It affects us all. We depend on it in our daily lives, and yet many of the tools of mathematics, such as geometry, algebra and trigonometry, are descended from ancient or non-Western civilizations.Introducing Mathematics traces the story of mathematics from the ancient world to modern times, describing the great discoveries and providing an accessible introduction to such topics as number-systems, geometry and algebra, the calculus, the theory of the infinite, statistical reasoning and chaos theory. It shows how the history of mathematics has seen progress and paradox go hand in hand - and how this is still happening today.

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

    Johannes Kepler, who discovered the three basic laws of planetary motion, was persecuted for his support of the Copernican system. After a neighbour accused his mother of witchcraft, Kepler quit his post as the Imperial mathematician to defend her.James Connor tells Kepler's story as a pilgrimage, a spiritual journey into the modern world through war and disease and terrible injustice, a journey reflected in the evolution of Kepler's geometrical model of the cosmos into a musical model, harmony into greater harmony. The leitmotif of the witch trial adds a third dimension to Kepler's biography by setting his personal life within his own times. The acts of this trial, including Kepler's letters and the accounts of the witnesses, although published in their original German dialects, had never before been translated into English. Echoing some of Dava Sobel's work for Galileo's Daughter, Connor has translated the witch trial documents into English. With a great respect for the history of these times and the life of this man, Connor's accessible story illuminates the life of Kepler, the man of science, but also Kepler, a man of uncommon faith and vision.

    . . 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.

    And every Star Trek fan knows about Klingon, which was nothing more than a television show's attempt to create a tough-sounding language befitting a warrior race with ridged foreheads. But few people have heard of Babm, Blissymbolics, and the nearly nine hundred other invented languages that represent the hard work, high hopes, and full-blown delusions of so many misguided souls over the centuries. In In The Land of Invented Languages, author Arika Okrent tells the fascinating and highly entertaining history of man's enduring quest to build a better language. Peopled with charming eccentrics and exasperating megalomaniacs, the land of invented languages is a place where you can recite the Lord's Prayer in John Wilkins's Philosophical Language, say your wedding vows in Loglan, and read Alice's Adventures in Wonderland in Lojban. A truly original new addition to the booming category of language books, In The Land of Invented Languages will be a must-have on the shelves of all word freaks, grammar geeks, and plain old language lovers.

    John Huth asks what is lost when modern technology substitutes for our innate capacity to find our way. Encyclopedic in breadth, weaving together astronomy, meteorology, oceanography, and ethnography, "The Lost Art of Finding Our Way" puts us in the shoes, ships, and sleds of early navigators for whom paying close attention to the environment around them was, quite literally, a matter of life and death.Haunted by the fate of two young kayakers lost in a fogbank off Nantucket, Huth shows us how to navigate using natural phenomena the way the Vikings used the sunstone to detect polarization of sunlight, and Arab traders learned to sail into the wind, and Pacific Islanders used underwater lightning and read waves to guide their explorations. Huth reminds us that we are all navigators capable of learning techniques ranging from the simplest to the most sophisticated skills of direction-finding. Even today, careful observation of the sun and moon, tides and ocean currents, weather and atmospheric effects can be all we need to find our way.Lavishly illustrated with nearly 200 specially prepared drawings, Huth s compelling account of the cultures of navigation will engross readers in a narrative that is part scientific treatise, part personal travelogue, and part vivid re-creation of navigational history. Seeing through the eyes of past voyagers, we bring our own world into sharper view."

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    And, like most consumers, he often reads the ingredients label -- without a clue as to what most of it means. So when his young daughter asked, "Daddy, what's polysorbate 60?" he was at a loss -- and determined to find out. From the phosphate mines in Idaho to the corn fields in Iowa, from gypsum mines in Oklahoma to the vanilla harvest in Madagascar, Twinkie, Deconstructed is a fascinating, thoroughly researched romp of a narrative that demystifies some of the most common processed food ingredients -- where they come from, how they are made, how they are used -- and why. Beginning at the source (hint: they're often more closely linked to rock and petroleum than any of the four food groups), we follow each Twinkie ingredient through the process of being crushed, baked, fermented, refined, and/or reacted into a totally unrecognizable goo or powder with a strange name -- all for the sake of creating a simple snack cake. An insightful exploration into the food industry, if you've ever wondered what you're eating when you consume foods containing mono- and diglycerides or calcium sulfate (the latter, a food-grade equivalent) this book is for you.

    Gates says, "we can work on a local, national, and global level to build the technologies, businesses, and industries to avoid the worst impacts of climate change." His interest in climate change is a natural outgrowth of the efforts by his foundation to reduce poverty and disease. Climate change, according to Gates, will have the biggest impact on the people who have done the least to cause it. As a technologist, he has seen first-hand how innovation can change the world. By investing in research, inventing new technologies, and by deploying them quickly at large scale, Gates believes climate change can be addressed in meaningful ways. According to Gates, "to prevent the worst effects of climate change, we have to get to net-zero emissions of greenhouse gases. This problem is urgent, and the debate is complex, but I believe we can come together to invent new carbon-zero technologies, deploy the ones we have, and ultimately avoid a climate catastrophe."

    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.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    His breaking of the German U-boat Enigma cipher in World War II ensured Allied-American control of the Atlantic. But Turing's vision went far beyond the desperate wartime struggle. Already in the 1930s he had defined the concept of the universal machine, which underpins the computer revolution. In 1945 he was a pioneer of electronic computer design. But Turing's true goal was the scientific understanding of the mind, brought out in the drama and wit of the famous "Turing test" for machine intelligence and in his prophecy for the twenty-first century.Drawn in to the cockpit of world events and the forefront of technological innovation, Alan Turing was also an innocent and unpretentious gay man trying to live in a society that criminalized him. In 1952 he revealed his homosexuality and was forced to participate in a humiliating treatment program, and was ever after regarded as a security risk. His suicide in 1954 remains one of the many enigmas in an astonishing life story.

    . . and then broke? How would you survive? Could you improve on humanity's original timeline? And how hard would it be to domesticate a giant wombat? With this book as your guide, you'll survive--and thrive--in any period in Earth's history. Bestselling author and time-travel enthusiast Ryan North shows you how to invent all the modern conveniences we take for granted--from first principles. This illustrated manual contains all the science, engineering, art, philosophy, facts, and figures required for even the most clueless time traveler to build a civilization from the ground up. Deeply researched, irreverent, and significantly more fun than being eaten by a saber-toothed tiger, How to Invent Everything will make you smarter, more competent, and completely prepared to become the most important and influential person ever.

    November 2015 is the 100th anniversary of Einstein’s discovery of the General Theory of Relativity.Levenson, head of MIT’s Science Writing Program, tells the captivating, unusual, and nearly-forgotten backstory behind Einstein’s invention of the Theory of Relativity, which completely changed the course of science forever. For over 50 years before Einstein developed his theory, the world’s top astronomers spent countless hours and energy searching for a planet, which came to be named Vulcan, that had to exist, it was thought, given Isaac Newton’s theories of gravity. Indeed, in the two centuries since Newton’s death, his theory had essentially become accepted as fact. It took Einstein’s genius to realize the mystery of the missing planet wasn’t a problem of measurements or math but of Newton’s theory of gravity itself. Einstein’s Theory of Relativity proved that Vulcan did not and could not exist, and that the decades-long search for it had merely been a quirk of operating under the wrong set of assumptions about the universe. Thomas Levenson tells this unique story, one of the strangest episodes in the history of science, with elegant simplicity, fast-paced drama, and lively characters sure to capture the attention of a wide group of readers.

    In Dataclysm, Christian Rudder uses it to show us who we truly are.   For centuries, we’ve relied on polling or small-scale lab experiments to study human behavior. Today, a new approach is possible. As we live more of our lives online, researchers can finally observe us directly, in vast numbers, and without filters. Data scientists have become the new demographers.   In this daring and original book, Rudder explains how Facebook "likes" can predict, with surprising accuracy, a person’s sexual orientation and even intelligence; how attractive women receive exponentially more interview requests; and why you must have haters to be hot. He charts the rise and fall of America’s most reviled word through Google Search and examines the new dynamics of collaborative rage on Twitter. He shows how people express themselves, both privately and publicly. What is the least Asian thing you can say? Do people bathe more in Vermont or New Jersey? What do black women think about Simon & Garfunkel? (Hint: they don’t think about Simon & Garfunkel.) Rudder also traces human migration over time, showing how groups of people move from certain small towns to the same big cities across the globe. And he grapples with the challenge of maintaining privacy in a world where these explorations are possible.   Visually arresting and full of wit and insight, Dataclysm is a new way of seeing ourselves—a brilliant alchemy, in which math is made human and numbers become the narrative of our time.