The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    What is needed is the courage to face the way things are, and the wisdom and imagination to work out how to make things better.'Australia's unprecedented run of economic growth has failed to deliver a more stable or harmonious society. Individualism is rampant. Income inequality is growing. Public education is under-resourced. The gender revolution is stalling. We no longer trust our major institutions or our political leaders. We are more socially fragmented, more anxious, more depressed, more overweight, more medicated, deeper in debt and increasingly addicted - whether to our digital devices, drugs, pornography or 'stuff'.Yet esteemed social researcher Hugh Mackay remains optimistic. Twenty-five years ago, he revolutionised Australian social analysis with the publication of Reinventing Australia. Now he takes another unflinching look at us and offers some compelling proposals for a more compassionate and socially cohesive Australia. You might not agree with everything he suggests, but you'll find it hard to get some of his ideas out of your head.Argued with intelligence and passion, this book is essential reading for everyone who loves Australia enough to want to make it a better place for us all.

    Evolutionists have never been able to completely explain why birdsong is so inventive and why many species devote so many hours to singing. The standard explanations of defending territories and attracting mates don't begin to account for the variety and energy that the commonest birds exhibit. Is it possible that birds sing because they like to? This seemingly naive explanation is starting to look more and more like the truth. Why Birds Sing is a lyric exploration of birdsong that blends the latest scientific research with a deep understanding of musical beauty and form. Drawing on conversations with neuroscientists, ecologists, and composers, it is the first book to investigate the elusive question of why birds sing and what their song means to both avian and human ears. Whether playing his clarinet with the whitecrested laughing thrush in Pittsburgh, or jamming in the Australian winter breeding grounds of the Albert's lyrebird, Rothenberg immerses himself in the heart and soul of birdsong. He approaches the subject as a naturalist, philosopher, musician, and investigator. An intimate look at the mostlovely of natural phenomena, Why Birds Sing is a beautifully written exploration of a phenomenon that's at once familiar and profoundly alien.

    Fascinating... may presage a paradigm shift in medicine." --Kirkus Reviews (starred review)Teeming with information and big ideas... Outstanding."--Booklist (starred review) The origin of asthma, autism, Alzheimer's, allergies, cancer, heart disease, obesity, and even some kinds of depression is now clear. Award-winning researcher on the microbiome, professor Rodney Dietert presents a new paradigm in human biology that has emerged in the midst of the ongoing global epidemic of noncommunicable diseases.The Human Superorganism makes a sweeping, paradigm-shifting argument. It demolishes two fundamental beliefs that have blinkered all medical thinking until very recently: 1) Humans are better off as pure organisms free of foreign microbes; and 2) the human genome is the key to future medical advances. The microorganisms that we have sought to eliminate have been there for centuries supporting our ancestors. They comprise as much as 90 percent of the cells in and on our bodies--a staggering percentage! More than a thousand species of them live inside us, on our skin, and on our very eyelashes. Yet we have now significantly reduced their power and in doing so have sparked an epidemic of noncommunicable diseases--which now account for 63 percent of all human deaths.Ultimately, this book is not just about microbes; it is about a different way to view humans. The story that Dietert tells of where the new biology comes from, how it works, and the ways in which it affects your life is fascinating, authoritative, and revolutionary. Dietert identifies foods that best serve you, the superorganism; not new fad foods but ancient foods that have made sense for millennia. He explains protective measures against unsafe chemicals and drugs. He offers an empowering self-care guide and the blueprint for a revolution in public health. We are not what we have been taught. Each of us is a superorganism. The best path to a healthy life is through recognizing that profound truth.

    But as architect William McDonough and chemist Michael Braungart point out in this provocative, visionary book, such an approach only perpetuates the one-way, "cradle to grave" manufacturing model, dating to the Industrial Revolution, that creates such fantastic amounts of waste and pollution in the first place. Why not challenge the belief that human industry must damage the natural world? In fact, why not take nature itself as our model for making things? A tree produces thousands of blossoms in order to create another tree, yet we consider its abundance not wasteful but safe, beautiful, and highly effective.Waste equals food. Guided by this principle, McDonough and Braungart explain how products can be designed from the outset so that, after their useful lives, they will provide nourishment for something new. They can be conceived as "biological nutrients" that will easily reenter the water or soil without depositing synthetic materials and toxins. Or they can be "technical nutrients" that will continually circulate as pure and valuable materials within closed-loop industrial cycles, rather than being "recycled" -- really, downcycled -- into low-grade materials and uses. Drawing on their experience in (re)designing everything from carpeting to corporate campuses, McDonough and Braungart make an exciting and viable case for putting eco-effectiveness into practice, and show how anyone involved with making anything can begin to do as well.

    The latest studies are revealing exciting new discoveries, such as how the DNA and related chemical compounds in our cells work together to direct the processes of life. Scientists are not only unraveling how life evolved in the ancient past, but are also finding the keys to creating a healthier future.  How does the minuscule chemical cluster in each of our 100 trillion cells accomplish the amazing feat of creating and maintaining our bodies? Frank Ryan, a physician and an evolutionary biologist, describes the complex ways in which the genome operates as a holistic system and not solely through genes coding for proteins—the building blocks of life. Also involved are elaborate switching mechanisms that regulate and control portions of our DNA, as well as the interplay of retroviruses and bacteria.This groundbreaking book explains that we are on the cusp of an amazing era of disease treatment and eradication.

    Is it in our genes? The structure of our brains? Our genome may determine our eye color and even aspects of our personality. But our friendships, failures, and passions also shape who we are. The question is: how?Sebastian Seung, a dynamic professor at MIT, is on a quest to discover the biological basis of identity. He believes it lies in the pattern of connections between the brain’s neurons, which change slowly over time as we learn and grow. The connectome, as it’s called, is where our genetic inheritance intersects with our life experience. It’s where nature meets nurture.Seung introduces us to the dedicated researchers who are mapping the brain’s connections, neuron by neuron, synapse by synapse. It is a monumental undertaking—the scientific equivalent of climbing Mount Everest—but if they succeed, it could reveal the basis of personality, intelligence, memory, and perhaps even mental disorders. Many scientists speculate that people with anorexia, autism, and schizophrenia are "wired differently," but nobody knows for sure. The brain’s wiring has never been clearly seen.In sparklingly clear prose, Seung reveals the amazing technological advances that will soon help us map connectomes. He also examines the evidence that these maps will someday allow humans to "upload" their minds into computers, achieving a kind of immortality.Connectome is a mind-bending adventure story, told with great passion and authority. It presents a daring scientific and technological vision for at last understanding what makes us who we are. Welcome to the future of neuroscience.

    A powerful and innovative argument that explores the complexity of the human relationship with material things, demonstrating how humans and societies are entrapped into the maintenance and sustaining of material worlds*Argues that the interrelationship of humans and things is a defining characteristic of human history and culture*Offers a nuanced argument that values the physical processes of things without succumbing to materialism*Discusses historical and modern examples, using evolutionary theory to show how long-standing entanglements are irreversible and increase in scale and complexity over time*Integrates aspects of a diverse array of contemporary theories in archaeology and related natural and biological sciences*Provides a critical review of many of the key contemporary perspectives from materiality, material culture studies and phenomenology to evolutionary theory, behavioral archaeology, cognitive archaeology, human behavioral ecology, Actor Network Theory and complexity theory

    Drawing upon new research into cat genetics, brain chemistry, evolution, social behavior, and interaction with humans and fellow felines, acclaimed author and scientist Stephen Budiansky explores the mysteries of these amazing creatures. Wide-ranging, lively, and engaging, The Character of Cats also covers the full spectrum of feline fact and lore, from history, superstition, and religious imagery to hunting patterns, sexual behavior, and preferred colors. This smart, wonderfully readable book finally gives cats their due.

    As they see matters, wealth in the form of means of production and wealth in the form of consumers’ goods are essentially indistinguishable. For all practical purposes, they have no awareness of the existence of capital and of its importance. Thus, capitalists are generally depicted as fat men, whose girth allegedly signifies an excessive consumption of food and of wealth in general, while their alleged victims, the wage earners, are typically depicted as substantially underweight, allegedly signifying their inability to consume, thanks to the allegedly starvation wages paid by the capitalists.The truth is that in a capitalist economic system, the wealth of the capitalists is not only overwhelmingly in the form of means of production, such as factory buildings, machinery, farms, mines, stores, warehouses, and means of transportation and communication, but all of this wealth is employed in producing for the market, where its benefit is made available to everyone in the economic system who is able to afford to buy its products.Consider. Whoever can afford to buy an automobile benefits from the existence of the automobile factory and its equipment where that car was made. He also benefits from the existence of all the other automobile factories, whose existence and competition served to reduce the price he had to pay for his automobile. He benefits from the existence of the steel mill that provided the steel for his car, and from the iron mine that provided the iron ore needed for the production of that steel, and, of course, from the existence of all the other steel mills and iron mines whose existence and competition served to hold down the prices of the steel and iron ore that contributed to the production of his car.And, thanks to the great magnitude of wealth employed as capital, the demand for labor, of which capital is the foundation, is great enough and thus wages are high enough that virtually everyone is able to afford to a substantial degree most of the products of the economic system. For the capital of the capitalists is the foundation both of the supply of products that everyone buys and of the demand for the labor that all wage earners sell. More capital—a greater amount of wealth in the possession of the capitalists—means a both a larger and better supply of products for wage earners to buy and a greater demand for the labor that wage earners sell. Everyone, wage earners and capitalists alike, benefits from the wealth of the capitalists, because, as I say, that wealth is the foundation of the supply of the products that everyone buys and of the demand for the labor that all wage earners sell. More capital in the hands of the capitalists always means a more abundant, better quality of goods and services offered for sale and a larger demand for labor. The further effect is lower prices and higher wages, and thus a higher standard of living for wage earners.Furthermore, the combination of the profit motive and competition operates continually to improve the products offered in the market and the efficiency with which they are produced, thus steadily further improving the standard of living of everyone.In the alleged conflict between the so-called 99 percent and the so-called 1 percent, the program of the 99 percent is to seize as far as possible the wealth of the 1 percent and consume it. To the extent that it is enacted, the effect of this program can only be to impoverish everyone, and the 99 percent to a far greater extent than the 1 percent. To the extent that the 1 percent loses its mansions, luxury cars, and champagne and caviar, 99 times as many people lose their houses, run-of-the mill cars, and steak and hamburger.

    It is the operation of these forces, in combination with the talent of Pasteur, that Bruno Latour sets before us as a prime example of science in action.Latour argues that the triumph of the biologist and his methodology must be understood within the particular historical convergence of competing social forces and conflicting interests. Yet Pasteur was not the only scientist working on the relationships of microbes and disease. How was he able to galvanize the other forces to support his own research? Latour shows Pasteur’s efforts to win over the French public—the farmers, industrialists, politicians, and much of the scientific establishment.Instead of reducing science to a given social environment, Latour tries to show the simultaneous building of a society and its scientific facts. The first section of the book, which retells the story of Pasteur, is a vivid description of an approach to science whose theoretical implications go far beyond a particular case study. In the second part of the book, “Irreductions,” Latour sets out his notion of the dynamics of conflict and interaction, of the “relation of forces.” Latour’s method of analysis cuts across and through the boundaries of the established disciplines of sociology, history, and the philosophy of science, to reveal how it is possible not to make the distinction between reason and force. Instead of leading to sociological reductionism, this method leads to an unexpected irreductionism.

    But Vidal was also a terrific conversationalist; indeed Dick Cavett once described him as “the best talker since Oscar Wilde.” Vidal was never more eloquent, or caustic, than when let loose on his favorite topic: the history and politics of the United States.This book is made up from four interviews conducted with his long-time interlocutor, the writer and radio host Jon Wiener, in which Vidal grapples with matters evidently close to his heart: the history of the American Empire, the rise of the National Security State, and his own life in politics, both as a commentator and candidate.The interviews cover a twenty-year span, from 1988 to 2008, when Vidal was at the height of his powers. His extraordinary facility for developing an argument, tracing connections between past and present, and drawing on an encyclopedic knowledge of America’s place in the world, are all on full display. And, of course, it being Gore Vidal, an ample sprinkling of gloriously acerbic one-liners is also provided.

    But natural selection has given us a suite of beneficial social features, including our capacity for love, friendship, cooperation, and learning. Beneath all of our inventions -- our tools, farms, machines, cities, nations -- we carry with us innate proclivities to make a good society.In Blueprint, Nicholas A. Christakis introduces the compelling idea that our genes affect not only our bodies and behaviors, but also the ways in which we make societies, ones that are surprisingly similar worldwide.With many vivid examples -- including diverse historical and contemporary cultures, communities formed in the wake of shipwrecks, commune dwellers seeking utopia, online groups thrown together by design or involving artificially intelligent bots, and even the tender and complex social arrangements of elephants and dolphins that so resemble our own -- Christakis shows that, despite a human history replete with violence, we cannot escape our social blueprint for goodness.In a world of increasing political and economic polarization, it's tempting to ignore the positive role of our evolutionary past. But by exploring the ancient roots of goodness in civilization, Blueprint shows that our genes have shaped societies for our welfare and that, in a feedback loop stretching back many thousands of years, societies are still shaping our genes today.

    Pulitzer Prize–winning author Siddhartha Mukherjee, a leading cancer physician and researcher, selects the year’s top science and nature writing from journalists who dive into their fields with curiosity and passion, delivering must-read articles from a wide array of fields.

    Our intellectual capacity, our introversion or extraversion, our vulnerability to mental illness, even whether we are a morning person - all of these aspects of our personality are profoundly shaped by our inherited DNA differences.In Blueprint, Robert Plomin, a pioneer in the field of behavioural genetics, draws on a lifetime's worth of research to make the case that DNA is the most important factor shaping who we are. Our families, schools and the environment around us are important, but they are not as influential as our genes. This is why, he argues, teachers and parents should accept children for who they are, rather than trying to mould them in certain directions. Even the environments we choose and the signal events that impact our lives, from divorce to addiction, are influenced by our genetic predispositions. Now, thanks to the DNA revolution, it is becoming possible to predict who we will become, at birth, from our DNA alone. As Plomin shows us, these developments have sweeping implications for how we think about parenting, education, and social mobility.A game-changing book by a leader in the field, Blueprint shows how the DNA present in the single cell with which we all begin our lives can impact our behaviour as adults.