But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    In this unconventional introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind's enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

    Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

    It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we'd have no nuclear power or nuclear bombs, no lasers, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering—at all. John Gribbin tells the complete story of quantum mechanics, a truth far stranger than any fiction. He takes us step-by-step into an ever more bizarre and fascinating place—requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrödinger's Cat—a search for quantum reality—as he brings every reader to a clear understanding of the most important area of scientific study today—quantum physics.

    For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    Dozens of examples in innumeracy show us how it affects not only personal economics and travel plans, but explains mis-chosen mates, inappropriate drug-testing, and the allure of pseudo-science.

    Puchner introduces us to numerous visionaries as he explores sixteen foundational texts selected from more than four thousand years of world literature and reveals how writing has inspired the rise and fall of empires and nations, the spark of philosophical and political ideas, and the birth of religious beliefs. Indeed, literature has touched the lives of generations and changed the course of history.At the heart of this book are works, some long-lost and rediscovered, that have shaped civilization: the first written masterpiece, the Epic of Gilgamesh; Ezra’s Hebrew Bible, created as scripture; the teachings of Buddha, Confucius, Socrates, and Jesus; and the first great novel in world literature, The Tale of Genji, written by a Japanese woman known as Murasaki. Visiting Baghdad, Puchner tells of Scheherazade and the stories of One Thousand and One Nights, and in the Americas we watch the astonishing survival of the Maya epic Popol Vuh. Cervantes, who invented the modern novel, battles pirates both real (when he is taken prisoner) and literary (when a fake sequel to Don Quixote is published). We learn of Benjamin Franklin’s pioneering work as a media entrepreneur, watch Goethe discover world literature in Sicily, and follow the rise in influence of The Communist Manifesto. We visit Troy, Pergamum, and China, and we speak with Nobel laureates Derek Walcott in the Caribbean and Orhan Pamuk in Istanbul, as well as the wordsmiths of the oral epic Sunjata in West Africa.Throughout The Written World, Puchner’s delightful narrative also chronicles the inventions—writing technologies, the printing press, the book itself—that have shaped religion, politics, commerce, people, and history. In a book that Elaine Scarry has praised as “unique and spellbinding,” Puchner shows how literature turned our planet into a written world.

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    In Turing’s Cathedral, George Dyson focuses on a small group of men and women, led by John von Neumann at the Institute for Advanced Study in Princeton, New Jersey, who built one of the first computers to realize Alan Turing’s vision of a Universal Machine. Their work would break the distinction between numbers that mean things and numbers that do things—and our universe would never be the same. Using five kilobytes of memory (the amount allocated to displaying the cursor on a computer desktop of today), they achieved unprecedented success in both weather prediction and nuclear weapons design, while tackling, in their spare time, problems ranging from the evolution of viruses to the evolution of stars. Dyson’s account, both historic and prophetic, sheds important new light on how the digital universe exploded in the aftermath of World War II. The proliferation of both codes and machines was paralleled by two historic developments: the decoding of self-replicating sequences in biology and the invention of the hydrogen bomb. It’s no coincidence that the most destructive and the most constructive of human inventions appeared at exactly the same time.  How did code take over the world? In retracing how Alan Turing’s one-dimensional model became John von Neumann’s two-dimensional implementation, Turing’s Cathedral offers a series of provocative suggestions as to where the digital universe, now fully three-dimensional, may be heading next.

    Gould's brilliant, funny, engaging prose dissects the motivations behind those who would judge intelligence, and hence worth, by cranial size, convolutions, or score on extremely narrow tests. How did scientists decide that intelligence was unipolar and quantifiable? Why did the standard keep changing over time? Gould's answer is clear and simple: power maintains itself. European men of the 19th century, even before Darwin, saw themselves as the pinnacle of creation and sought to prove this assertion through hard measurement. When one measure was found to place members of some "inferior" group such as women or Southeast Asians over the supposedly rightful champions, it would be discarded and replaced with a new, more comfortable measure. The 20th-century obsession with numbers led to the institutionalization of IQ testing and subsequent assignment to work (and rewards) commensurate with the score, shown by Gould to be not simply misguided--for surely intelligence is multifactorial--but also regressive, creating a feedback loop rewarding the rich and powerful. The revised edition includes a scathing critique of Herrnstein and Murray's The Bell Curve, taking them to task for rehashing old arguments to exploit a new political wave of uncaring belt tightening. It might not make you any smarter, but The Mismeasure of Man will certainly make you think.--Rob LightnerThis edition is revised and expanded, with a new introduction