"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    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.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    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.

    The real identity of the person who chose to write under the pseudonym of Dionysius the Areopagite is unknown. Even the exact dates of his writings have never been determined. Moreover the texts themselves, though relatively short, are at points seemingly impenetrable and have mystified readers over the centuries. Yet the influence of this shadowy figure on broad range of mystical writers from the early middle ages on is readily discernible. His formulation of a method of negative theology that stresses the impotence of humans' attempt to penetrate the "cloud of unknowing" is famous as is his meditation on the divine names.Despite his influence, relatively few attempts have been made to translate the entire corpus of his written into English. Here in one volume are collected all of the Pseudo-Dionysius' works. Each has been translated from the Migne edition, with reference to the forthcoming Göttingen critical edition of A.M. Ritter, G. Heil, and B. Suchla.To present these works to the English-speaking public, an outstanding team of six research scholars has been assembled. The lucid translation of Colm Luibheid has been augmented by Paul Rorem's notes and textual collaboration. The reader is presented a rich and varied examination of the main themes of Dionysian spirituality by René Roques, an incisive discussion of the original questions of the authenticity and alleged heresies in the Dionysian corpus by Jaroslav Pelikan, a comprehensive tracing Dionysius' influence on medieval authors by Jean Leclercq, and a survey by Karlfried Froehlich of the reception given the corpus by Humanists and sixteenth-century Reformers.

    Topics include: Limits, Derivatives, and Integrations.

    Gonick’s The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere.

    Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200 increasingly complex problems. The puzzles delve into Gödel’s undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Detailed solutions follow each puzzle.

    By spinning 28 mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human.

    By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

    Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the real world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century.THE JOY OF MATHEMATICS is designed to be opened at random...it's mini essays are self-contained providing the reader with an enjoyable way to explore and experience mathematics at its best.

    Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    Although each instance of creativity is singular and specific, Kyna Leski tells us, the creative process is universal. Artists, architects, poets, inventors, scientists, and others all navigate the same stages of the process in order to discover something that does not yet exist. All of us must work our way through the empty page, the blank screen, writer's block, confusion, chaos, and doubt. In this book, Leski draws from her observations and experiences as a teacher, student, maker, writer, and architect to describe the workings of the creative process.Leski sees the creative process as being like a storm; it slowly begins to gather and take form until it overtakes us--if we are willing to let it. It is dynamic, continually in motion; it starts, stops, rages and abates, ebbs and flows. In illustrations that accompany each chapter, she maps the arc of the creative process by tracing the path of water droplets traveling the stages of a storm.Leski describes unlearning, ridding ourselves of preconceptions; only when we realize what we don't know can we pose the problem that we need to solve. We gather evidence--with notebook jottings, research, the collection of objects--propelling the process. We perceive and conceive; we look ahead without knowing where we are going; we make connections. We pause, retreat, and stop, only to start again. To illustrate these stages of the process, Leski draws on examples of creative practice that range from Paul Klee to Steve Jobs, from the discovery of continental drift to the design of Antoni Gaud�'s Sagrada Familia.Creativity, Leski tells us, is a path with no beginning or end; it is ongoing. This revelatory view of the creative process will be an essential guide for anyone engaged in creative discovery.The Creative ProcessUnlearningProblem MakingGathering and TrackingPropellingPerceiving and ConceivingSeeing AheadConnectingPausingContinuing