gotten a lot richer these past few decades while most Americans haven’t. In fact, the exorbitantly paid have continued to thrive during the current economic crisis, even as the rest of Americans have continued to fall behind. Why do the “haveit- alls” have so much more? And how have they managed to restructure the economy to reap the lion’s share of the gains and shift the costs of their new economic playground downward, tearing new holes in the safety net and saddling all of us with increased debt and risk? Lots of so-called experts claim to have solved this great mystery, but no one has really gotten to the bottom of it—until now. In their lively and provocative Winner-Take-All Politics, renowned political scientists Jacob S. Hacker and Paul Pierson demonstrate convincingly that the usual suspects—foreign trade and financial globalization, technological changes in the workplace, increased education at the top—are largely innocent of the charges against them. Instead, they indict an unlikely suspect and take us on an entertaining tour of the mountain of evidence against the culprit. The guilty party is American politics. Runaway inequality and the present economic crisis reflect what government has done to aid the rich and what it has not done to safeguard the interests of the middle class. The winner-take-all economy is primarily a result of winner-take-all politics. In an innovative historical departure, Hacker and Pierson trace the rise of the winner-take-all economy back to the late 1970s when, under a Democratic president and a Democratic Congress, a major transformation of American politics occurred. With big business and conservative ideologues organizing themselves to undo the regulations and progressive tax policies that had helped ensure a fair distribution of economic rewards, deregulation got under way, taxes were cut for the wealthiest, and business decisively defeated labor in Washington. And this transformation continued under Reagan and the Bushes as well as under Clinton, with both parties catering to the interests of those at the very top. Hacker and Pierson’s gripping narration of the epic battles waged during President Obama’s first two years in office reveals an unpleasant but catalyzing truth: winner-take-all politics, while under challenge, is still very much with us. Winner-Take-All Politics—part revelatory history, part political analysis, part intellectual journey— shows how a political system that traditionally has been responsive to the interests of the middle class has been hijacked by the superrich. In doing so, it not only changes how we think about American politics, but also points the way to rebuilding a democracy that serves the interests of the many rather than just those of the wealthy few.

    Why do well-intentioned plans for improving the human condition go tragically awry?In this wide-ranging and original book, James C. Scott analyzes failed cases of large-scale authoritarian plans in a variety of fields. Centrally managed social plans misfire, Scott argues, when they impose schematic visions that do violence to complex interdependencies that are not—and cannot—be fully understood. Further, the success of designs for social organization depends upon the recognition that local, practical knowledge is as important as formal, epistemic knowledge. The author builds a persuasive case against "development theory" and imperialistic state planning that disregards the values, desires, and objections of its subjects. He identifies and discusses four conditions common to all planning disasters: administrative ordering of nature and society by the state; a "high-modernist ideology" that places confidence in the ability of science to improve every aspect of human life; a willingness to use authoritarian state power to effect large- scale interventions; and a prostrate civil society that cannot effectively resist such plans.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    The selections range from his earliest days as a theoretical physicist to his death in 1955; from such subjects as relativity, nuclear war or peace, and religion and science, to human rights, economics, and government.

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    Based on exhaustive research and interviews with driving experts and traffic officials around the globe, Traffic gets under the hood of the everyday activity of driving to uncover the surprisingly complex web of physical, psychological, and technical factors that explain how traffic works, why we drive the way we do, and what our driving says about us. Vanderbilt examines the perceptual limits and cognitive underpinnings that make us worse drivers than we think we are. He demonstrates why plans to protect pedestrians from cars often lead to more accidents. He shows how roundabouts, which can feel dangerous and chaotic, actually make roads safer and reduce traffic in the bargain. He uncovers who is more likely to honk at whom, and why. He explains why traffic jams form, outlines the unintended consequences of our quest for safety, and even identifies the most common mistake drivers make in parking lots. The car has long been a central part of American life; whether we see it as a symbol of freedom or a symptom of sprawl, we define ourselves by what and how we drive. As Vanderbilt shows, driving is a provocatively revealing prism for examining how our minds work and the ways in which we interact with one another. Ultimately, Traffic is about more than driving: it s about human nature. This book will change the way we see ourselves and the world around us. And who knows? It may even make us better drivers."

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.