Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

    . . a book that enriches our understanding of how the struggle to think new thoughts is shared across time and space and people.”—The Sunday Telegraph (London)Christmas, 1859. Just one month after the publication of On the Origin of Species, Charles Darwin received an unsettling letter. He had expected criticism; in fact, letters were arriving daily, most expressing outrage and accusations of heresy. But this letter was different. It accused him of failing to acknowledge his predecessors, of taking credit for a theory that had already been discovered by others. Darwin realized that he had made an error in omitting from Origin of Species any mention of his intellectual forebears. Yet when he tried to trace all of the natural philosophers who had laid the groundwork for his theory, he found that history had already forgotten many of them.Darwin’s Ghosts tells the story of the collective discovery of evolution, from Aristotle, walking the shores of Lesbos with his pupils, to Al-Jahiz, an Arab writer in the first century, from Leonardo da Vinci, searching for fossils in the mine shafts of the Tuscan hills, to Denis Diderot in Paris, exploring the origins of species while under the surveillance of the secret police, and the brilliant naturalists of the Jardin de Plantes, finding evidence for evolutionary change in the natural history collections stolen during the Napoleonic wars. Evolution was not discovered single-handedly, Rebecca Stott argues, contrary to what has become standard lore, but is an idea that emerged over many centuries, advanced by daring individuals across the globe who had the imagination to speculate on nature’s extraordinary ways, and who had the courage to articulate such speculations at a time when to do so was often considered heresy.With each chapter focusing on an early evolutionary thinker, Darwin’s Ghosts is a fascinating account of a diverse group of individuals who, despite the very real dangers of challenging a system in which everything was presumed to have been created perfectly by God, felt compelled to understand where we came from. Ultimately, Stott demonstrates, ideas—including evolution itself—evolve just as animals and plants do, by intermingling, toppling weaker notions, and developing over stretches of time. Darwin’s Ghosts presents a groundbreaking new theory of an idea that has changed our very understanding of who we are.

    Even before he won the Nobel Prize in 1965, his unorthodox and spellbinding lectures on physics secured his reputation amongst students and seekers around the world. It was his outsized love for life, however, that earned him the status of an American cultural icon - here was an extraordinary intellect devoted to the proposition that the thrill of discovery was matched only by the joy of communicating it to others." In this career-spanning collection of letters, many published here for the first time, we are able to see this side of Feynman like never before. Perfectly Reasonable Deviations from the Beaten Track covers a dazzling array of topics and themes, scientific developments and personal histories. With missives to and from scientific luminaries, as well as letters to and from fans, family, students, crackpots, as well as everyday people eager for Feynman's wisdom and counsel, the result is a de facto guide to life, and eloquent testimony to the human quest for knowledge at all levels.Published in the UK as Don't You Have Time to Think?

    We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

    Silver translates our most important, and often most obscure, scientific developments into a vernacular that is not only accessible and illuminating but also enjoyable. Silver makes his comprehensive case with much clarity and insight; his book aptly locates science as the apex of human reason, and reason as our best path to the truth. For all readers curious about--or else perhaps intimidated by--what Silver calls the scientific campaign up to now in his Preface, The Ascent of Science will be fresh, vivid, and fascinating reading.

    In Human-Built World, thankfully, Thomas Hughes restores to technology the conceptual richness and depth it deserves by chronicling the ideas about technology expressed by influential Western thinkers who not only understood its multifaceted character but who also explored its creative potential.Hughes draws on an enormous range of literature, art, and architecture to explore what technology has brought to society and culture, and to explain how we might begin to develop an "ecotechnology" that works with, not against, ecological systems. From the "Creator" model of development of the sixteenth century to the "big science" of the 1940s and 1950s to the architecture of Frank Gehry, Hughes nimbly charts the myriad ways that technology has been woven into the social and cultural fabric of different eras and the promises and problems it has offered. Thomas Jefferson, for instance, optimistically hoped that technology could be combined with nature to create an Edenic environment; Lewis Mumford, two centuries later, warned of the increasing mechanization of American life.Such divergent views, Hughes shows, have existed side by side, demonstrating the fundamental idea that "in its variety, technology is full of contradictions, laden with human folly, saved by occasional benign deeds, and rich with unintended consequences." In Human-Built World, he offers the highly engaging history of these contradictions, follies, and consequences, a history that resurrects technology, rightfully, as more than gadgetry; it is in fact no less than an embodiment of human values.

    • Assess for yourself the stunning visual evidence presented in some 200 photographs. • Examine previously unpublished testimony from expert informants. • Discover new research undertaken by von Däniken after the opening up of previously inaccessible regions, such as the jungle city “Buritaca 200” in Colombia.

    Beginning at the 'arts' end of the subject with the common origins of languages, and finishing at the 'science' end with the newest discoveries regarding language in the brain, this stimulating guide covers all the major aspects of linguistics from a refreshing and insightful angle. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Author Manuel Velasquez combines clear prose and primary source readings to take you on a meaningful exploration of a range of philosophical topics, such as human nature, feminist theory, diversity, and aesthetics. Plus, the text's carefully crafted built-in learning aids will help you succeed in your course.

    This book describes the principles of alchemy and how they can be used to effect spiritual, mental, emotional and physical transformation.

    Dreams aren't really anything like reality. Dreams are, well, they're more dreamy. You can just tell. Things happen in dreams that don't happen in reality. Usually, anyway. An intriguing tale that will instill readers with an abiding sense of philosophical wonder. If you're smitten with Sophie's World, you're sure to be entranced by The Dream Weaver. - Christopher Phillips, author, Socrates Cafe. Jack Bowen's novel is like traveling with Alice to a Wonderland inhabited by the greatest philosophers and scientists who ever lived... A triumph! - Wenda O'Reilly, Ph.D., President, Birdcage Press and author, The Impressionist Art Game. The Dream Weaver is an outstanding how-to-think book... This book is a philosophical odyssey that tackles the mysteries of life, of science, and of the meaning of reality. - Susanne Pari, author, The Fortune Catcher.

    

    Hungarian-born Erdős believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century's leading number theorist and the most prolific mathematician who ever lived. Erdős's important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers. Witty and filled with the sort of mathematical puzzles that intrigued Erdős and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    For two decades, historian Alice Dreger has led a life of extraordinary engagement, combining activist service to victims of unethical medical research with defense of scientists whose work has outraged identity politics activists. With spirit and wit, Dreger offers in Galileo’s Middle Finger an unforgettable vision of the importance of rigorous truth seeking in today’s America, where both the free press and free scholarly inquiry struggle under dire economic and political threats.This illuminating chronicle begins with Dreger’s own research into the treatment of people born intersex (once called hermaphrodites). Realization of the shocking surgical and ethical abuses conducted in the name of “normalizing” intersex children’s gender identities moved Dreger to become an internationally recognized patient rights’ activist. But even as the intersex rights movement succeeded, Dreger began to realize how some fellow progressive activists were employing lies and personal attacks to silence scientists whose data revealed uncomfortable truths about humans. In researching one such case, Dreger suddenly became the target of just these kinds of attacks.Troubled, she decided to try to understand more—to travel the country to ferret out the truth behind various controversies, to obtain a global view of the nature and costs of these battles. Galileo’s Middle Finger describes Dreger’s long and harrowing journeys between the two camps for which she felt equal empathy: social justice activists determined to win and researchers determined to put hard truths before comfort. Ultimately what emerges is a lesson about the intertwining of justice and of truth—and a lesson of the importance of responsible scholars and journalists to our fragile democracy.