This ideal guide shows us how mathematics can illuminate the human condition.

    This is the amazing story of how the "map problem" was solved.The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm.Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.

    Mathematics, Applied & Natural Sciences

    Tender and joyous, it is a celebration of art's power to transform the darkest of human experience and give voice to the grandest of human hopes.

    Although his writings on philosophical aesthetics have shown him to be a leading authority in the field, his defence of political conservatism has marked him out in academic circles as public enemy number one. Whether it is Scruton's opinions that get up the nose of his critics, or the wit and erudition with which he expresses them, there is no doubt that their noses are vastly distended by his presence, and constantly on the verge of a collective sneeze. Contrary to orthodox opinion, however, Roger Scruton is a human being, and Gentle Regrets contains the proof of it - a quiet, witty but also serious and moving account of the ways in which life brought him to think what he thinks, and to be what he is. His moving vignettes of his childhood and later influences illuminate this book. Love him or hate him, he will engage you in an argument that is both intellectually stimulating and informed by humour.

    After spending two years in bed with Lyme disease, Steven Kotler had lost everything: his health, his job, his girl, and, he was beginning to suspect, his mind. Kotler, not a religious man, suddenly found himself drawn to the sport of surfing as if it were the cornerstone of a new faith. Why, he wondered, when there was nothing left to believe in, could he begin to believe in something as unlikely as surfing. What was belief anyway? How did it work in the body, the brain, our culture, and human history?Into this mix came a strange story. In 2003, on a surf trip through Mexico, Kotler heard of "the conductor," a mythical surfer who could control the weather. He'd heard this same tale eight years earlier, in Indonesia, but this time something clicked. With the help of everyone from rebel surfers to rocket scientists, Kotler undertakes a three year globetrotting quest for the origins of this legend. The results are a startling mix of big waves and bigger ideas: a surfer's journey into the biological underpinnings of belief itself.

    Contains 640 problems including solutions; additional practice problems with answers; explanations of complex variable theory; coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions.

    Our fortunes were once founded on sheep, and this book tells a story of wool and money and history, of merchants and farmers and shepherds, of English yeomen and how they got their freedom, and above all, of the soil. Sheep have helped define our culture and topography, impacting on everything from accent and idiom, architecture, roads and waterways, to social progression and wealth. With his eye for the idiosyncratic, Philip meets the native breeds that thrive in this country; he tells stories about each breed, meets their shepherds and owners, learns about their past - and confronts the present realities of sheep farming. Along the way, Philip meets the people of the countryside and their many professions: the mole-catchers, the stick-makers, the tobacco-twisters and clog-wrights. He explores this artisan heritage as he re-discovers the countryside, and finds a lifestyle parallel to modern existence, struggling to remain unchanged - and at its heart, always sheep.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    What are miracles, and why do so many people believe in them? What do they tell us about ourselves? And what do we do with experiences that we cannot explain? In  Miracles, Eric Metaxas offers compelling -- sometimes electrifying -- evidence that there’s something real to be reckoned with, whatever one has thought of the topic before. Miracles is also a timely, thoughtful, and civil answer to the books of the "New Atheists" -- Richard Dawkins, Christopher Hitchens, and Sam Harris -- who have passionately asserted not just the impossibility of miracles and the supernatural, but the outright harmfulness of belief in them.  Metaxas -- whom ABC News has called a "witty ambassador for faith" -- provides the measured and wide-ranging treatment the subject deserves, from serious discussion of the compatibility between faith and science to astonishing but well-documented stories of actual miracles from people he knows. A more current, anecdotal, and personal version of C. S. Lewis’s 1947 book on the subject, Miracles is a powerfully winsome challenge that miracles are not only possible but are far more widespread than most of us ever might have imagined.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    In Evolution Impossible, Dr. John Ashton uses discoveries in genetics, biochemistry, geology, radiometric dating, and other scientific disciplines to explain why the theory of evolution is a myth. Regardless of your level of scientific education, you will finish this book able to cite 12 reasons why evolution cannot explain the origin of life.

    With a hundred dollars in his pocket, a beat up cavalry saddle, and a faraway look in his eye, John Egenes saddled his horse Gizmo and started down the trail on an adventure across the North American continent. Their seven month journey took them across 11 states from California to Virginia, ocean to ocean.. As they left the pressing confinement of the city behind them, the pair experienced the isolation and loneliness of the southwestern deserts, the vastness of the prairie, and the great landscapes that make up America. Across hundreds of miles of empty land they slept with coyotes and wild horses under the stars, and in urban areas they camped alone in graveyards and abandoned shacks. Along the way John and Gizmo were transformed from inexperienced horse and rider to veterans of the trail. With his young horse as his spiritual guide John slowly began to comprehend his own place in the world and to find peace within himself. Full of heart and humor, Egenes serves up a tale that's as big as the America he witnessed, an America that no longer exists. It was a journey that could only have been experienced step by step, mile by mile, from the view between a horse's ears.

    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.