Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.

    Most of the major schools of contemporary philosophy, from Marxism to Existentialism, are reactions to Hegelianism and all, if they are to be understood, require some understanding of Hegel's Science of Logic.

    Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.

    Friedmann, Natural Law Forum

    The author's work can serve either as a textbook in a university course on metaphysics or as an introduction to metaphysical thinking for the interested reader. This second edition, revised though not fundamentally changed, includes the basis of the first edition with a new chapter on the nature of time.

    Accessible to serious general readers.

    Two books bound as one.

    From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a simple and lively way. Readers who are more mathematically adventurous will find optional sections introducing rather more challenging material. 'A lively and stimulating book' Philosophy

    Bodily and psychic transformations do nothing but reinforce the permanence of identity. But as a result of serious trauma, or sometimes for no reason at all, a subject's history splits and a new, unprecedented persona comes to live with the former person - an unrecognizable persona whose present comes from no past and whose future harbors nothing to come; an existential improvisation, a form born of the accident and by accident. Out of a deep cut opened in a biography, a new being comes into the world for a second time. What is this form? A face? A psychological profile? What ontology can it account for, if ontology has always been attached to the essential, forever blind to the alea of transformations? What history of being can the plastic power of destruction explain? What can it tell us about the explosive tendency of existence that secretly threatens each one of us? Continuing her reflections on destructive plasticity, split identities and the psychic consequences experienced by those who have suffered brain injury or have been traumatized by war and other catastrophes, Catherine Malabou invites us to join her in a philosophic and literary adventure in which Spinoza, Deleuze and Freud cross paths with Proust and Duras.

    In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity, to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader’s eyes to the hidden reality of the strange yet familiar entities that are numbers.

    Mackie, formerly of University College, Oxford

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    They deal with such broad topics as the relationship between popular and genuine culture, strategies for cultural reform, the task of philosophy, the nature of education, and the relationship among art, science and life. This new edition presents R. J. Hollingdale's translation of the essays and a new introduction by Daniel Breazeale, who places them in their historical context and discusses their significance for Nietzsche's philosophy.

    It is many years since a major work in English has ranged so widely over philosophy's fundamental concerns: the identity of the self, knowledge and skepticism, free will, the question of why there is something rather than nothing, the foundations of ethics, the meaning of life.Writing in a distinctive and personal philosophical voice, Mr. Nozick presents a new mode of philosophizing. In place of the usual semi-coercive philosophical goals of proof, of forcing people to accept conclusions, this book seeks philosophical explanations and understanding, and thereby stays truer to the original motivations for being interested in philosophy.Combining new concepts, daring hypotheses, rigorous reasoning, and playful exploration, the book exemplifies how philosophy can be part of the humanities.