It would become the world's most baffling mathematical mystery. Simple, elegant, and utterly impossible to prove, Fermat's Last Theorem captured the imaginations of amateur and professional mathematicians for over three centuries. For some it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Dr. Amir Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph. From formulas devised for the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, "Fermat's Last Theorem" brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    To the public he is a figure of tragic dimensions - a brilliant scientist and author of the phenomenal best-seller A Brief History of Time, and yet confined to a wheelchair, unable to speak or write. Hawking has mastered the two great theories of 20th-century physics - Einstein's General Theory of Relativity and Quantum Mechanics - and has made breathtaking discoveris about where they break down or overlap, such as on the edge of a Black Hole or at the Big Bang origin of the Universe. Here is the perfect introduction to Hawking's work by the author, who was helped by several long discussions with Hawking in researching the book.

    Many people think of microbes as germs to be eradicated, but those that live with us—the microbiome—build our bodies, protect our health, shape our identities, and grant us incredible abilities. In this astonishing book, Ed Yong takes us on a grand tour through our microbial partners, and introduces us to the scientists on the front lines of discovery. Yong, whose humor is as evident as his erudition, prompts us to look at ourselves and our animal companions in a new light—less as individuals and more as the interconnected, interdependent multitudes we assuredly are. The microbes in our bodies are part of our immune systems and protect us from disease. Those in cows and termites digest the plants they eat. In the deep oceans, mysterious creatures without mouths or guts depend on microbes for all their energy. Bacteria provide squids with invisibility cloaks, help beetles to bring down forests, and allow worms to cause diseases that afflict millions of people. I Contain Multitudes is the story of these extraordinary partnerships, between the creatures we are familiar with and those we are not. It reveals how we humans are disrupting these partnerships and how we might manipulate them for our own good. It will change both our view of nature and our sense of where we belong in it.

    One of the most important achievements of the past millennium, it did for biology what Galileo did for astronomy: made it into a single science rather than a collection of unrelated facts. Important though Origin remains, its examples and intricate Victorian prose are now a century and a half old. They are ripe for renewal and reaffirmation. Writing as "Darwin's ghost," eminent geneticist Steve Jones updates this seminal work—and restates evolution's case for the 21st century.Jones is a writer of engaging wit and dazzling erudition and has been called "the British Carl Sagan." Using modern examples—the AIDS virus, the puzzles of sexual selection, the physiology and psychology of pets, and the unparalleled genetic success of our own species—he shows the power and immediacy of Darwin's great argument and makes us appreciate how it makes life make sense. Eye-opening and entertaining, filled with astonishing facts, amusing anecdotes, and the very latest research, Darwin's Ghost is contemporary science writing at its very best.

    Before the decade is out, telltale signs that they harbor life may be found. If they are, the ramifications for all areas of human thought and endeavor--from religion and philosophy to art and biology--will be breathtaking. In Strange New Worlds, renowned astronomer Ray Jayawardhana brings news from the front lines of the epic quest to find planets--and alien life--beyond our solar system.Only in the past fifteen years, after millennia of speculation, have astronomers begun to discover planets around other stars--hundreds in fact. But the hunt to find a true Earth-like world goes on. In this book, Jayawardhana vividly recounts the stories of the scientists and the remarkable breakthroughs that have ushered in this extraordinary age of exploration. He describes the latest findings--including his own--that are challenging our view of the cosmos and casting new light on the origins and evolution of planets and planetary systems. He reveals how technology is rapidly advancing to support direct observations of Jupiter-like gas giants and super-Earths--rocky planets with several times the mass of our own planet--and how astronomers use biomarkers to seek possible life on other worlds.Strange New Worlds provides an insider's look at the cutting-edge science of today's planet hunters, our prospects for discovering alien life, and the debates and controversies at the forefront of extrasolar-planet research.

    Yet as bestselling author and astrophysicist Jeffrey Bennett points out, black holes don't suck. With that simple idea in hand, Bennett begins an entertaining introduction to Einstein's theories, describing the amazing phenomena readers would actually experience if they took a trip through a black hole.The theory of relativity also gives us the cosmic speed limit of the speed of light, the mind-bending ideas of time dilation and curvature of spacetime, and what may be the most famous equation in history: e = mc2. Indeed, the theory of relativity shapes much of our modern understanding of the universe, and it is not "just a theory: " every major prediction of relativity has been tested to exquisite precision and its practical applications include the Global Positioning System (GPS). Bennett proves anyone can understand the basics of Einstein's ideas. His intuitive, nonmathematical approach gives a wide audience its first real taste of how relativity works and why it is so important not only to science but also to the way we view ourselves as human beings.

    Its presence in nature was dismissed as a desperate response to starvation or other life-threatening circumstances, and few spent time studying it. A taboo subject in our culture, the behavior was portrayed mostly through horror movies or tabloids sensationalizing the crimes of real-life flesh-eaters. But the true nature of cannibalism--the role it plays in evolution as well as human history--is even more intriguing (and more normal) than the misconceptions we've come to accept as fact. In Cannibalism: A Perfectly Natural History, zoologist Bill Schutt sets the record straight, debunking common myths and investigating our new understanding of cannibalism's role in biology, anthropology, and history in the most fascinating account yet written on this complex topic. Schutt takes readers from Arizona's Chiricahua Mountains, where he wades through ponds full of tadpoles devouring their siblings, to the Sierra Nevadas, where he joins researchers who are shedding new light on what happened to the Donner Party--the most infamous episode of cannibalism in American history. He even meets with an expert on the preparation and consumption of human placenta (and, yes, it goes well with Chianti). Bringing together the latest cutting-edge science, Schutt answers questions such as why some amphibians consume their mother's skin; why certain insects bite the heads off their partners after sex; why, up until the end of the twentieth century, Europeans regularly ate human body parts as medical curatives; and how cannibalism might be linked to the extinction of the Neanderthals. He takes us into the future as well, investigating whether, as climate change causes famine, disease, and overcrowding, we may see more outbreaks of cannibalism in many more species--including our own.Cannibalism places a perfectly natural occurrence into a vital new context and invites us to explore why it both enthralls and repels us.

    We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

    Few episodes in the development of scientific theory show so clearly how the solution to a highly technical problem can alter our basic thought processes and attitudes. Understanding the processes which underlay the Revolution gives us a perspective, in this scientific age, from which to evaluate our own beliefs more intelligently. With a constant keen awareness of the inseparable mixture of its technical, philosophical, and humanistic elements, Thomas S. Kuhn displays the full scope of the Copernican Revolution as simultaneously an episode in the internal development of astronomy, a critical turning point in the evolution of scientific thought, and a crisis in Western man's concept of his relation to the universe and to God.The book begins with a description of the first scientific cosmology developed by the Greeks. Mr. Kuhn thus prepares the way for a continuing analysis of the relation between theory and observation and belief. He describes the many functions--astronomical, scientific, and nonscientific--of the Greek concept of the universe, concentrating especially on the religious implications. He then treats the intellectual, social, and economic developments which nurtured Copernicus' break with traditional astronomy. Although many of these developments, including scholastic criticism of Aristotle's theory of motion and the Renaissance revival of Neoplatonism, lie entirely outside of astronomy, they increased the flexibility of the astronomer's imagination. That new flexibility is apparent in the work of Copernicus, whose De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres) is discussed in detail both for its own significance and as a representative scientific innovation.With a final analysis of Copernicus' life work--its reception and its contribution to a new scientific concept of the universe--Mr. Kuhn illuminates both the researches that finally made the heliocentric arrangement work, and the achievements in physics and metaphysics that made the planetary earth an integral part of Newtonian science. These are the developments that once again provided man with a coherent and self-consistent conception of the universe and of his own place in it.This is a book for any reader interested in the evolution of ideas and, in particular, in the curious interplay of hypothesis and experiment which is the essence of modern science. Says James Bryant Conant in his Foreword: "Professor Kuhn's handling of the subject merits attention, for...he points the way to the road which must be followed if science is to be assimilated into the culture of our times."

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    Einstein predicted these tiny ripples in the fabric of spacetime nearly a hundred years ago, but they were never perceived directly until now. Decades in the making, this momentous discovery has given scientists a new understanding of the cataclysmic events that shape the universe and a new confirmation of Einstein's theory of general relativity. Ripples in Spacetime is an engaging account of the international effort to complete Einstein's project, capture his elusive ripples, and launch an era of gravitational-wave astronomy that promises to explain, more vividly than ever before, our universe's structure and origin.The quest for gravitational waves involved years of risky research and many personal and professional struggles that threatened to derail one of the world's largest scientific endeavors. Govert Schilling takes readers to sites where these stories unfolded--including Japan's KAGRA detector, Chile's Atacama Cosmology Telescope, the South Pole's BICEP detectors, and the United States' LIGO labs. He explains the seeming impossibility of developing technologies sensitive enough to detect waves from two colliding black holes in the very distant universe, and describes the astounding precision of the LIGO detectors. Along the way Schilling clarifies concepts such as general relativity, neutron stars, and the big bang using language that readers with little scientific background can grasp.Ripples in Spacetime provides a window into the next frontiers of astronomy, weaving far-reaching predictions and discoveries into a gripping story of human ambition and perseverance.

    But as animals can only be spied on by getting quite close Heinrich adopts ravens, thereby becoming a "raven father," as well as observing them in their natural habitat, studying their daily routines, and in the process painting a vivid picture of the world as lived by the ravens. At the heart of this book are Heinrich's love and respect for these complex and engaging creatures, and through his keen observation andanalysis, we become their intimates too.Throughout history there has existed an extraordinary relationship between humans and ravens. Ravens, like early humans, are scavengers on the kills of great carnivores. As scavengers, ravens were associated with hunters they found in the north: wolves and, later, men. The trinity of wolf, man, and raven in the hunt is an extremely ancient one. In considering the appeal of the raven, Bernd Heinrich suspects that a meeting of the minds might reside in that hunting trinity.Heinrich's passion for ravens has led him around the world in his research. Mind of the Raven takes you on an exotic journey--from New England to Germany, Montana to Baffin Island in the high Arctic--offering dazzling accounts of how science works in the field, filtered through the eyes of a passionate observer of nature.Heinrich has a true gift; through his stories, his beautiful writing, illustrations, and photography, the ravens come alive. Each new discovery and insight into their behavior is thrilling to read. just as the title promises, the reader is given a rare glimpse into the mind of these wonderful creatures.Following the dictum of Leonardo da Vinci--"It is not enough to believe what you see. YOU Must also understand what you see"--Bernd Heinrich enables us to see the natural world through the eyes of a scientist. At once lyrical and scientific, Mind of the Raven is bound to be a modern classic.