Five Equations That Changed the World

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Amir D. Aczel

"Bestselling popular science author Amir Aczel selects the most fascinating individuals and stories in the history of mathematics, presenting a colorful narrative that explores the quirky personalities behind some of the most profound, enduring theorems. Through such mathematical geniuses as Archimedes, Leonardo of Pisa (a.k.a. Fibonacci), Tartaglia ("the stutterer"), Descartes, Gottfried Liebniz, Carl Gauss, Joseph Fourier (Napoleon's mathematician), Evariste Galois, Georg Cantor, Ramanujan, and "Nicholas Bourbaki," we gather little known details about the alliances and rivalries that profoundly impacted the development of what the scheming doctor-turned-mathematician Geronimo Cardano called "The Great Art." This story of mathematics is not your dry "college textbook" account; tales of duels, battlefield heroism, flamboyant arrogance, pranks, secret societies, imprisonment, feuds, theft, and even some fatal errors of judgment fill these pages (clearly, genius doesn't guarantee street smarts). Ultimately, readers will come away from this book entertained, with a newfound appreciation of the tenacity, complexity, eccentricity, and brilliance of the mathematical genius"--

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Douglas R. Hofstadter

Winner of the Pulitzer Prize A metaphorical fugue on minds and machines in the spirit of Lewis Carroll Douglas Hofstadter's book is concerned directly with the nature of "maps" or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

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Peter Poellner

This book offers a new and comprehensive interpretation and a detailed critical assessment of Nietzsche's later ideas on epistemology and metaphysics, drawing extensively not only on his published works but also his voluminous notebooks, largely unpublished in English. The author examines Nietzsche's various distinct lines of thought on the traditionally central areas of philosophy and shows in what specific sense Nietzsche, as he himself claimed, might be said to have moved beyond these questions. Throughout the book, considerable attention is paid both to the historical context of his writings and to subsequent developments in philosophy - English-language as well as Continental European. Among the themes discussed are Nietzsche's relation to scepticism and to evolutionary epistemology; his analysis of 'objective reality' and the associated 'perspectivism'; his criticism of the metaphysician's 'will to truth' and the related analysis of the intellectual paradigm he called the 'ascetic ideal'; his notion of unconscious mental states; and the concept of the will to power and its relation to metaphysics. Dr Poellner, while recognizing the originality of Nietzsche's influential new philosophical paradigm, shows that his thought has closer affinities to the philosophical tradition than is often supposed.

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Frank J. Tipler

Frank J. Tipler is a major theoretician in the field of global general relativity, the rarefied branch of physics created by Stephen Hawking and Roger Penrose. Like most modern scientists, Tipler was an atheist who gave little thought to questions of theology. Yet, in devising a mathematical model of the end of the universe, Tipler came to a stunning conclusion: Using the most advanced and sophisticated methods of modern physics, relying solely on the rigorous procedures of logic that science demands, he had created a proof of the existence of God. Tipler's model of the universal end-time is called the Omega Point Theory. For the last seventeen years, Tipler has explored the implications of the Omega Point Theory, one of which is even more astonishing than the evidence of God's existence: It is not only possible, but likely, that every human being who ever lived will be resurrected from the dead. As Tipler writes in his preface, he arrived at his proofs of God and immortality "in exactly the same way physicists calculate the properties of the electron.". In The Physics of Immortality Tipler guides the general reader through the details of his exhilarating discoveries. Displaying an awesome command of disciplines as diverse as computer science, economics, particle physics, cosmology, and evolutionary biology, Tipler constructs a stunningly plausible argument for God and the universal resurrection. Lucid in style, audacious in aim, breathtaking in scope, powerfully argued, and, finally, deeply moving, this is a book that will change the way you think. No reader, whether skeptic or believer, will look at the universe in the same way after encountering this remarkable work.