xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    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.

    Albert-László Barabási, the nation’s foremost expert in the new science of networks and author of Bursts, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information. Just as James Gleick and the Erdos–Rényi model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barabási–Albert model.

    Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, computation, and knowledge with quantum physics. Considered jointly, these four strands of explanation reveal a unified fabric of reality that is both objective and comprehensible, the subject of this daring, challenging book. The Fabric of Reality explains and connects many topics at the leading edge of current research and thinking, such as quantum computers (which work by effectively collaborating with their counterparts in other universes), the physics of time travel, the comprehensibility of nature and the physical limits of virtual reality, the significance of human life, and the ultimate fate of the universe. Here, for scientist and layperson alike, for philosopher, science-fiction reader, biologist, and computer expert, is a startlingly complete and rational synthesis of disciplines, and a new, optimistic message about existence.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces basic counting systems; significant numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; how numbers affect architecture. Lundy explains why the ideas of Pythagoras still resonate, and she profiles each number from one to ten to show its distinct qualities: why, for example, the golden section is associated with five, and seven with the Virgin Mary.

    For even as she sets out to determine how big “really big” may be, Levin gives us an intimate look at the day-to-day life of a globe-trotting physicist, complete with jet lag and romantic disturbances.Nimbly synthesizing geometry, topology, chaos and string theories, Levin shows how the pattern of hot and cold spots left over from the big bang may one day reveal the size and shape of the cosmos. She does so with such originality, lucidity—and even poetry—that How the Universe Got Its Spots becomes a thrilling and deeply personal communication between a scientist and the lay reader.

    This indispensable collection of forty-eight pieces from his brilliant oeuvre includes selections from classics such as Ever Since Darwin and The Mismeasure of Man, plus articles and speeches never before published in book form.This volume, the last that will bear his name, spotlights his elegance, depth, and sheer pleasure in our world—a true celebration of an extraordinary mind.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    New emphasis has been given to complexity, networks, and patterns of organisation, leading to a novel kind of 'systemic' thinking. This volume integrates the ideas, models, and theories underlying the systems view of life into a single coherent framework. Taking a broad sweep through history and across scientific disciplines, the authors examine the appearance of key concepts such as autopoiesis, dissipative structures, social networks, and a systemic understanding of evolution. The implications of the systems view of life for health care, management, and our global ecological and economic crises are also discussed. Written primarily for undergraduates, it is also essential reading for graduate students and researchers interested in understanding the new systemic conception of life and its implications for a broad range of professions - from economics and politics to medicine, psychology and law.

     Ignoring the boundaries of disciplines and schools and searching for novel fundamental ideas, theories, and practices, this international community integrates the full range of scientific inquiries that will help us to understand and survive on a complex planet. This volume collects essays from the past thirty years of research, in which contributors explain in clear and accessible language many of the deepest challenges and insights of complexity science. Explore the evolution of complex systems science with chapters from Nobel Laureates Murray Gell-Mann and Kenneth Arrow, as well as numerous pioneering complexity researchers, including John Holland, Brian Arthur, Robert May, Richard Lewontin, Jennifer Dunne, and Geoffrey West.

    But in Art & Physics, Leonard Shlain tracks their breakthroughs side by side throughout history to reveal an astonishing correlation of visions.From teh classical Greek sculptors to Andy Warhol and Jasper Johns, and from Aristotle to Einstein, aritsts have foreshadowed the discoveries of scientists, such as when Money and Cezanne intuited the coming upheaval in physics that Einstein would initiate. In this lively and colorful narrative, Leonard Shlain explores how artistic breakthroughs could have prefigured the visionary insights of physicists on so many occasions throughtout history.Provacative and original, Art & Physics is a seamless integration of the romance of art and the drama of science...and exhilarating history of ideas.

    "The Theory of Everything" presents the most complex theories, both past and present, of physics; yet it remains clear and accessible. It will enlighten readers and expose them to the rich history of scientific thought and the complexities of the universe in which we live.

    Now astrophysicist John Gribbin draws on his expertise to explore, in prose that communicates not only the wonder but the substance of cutting-edge science, the principles behind chaos and complexity. He reveals the remarkable ways these two revolutionary theories have been applied over the last twenty years to explain all sorts of phenomena–from weather patterns to mass extinctions.Grounding these paradigm-shifting ideas in their historical context, Gribbin also traces their development from Newton to Darwin to Lorenz, Prigogine, and Lovelock, demonstrating how–far from overturning all that has gone before–chaos and complexity are the triumphant extensions of simple scientific laws. Ultimately, Gribbin illustrates how chaos and complexity permeate the universe on every scale, governing the evolution of life and galaxies alike.

    Now Sobel brings her full talents to bear on what is perhaps her most ambitious topic to date-the planets of our solar system. Sobel explores the origins and oddities of the planets through the lens of popular culture, from astrology, mythology, and science fiction to art, music, poetry, biography, and history. Written in her characteristically graceful prose, The Planets is a stunningly original celebration of our solar system and offers a distinctive view of our place in the universe. * A New York Times extended bestseller * A Featured Alternate of the Book-of-the-Month Club, History Book Club, Scientific American Book Club, and Natural Science Book Club * Includes 11 full-color illustrations by artist Lynette R. Cook BACKCOVER: "[The Planets] lets us fall in love with the heavens all over again." -The New York Times Book Review "Playful . . . lyrical . . . a guided tour so imaginative that we forget we're being educated as we're being entertained." -Newsweek " [Sobel] has outdone her extraordinary talent for keeping readers enthralled. . . . Longitude and Galileo's Daughter were exciting enough, but The Planets has a charm of its own . . . . A splendid and enticing book." -San Francisco Chronicle "A sublime journey. [Sobel's] writing . . . is as bright as the sun and its thinking as star-studded as the cosmos." -The Atlanta Journal-Constitution "An incantatory serenade to the Solar System. Grade A-" -Entertainment Weekly "Like Sobel's [Longitude and Galileo's Daughter] . . . [The Planets] combines masterful storytelling with clear, engaging explanations of the essential scientific facts." -Physics World