As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    The effects of homeopathy don’t go away under rigorous scientific conditions. The laws of nature aren’t what they used to be. Thirty years on, no one has an explanation for a seemingly intelligent signal received from outer space. The US Department of Energy is re-examining cold fusion because the experimental evidence seems too solid to ignore. The placebo effect is put to work in medicine while doctors can’t agree whether it even exists.In an age when science is supposed to be king, scientists are beset by experimental results they simply can’t explain. But, if the past is anything to go by, these anomalies contain the seeds of future revolutions. While taking readers on an entertaining tour d’horizon of the strangest of scientific findings – involving everything from our lack of free will to Martian methane that offers new evidence of life on the planet – Michael Brooks argues that the things we don’t understand are the key to what we are about to discover.This mind-boggling but entirely accessible survey of the outer limits of human knowledge is based on a short article by Michael Brooks for New Scientist magazine. It became the sixth most circulated story on the internet in 2005, and provoked widespread comment and compliments (Google “13 things that do not make sense” to see).Michael Brooks has now dug deeply into those mysteries, with extraordinary results.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    From Quantum Mechanics to Natural Selection, what we have instead are theories - ideas explain why things happen the way they do. We don't know for certain these are correct - no one ever saw the Big Bang - but with them we can paint beautiful, breathtaking pictures of everything from human behaviour to what the future may hold. Profiling the key scientists behind each theory, "30-Second Theories" presents each entry in a unique, eye-catching full-colour design, with thought-provoking extras and stylish illustrations. It is essential for anyone keen on expanding their mind with science's most thrilling ideas.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context.  Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.

    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.

    In Consilience  (a word that originally meant "jumping together"), Edward O. Wilson renews the Enlightenment's search for a unified theory of knowledge in disciplines that range from physics to biology, the social sciences and the humanities.Using the natural sciences as his model, Wilson forges dramatic links between fields. He explores the chemistry of the mind and the genetic bases of culture. He postulates the biological principles underlying works of art from cave-drawings to Lolita. Presenting the latest findings in prose of wonderful clarity and oratorical eloquence, and synthesizing it into a dazzling whole, Consilience is science in the path-clearing traditions of Newton, Einstein, and Richard Feynman.

    He turns out to be a bird who discusses maths with anyone who will listen. So when Mr Ruche learns of his friend's mysterious death in the rainforests of Brazil he decides that with the parrot's help he will use these books to teach Max and his twin brother and sister the mysteries and wonders of numbers and shapes.But soon it becomes clear that Mr Ruche has inherited the library for reasons other than pure enlightenment, and before he knows it the household are caught up in a race to prevent the vital theorems falling into the wrong hands.Charming, fresh, with a narrative which races along, the novel takes the reader on a delightful journey through the history of mathematics.

    Here is the Naked Ape at his most primal in love, at work, at war. Meet man as he really is: relative to the apes, stripped of his veneer as we see him courting, making love, sleeping, socializing, grooming, playing. The Naked Ape takes its place alongside Darwin’s Origin of the Species, presenting man not as a fallen angel, but as a risen ape, remarkable in his resilience, energy and imagination, yet an animal nonetheless, in danger of forgetting his origins. With its penetrating insights on man's beginnings, sex life, habits and our astonishing bonds to the animal kingdom, The Naked Ape is a landmark, at once provocative, compelling and timeless.

    Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, computation, and knowledge with quantum physics. Considered jointly, these four strands of explanation reveal a unified fabric of reality that is both objective and comprehensible, the subject of this daring, challenging book. The Fabric of Reality explains and connects many topics at the leading edge of current research and thinking, such as quantum computers (which work by effectively collaborating with their counterparts in other universes), the physics of time travel, the comprehensibility of nature and the physical limits of virtual reality, the significance of human life, and the ultimate fate of the universe. Here, for scientist and layperson alike, for philosopher, science-fiction reader, biologist, and computer expert, is a startlingly complete and rational synthesis of disciplines, and a new, optimistic message about existence.

    In The Mind of God, physicist Paul Davies explores whether modern science can provide the key that will unlock this last secret. In his quest for an ultimate explanation, Davies reexamines the great questions that have preoccupied humankind for millennia, and in the process explores, among other topics, the origin and evolution of the cosmos, the nature of life and consciousness, and the claim that our universe is a kind of gigantic computer. Charting the ways in which the theories of such scientists as Newton, Einstein, and more recently Stephen Hawking and Richard Feynman have altered our conception of the physical universe. Davies puts these scientists' discoveries into context with the writings of philosophers such as Plato. Descartes, Hume, and Kant. His startling conclusion is that the universe is "no minor byproduct of mindless, purposeless forces. We are truly meant to be here." By the means of science, we can truly see into the mind of God.

    In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    Michael Hanlon identifies ten scientific questions that we simply can't seem to answer and explains why these compelling mysteries will remain unsolved for years to comeHow did life begin? Why are there two sexes? Where did language originate? In Hanlon's characteristically witty style, he ponders the ways these questions have persisted in frustrating the best minds and asks what might be needed to get to the bottom of it all. From politics to lack of technology, each question has its own set of circumstances holding it back. By exploring these unanswerable questions, Hanlon exposes some of science's greatest failings and missteps--and charts a hopeful direction for getting science back on the road to discovery.