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.

    Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.Also available as an eBook

    “They are both brilliantly original and outsiders,” the narrator tells us. “They are both besotted with mathematics. But for all their devotion, mathematics is indifferent, unaltered by any of their dramas . . . Against indifference, I want to tell their stories.” Which she does in a haunting, incantatory voice, the two lives unfolding in parallel narratives that overlap in the magnitude of each man’s achievement and demise: Gödel, delusional and paranoid, would starve himself to death; Turing, arrested for homosexual activities, would be driven to suicide. And they meet as well in the narrator’s mind, where facts are interwoven with her desire and determination to find meaning in the maze of their stories: two men devoted to truth of the highest abstract nature, yet unable to grasp the mundane truths of their own lives.A unique amalgam of luminous imagination and richly evoked historic character and event—A Madman Dreams of Turing Machines is a story about the pursuit of truth and its effect on the lives of two men. A story of genius and madness, incredible yet true.

    Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories.Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores what that implies and why some founders of the theory became the foremost objectors to it. Schr�dinger showed that it absurdly allowed a cat to be in a superposition simultaneously dead and alive. Einstein derided the theory's spooky interactions. With Bell's Theorem, we now know Schr�dinger's superpositions and Einstein's spooky interactions indeed exist.Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation.Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial.Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing.Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves.

    From the sudden expansion of a cloud of gas to the cooling of hot metal--everything is moved or restrained by four simple laws. Written by Peter Atkins, one of the world's leading authorities on thermodynamics, this powerful and compact introduction explains what these four laws are and how they work, using accessible language and virtually no mathematics. Guiding the reader a step at a time, Atkins begins with Zeroth (so named because the first two laws were well established before scientists realized that a third law, relating to temperature, should precede them--hence the jocular name zeroth), and proceeds through the First, Second, and Third Laws, offering a clear account of concepts such as the availability of work and the conservation of energy. Atkins ranges from the fascinating theory of entropy (revealing how its unstoppable rise constitutes the engine of the universe), through the concept of free energy, and to the brink, and then beyond the brink, of absolute zero. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.

    At its heart is the discovery of the order that lies deep within the most complex of systems, from the origin of life, to the workings of giant corporations, to the rise and fall of greatcivilizations. And more than anyone else, this revolution is the work of one man, Stuart Kauffman, a MacArthur Fellow and visionary pioneer of the new science of complexity. Now, in At Home in the Universe, Kauffman brilliantly weaves together the excitement of intellectual discovery and a fertilemix of insights to give the general reader a fascinating look at this new science--and at the forces for order that lie at the edge of chaos. We all know of instances of spontaneous order in nature--an oil droplet in water forms a sphere, snowflakes have a six-fold symmetry. What we are only now discovering, Kauffman says, is that the range of spontaneous order is enormously greater than we had supposed. Indeed, self-organization is agreat undiscovered principle of nature. But how does this spontaneous order arise? Kauffman contends that complexity itself triggers self-organization, or what he calls order for free, that if enough different molecules pass a certain threshold of complexity, they begin to self-organize into a newentity--a living cell. Kauffman uses the analogy of a thousand buttons on a rug--join two buttons randomly with thread, then another two, and so on. At first, you have isolated pairs; later, small clusters; but suddenly at around the 500th repetition, a remarkable transformation occurs--much likethe phase transition when water abruptly turns to ice--and the buttons link up in one giant network. Likewise, life may have originated when the mix of different molecules in the primordial soup passed a certain level of complexity and self-organized into living entities (if so, then life is not ahighly improbable chance event, but almost inevitable). Kauffman uses the basic insight of order for free to illuminate a staggering range of phenomena. We see how a single-celled embryo can grow to a highly complex organism with over two hundred different cell types. We learn how the science ofcomplexity extends Darwin's theory of evolution by natural selection: that self-organization, selection, and chance are the engines of the biosphere. And we gain insights into biotechnology, the stunning magic of the new frontier of genetic engineering--generating trillions of novel molecules tofind new drugs, vaccines, enzymes, biosensors, and more. Indeed, Kauffman shows that ecosystems, economic systems, and even cultural systems may all evolve according to similar general laws, that tissues and terra cotta evolve in similar ways. And finally, there is a profoundly spiritual element toKauffman's thought. If, as he argues, life were bound to arise, not as an incalculably improbable accident, but as an expected fulfillment of the natural order, then we truly are at home in the universe. Kauffman's earlier volume, The Origins of Order, written for specialists, received lavish praise. Stephen Jay Gould called it a landmark and a classic. And Nobel Laureate Philip Anderson wrote that there are few people in this world who ever ask the right questions of science, and they are theones who affect its future most profoundly. Stuart Kauffman is one of these. In At Home in the Universe, this visionary thinker takes you along as he explores new insights into the nature of life.

     In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone.Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

    “I walk with a new spring in my step and I look at life through physics-colored eyes,” wrote one such fan. When Lewin’s lectures were made available online, he became an instant YouTube celebrity, and The New York Times declared, “Walter Lewin delivers his lectures with the panache of Julia Child bringing French cooking to amateurs and the zany theatricality of YouTube’s greatest hits.” For more than thirty years as a beloved professor at the Massachusetts Institute of Technology, Lewin honed his singular craft of making physics not only accessible but truly fun, whether putting his head in the path of a wrecking ball, supercharging himself with three hundred thousand volts of electricity, or demonstrating why the sky is blue and why clouds are white. Now, as Carl Sagan did for astronomy and Brian Green did for cosmology, Lewin takes readers on a marvelous journey in For the Love of Physics, opening our eyes as never before to the amazing beauty and power with which physics can reveal the hidden workings of the world all around us. “I introduce people to their own world,” writes Lewin, “the world they live in and are familiar with but don’t approach like a physicist—yet.” Could it be true that we are shorter standing up than lying down? Why can we snorkel no deeper than about one foot below the surface? Why are the colors of a rainbow always in the same order, and would it be possible to put our hand out and touch one? Whether introducing why the air smells so fresh after a lightning storm, why we briefly lose (and gain) weight when we ride in an elevator, or what the big bang would have sounded like had anyone existed to hear it, Lewin never ceases to surprise and delight with the extraordinary ability of physics to answer even the most elusive questions. Recounting his own exciting discoveries as a pioneer in the field of X-ray astronomy—arriving at MIT right at the start of an astonishing revolution in astronomy—he also brings to life the power of physics to reach into the vastness of space and unveil exotic uncharted territories, from the marvels of a supernova explosion in the Large Magellanic Cloud to the unseeable depths of black holes. “For me,” Lewin writes, “physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.” His wonderfully inventive and vivid ways of introducing us to the revelations of physics impart to us a new appreciation of the remarkable beauty and intricate harmonies of the forces that govern our lives.

    Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men.  Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.  This absorbing narrative of people, science and ideas  chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it.  Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

    Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

    Most know Richard Feynman for the hilarious anecdotes and exploits in his best-selling books Surely You're Joking, Mr. Feynman! and What DoYou Care What Other People Think? But not always obvious in those stories was his brilliance as a pure scientist—one of the century's greatest physicists. With this book and CD, we hear the voice of the great Feynman in all his ingenuity, insight, and acumen for argument. This breathtaking lecture—"The Motion of the Planets Around the Sun"—uses nothing more advanced than high-school geometry to explain why the planets orbit the sun elliptically rather than in perfect circles, and conclusively demonstrates the astonishing fact that has mystified and intrigued thinkers since Newton: Nature obeys mathematics. David and Judith Goodstein give us a beautifully written short memoir of life with Feynman, provide meticulous commentary on the lecture itself, and relate the exciting story of their effort to chase down one of Feynman's most original and scintillating lectures.

    Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.

    In so doing, he reaches a provocative conclusion: science, the main tool we use to find answers, is fundamentally limited.These limits to our knowledge arise both from our tools of exploration and from the nature of physical reality: the speed of light, the uncertainty principle, the impossibility of seeing beyond the cosmic horizon, the incompleteness theorem, and our own limitations as an intelligent species. Recognizing limits in this way, Gleiser argues, is not a deterrent to progress or a surrendering to religion. Rather, it frees us to question the meaning and nature of the universe while affirming the central role of life and ourselves in it. Science can and must go on, but recognizing its limits reveals its true mission: to know the universe is to know ourselves.Telling the dramatic story of our quest for understanding, The Island of Knowledge offers a highly original exploration of the ideas of some of the greatest thinkers in history, from Plato to Einstein, and how they affect us today. An authoritative, broad-ranging intellectual history of our search for knowledge and meaning, The Island of Knowledge is a unique view of what it means to be human in a universe filled with mystery.

    Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The language of symbols and infinitely large (and small) regions of mathematics should be rendered with clarity for the general reader.