Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    He was never seen again. In A Brilliant Darkness, theoretical physicist João Magueijo tells the story of Majorana and his research group, “the Via Panisperna Boys,” who discovered atomic fission in 1934. As Majorana, the most brilliant of the group, began to realize the implications of what they had found, he became increasingly unstable. Did he commit suicide that night in Palermo? Was he kidnapped? Did he stage his own death?A Brilliant Darkness chronicles Majorana’s invaluable contributions to science—including his major discovery, the Majorana neutrino—while revealing the truth behind his fascinating and tragic life.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Presenting to the world his remarkable observations using the recently invented telescope--the craters of the moon, the satellites of Jupiter--Galileo dramatically challenged our idea of the perfection of the heavens and the centrality of the Earth in the universe. Indeed, the appearance of the little book is regarded as one of the great moments in the history of science. Planned to coincide with the 400th anniversary of the publication of the Starry Messenger, this is a major new biography of Galileo, a fresh and much more rounded view of the great scientist than found in earlier works. Unlike previous biographers, Heilbron shows us that Galileo was far more than a mathematician: he was deeply knowledgeable in the arts, an expert on the epic poet Ariosto, a fine lutenist. More important, Heilbron notes that years of reading the poets and experimenting with literary forms were not mere sidebars--they enabled Galileo to write clearly and plausibly about the most implausible things. Indeed, Galileo changed the world not simply because he revolutionized astronomy, but because he conveyed his discoveries so clearly and crisply that they could not be avoided or denied. If ever a discoverer was perfectly prepared to make and exploit his discovery, it was the dexterous humanist Galileo aiming his first telescope at the sky. In Galileo, John Heilbron captures not only the great scientist, but also the creative, artistic younger man who would ultimately become the champion of Copernicus, the bête-noire of the Jesuits, and the best-known of all martyrs to academic freedom.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    His inventions, patents, and theoretical work formed the basis of modern AC electricity, and contributed to the development of radio and television. Like his competitor Thomas Edison, Tesla was one of America's first celebrity scientists, enjoying the company of New York high society and dazzling the likes of Mark Twain with his electrical demonstrations. An astute self-promoter and gifted showman, he cultivated a public image of the eccentric genius. Even at the end of his life when he was living in poverty, Tesla still attracted reporters to his annual birthday interview, regaling them with claims that he had invented a particle-beam weapon capable of bringing down enemy aircraft.Plenty of biographies glamorize Tesla and his eccentricities, but until now none has carefully examined what, how, and why he invented. In this groundbreaking book, W. Bernard Carlson demystifies the legendary inventor, placing him within the cultural and technological context of his time, and focusing on his inventions themselves as well as the creation and maintenance of his celebrity. Drawing on original documents from Tesla's private and public life, Carlson shows how he was an idealist inventor who sought the perfect experimental realization of a great idea or principle, and who skillfully sold his inventions to the public through mythmaking and illusion.This major biography sheds new light on Tesla's visionary approach to invention and the business strategies behind his most important technological breakthroughs.

    40 illustrations throughout.

    This work represents the views of a mathematician on the analogies between computing machines and the living human brain.

    “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.

    presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.

    Its tale is one riddled with jealousy, rivalry, missed opportunities and moments of genius. Piers Bizony tells the story of the young misfit New Zealander, Ernest Rutherford, who showed that the atom consisted mainly of empty space, a discovery that turned 200 years of classical physics on its head, and the brilliant Dane, Niels Bohr, who made the next great leap into the incredible world of quantum theory. Yet he and a handful of other Young Turks in this revolutionary new science weren't prepared for the shocks that Nature had up her sleeve. At the dawn of the Atomic Age, a dangerous new force was unleashed with terrifying speed...

    Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman, the course also featured, as occasional guest speakers, some of the most brilliant men in science at that time, including Marvin Minsky, Charles Bennett, and John Hopfield. Although the lectures are now thirteen years old, most of the material is timeless and presents a “Feynmanesque” overview of many standard and some not-so-standard topics in computer science such as reversible logic gates and quantum computers.

    This time physicist Robert Gilmore takes us on a journey with Dorothy, following the yellow building block road through the land of the Wizard of Quarks. Using characters and situations based on the Wizard of Oz story, we learn along the way about the fascinating world of particle physics. Classes of particles, from quarks to leptons are shown in an atomic garden, where atoms and molecules are produced. See how Dorothy, The Tin Geek, and the Cowardly Lion experience the bizarre world of subatomic particles.

    Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating.Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others.For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others."The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.

    It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks." Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists.