Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    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.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    It is without question Schopenhauer's greatest work. Conceived and published before the philosopher was 30 and expanded 25 years later, it is the summation of a lifetime of thought.For 70 years, the only unabridged English translation of this work was the Haldane-Kemp collaboration. In 1958, a new translation by E. F. J. Payne appeared that decisively supplanted the older one. Payne's translation is superior because it corrects nearly 1,000 errors and omissions in the Haldane-Kemp translation, and it is based on the definitive 1937 German edition of Schopenhauer's work prepared by Dr. Arthur Hübscher. Payne's edition is the first to translate into English the text's many quotations in half a dozen languages. It is thus the most useful edition for the student or teacher.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    This book, which presents Spinoza's main ideas in dictionary form, has as its subject the opposition between ethics and morality, and the link between ethical and ontological propositions. His ethics is an ethology, rather than a moral science. Attention has been drawn to Spinoza by deep ecologists such as Arne Naess, the Norwegian philosopher; and this reading of Spinoza by Deleuze lends itself to a radical ecological ethic. As Robert Hurley says in his introduction, "Deleuze opens us to the idea that the elements of the different individuals we compose may be nonhuman within us. One wonders, finally, whether Man might be defined as a territory, a set of boundaries, a limit on existence."Gilles Deleuze, known for his inquiries into desire, language, politics, and power, finds a kinship between Spinoza and Nietzsche. He writes, "Spinoza did not believe in hope or even in courage; he believed only in joy and in vision . . . he more than any other gave me the feeling of a gust of air from behind each time I read him, of a witch's broom that he makes one mount."Gilles Deleuze (1925-1995) was a French philosopher whose writings influenced many philosophical disciplines such as literary theory, post-structuralism, and postmodernism. He also taught philosophy at the University of Paris at Vicennes.Robert Hurley was a translator for many French philosophers including Michael Foucault (History of Sexuality), Gilles Deleuze, and George Bataille (Theory of Religion).

    It is also an exploration of some of the preeminent thinkers of the seventeenth and eighteenth centuries, such as Descartes, Newton, Locke, and Kant.The ultimate edition of Whitehead’s magnum opus, Process and Reality is a standard reference for scholars of all backgrounds.

    Like you, the elements have lives: personalities and attitudes, talents and shortcomings, stories rich with meaning. You may think of them as the inscrutable letters of the periodic table but you know them much better than you realise. Welcome to a dazzling tour through history and literature, science and art. Here you'll meet iron that rains from the heavens and noble gases that light the way to vice. You'll learn how lead can tell your future while zinc may one day line your coffin. You'll discover what connects the bones in your body with the Whitehouse in Washington, the glow of a streetlamp with the salt on your dinner table. From ancient civilisations to contemporary culture, from the oxygen of publicity to the phosphorus in your pee, the elements are near and far and all around us. Unlocking their astonishing secrets and colourful pasts, Periodic Tales will take you on a voyage of wonder and discovery, excitement and novelty, beauty and truth. Along the way, you'll find that their stories are our stories, and their lives are inextricable from our own.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    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.

    It presents a profound and challenging investigation into the nature of human reason, its knowledge and its illusions. Reason, Kant argues, is the seat of certain concepts that precede experience and make it possible, but we are not therefore entitled to draw conclusions about the natural world from these concepts. The Critique brings together the two opposing schools of philosophy: rationalism, which grounds all our knowledge in reason, and empiricism, which traces all our knowledge to experience. Kant's transcendental idealism indicates a third way that goes far beyond these alternatives.

    A scholar, wit, lawyer and statesman, he wrote widely on politics, philosophy and science - declaring early in his career that 'I have taken all knowledge as my province'. In this, his most famous work, he considers a diverse range of subjects, such as death and marriage, ambition and atheism, in prose that is vibrant and rich in Renaissance learning. Bacon believed that rhetoric - the force of eloquence and persuasion - could lead the mind to the pure light of reason, and his own rhetorical genius is nowhere better expressed than in these vivid essays.

    In his acclaimed book―based on his legendary Harvard course―Sandel offers a rare education in thinking through the complicated issues and controversies we face in public life today. It has emerged as a most lucid and engaging guide for those who yearn for a more robust and thoughtful public discourse. "In terms we can all understand," wrote Jonathan Rauch in The New York Times, Justice "confronts us with the concepts that lurk . . . beneath our conflicts."Affirmative action, same-sex marriage, physician-assisted suicide, abortion, national service, the moral limits of markets―Sandel relates the big questions of political philosophy to the most vexing issues of the day, and shows how a surer grasp of philosophy can help us make sense of politics, morality, and our own convictions as well.Justice is lively, thought-provoking, and wise―an essential new addition to the small shelf of books that speak convincingly to the hard questions of our civic life.

    For this question and other ones like it have been the stuff of philosophical rumination from Plato to Popper. In a series of accessible and engagingly written essays, "50 Philosophy Ideas You Really Need to Know" introduces and explains the problems of knowledge, consciousness, identity, ethics, belief, justice and aesthetics that have engaged the attention of thinkers from the era of the ancient Greeks to the present day.