Our eyes and minds are drawn to symmetrical objects, from the pyramid to the pentagon. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. In chemistry and physics, the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; and symmetry—and the breaking of it—is central to ideas in art, architecture, and music.Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry's elusive qualities. He explores what is perhaps the most exciting discovery to date—the summit of mathematicians' mastery in the field—the Monster, a huge snowflake that exists in 196,883-dimensional space with more symmetries than there are atoms in the sun.What is it like to solve an ancient mathematical problem in a flash of inspiration? What is it like to be shown, ten minutes later, that you've made a mistake? What is it like to see the world in mathematical terms, and what can that tell us about life itself? In Symmetry, Marcus du Sautoy investigates these questions and shows mathematical novices what it feels like to grapple with some of the most complex ideas the human mind can comprehend.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the humanist idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

    Walter Sinnott-Armstrong argues that God is not only not essential to morality, but that our moral behavior should be utterly independent of religion. He attacks several core ideas: that atheists are inherently immoral people; that any society will sink into chaos if it is becomes too secular; that without religion, we have no reason to be moral; that absolute moral standards require the existence of God; and that without religion, we simply couldn't know what is wrong and what is right.Sinnott-Armstrong brings to bear convincing examples and data, as well as a lucid, elegant, and easy to understand writing style. This book should fit well with the debates raging over issues like evolution and intelligent design, atheism, and religion and public life as an example of a pithy, tightly-constructed argument on an issue of great social importance.In his call for sincere dialogue with theists, Sinnott-Armstrong provides a welcome relief from the apoplectic excesses of Richard Dawkins and Christopher Hitchens, while also addressing objections to homosexuality and evolution frequently raised by evangelical Christians. --Publishers Weekly [I]t is accessible and lively, my hope is that it will be widely read, especially by theists.--Peter Lamal, The Humanist ... the clarity of this text successfully defuses many erroneous claims about religion and morality, both popular and academic; this volume certainly deserves a wide audience in this increasingly secular and skeptical world. -ChoiceMorality Without God? is an engaging, pithy book arguing against the necessity of God and religion for a robust morality. Walter Sinnott-Armstrong has distinguished himself as a leading philosopher in his work on metaethics and moral psychology, as well as books on moral and epistemological skepticism, and in Morality Without God? he commendably succeeds in writing a philosophically respectable introduction to the problems facing religious morality suitable for virtually any audience. --Philosophia Christi

    Next, he examines the three critiques that currently challenge this classic Darwinian edifice: that selection operates on multiple levels, from the gene to the group; that evolution proceeds by a variety of mechanisms, not just natural selection; and that causes operating at broader scales, including catastrophes, have figured prominently in the course of evolution.Then, in a stunning tour de force that will likely stimulate discussion and debate for decades, Gould proposes his own system for integrating these classical commitments and contemporary critiques into a new structure of evolutionary thought.In 2001 the Library of Congress named Stephen Jay Gould one of America's eighty-three Living Legends--people who embody the quintessentially American ideal of individual creativity, conviction, dedication, and exuberance. Each of these qualities finds full expression in this peerless work, the likes of which the scientific world has not seen--and may not see again--for well over a century.

    However, Todd May organizes his introduction around a central question at the heart of Deleuze's philosophy: How might we live? He demonstrates how Deleuze offers a view of the cosmos as a living entity that provides ways of conducting our lives that we may not have even dreamed of.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    Francis Bacon held some of the highest public offices in the land and in his spare time studied natural philosophy and a wide variety of other subjects. His systematic classification of all branches of knowledge became the basis for all later constructions, and his Essays are unsurpassed in their observations on society and human behavior. This extensive anthology includes the major English literary works on which his reputation rests: The Advancement of Learning, The Essays (1625, as well as the earliest version of 1597), and the posthumously published Utopian fable The New Atlantis (1626). In addition it reprints other works which illustrate Bacon's abilities in politics, law, theology, and poetry. A special feature of the edition is its extensive annotation which identifies Bacon's sources and allusions, and elucidates his vocabulary.

    G. Wells predicted that statistical thinking would be as necessary for citizenship in a technological world as the ability to read and write. But in the twenty-first century, we are often overwhelmed by a baffling array of percentages and probabilities as we try to navigate in a world dominated by statistics. Cognitive scientist Gerd Gigerenzer says that because we haven't learned statistical thinking, we don't understand risk and uncertainty. In order to assess risk -- everything from the risk of an automobile accident to the certainty or uncertainty of some common medical screening tests -- we need a basic understanding of statistics.Astonishingly, doctors and lawyers don't understand risk any better than anyone else. Gigerenzer reports a study in which doctors were told the results of breast cancer screenings and then were asked to explain the risks of contracting breast cancer to a woman who received a positive result from a screening. The actual risk was small because the test gives many false positives. But nearly every physician in the study overstated the risk. Yet many people will have to make important health decisions based on such information and the interpretation of that information by their doctors.Gigerenzer explains that a major obstacle to our understanding of numbers is that we live with an illusion of certainty. Many of us believe that HIV tests, DNA fingerprinting, and the growing number of genetic tests are absolutely certain. But even DNA evidence can produce spurious matches. We cling to our illusion of certainty because the medical industry, insurance companies, investment advisers, and election campaigns have become purveyors of certainty, marketing it like a commodity.To avoid confusion, says Gigerenzer, we should rely on more understandable representations of risk, such as absolute risks. For example, it is said that a mammography screening reduces the risk of breast cancer by 25 percent. But in absolute risks, that means that out of every 1,000 women who do not participate in screening, 4 will die; while out of 1,000 women who do, 3 will die. A 25 percent risk reduction sounds much more significant than a benefit that 1 out of 1,000 women will reap.This eye-opening book explains how we can overcome our ignorance of numbers and better understand the risks we may be taking with our money, our health, and our lives.

    This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set- theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    In The Monstrosity of Christ, Žižek and Milbank go head to head for three rounds, employing an impressive arsenal of moves to advance their positions and press their respective advantages. By the closing bell, they have not only proven themselves worthy adversaries, they have shown that faith and reason are not simply and intractably opposed. Žižek has long been interested in the emancipatory potential offered by Christian theology. And Milbank, seeing global capitalism as the new century's greatest ethical challenge, has pushed his own ontology in more political and materialist directions.Their debate in The Monstrosity of Christ concerns the future of religion, secularity, and political hope in light of a monsterful event—God becoming human. For the first time since Žižek's turn toward theology, we have a true debate between an atheist and a theologian about the very meaning of theology, Christ, the Church, the Holy Ghost, Universality, and the foundations of logic. The result goes far beyond the popularized atheist/theist point/counterpoint of recent books by Christopher Hitchens, Richard Dawkins, and others. Žižek begins, and Milbank answers, countering dialectics with “paradox.” The debate centers on the nature of and relation between paradox and parallax, between analogy and dialectics, between transcendent glory and liberation.

    The remaining lectures build on that idea, examining the possibility of building a relativistic quantum theory on curved surfaces or flat surfaces.

    

    These profound teachings point the way to love, peace, bliss and freedom, encouraging a transformation of consciousness and spiritual awakening.