Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men.  Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.  This absorbing narrative of people, science and ideas  chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it.  Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

    Using Everett's unpublished papers (recently discovered in his son's basement) and dozens of interviews with his friends, colleagues, and surviving family members, Byrne paints, for the general reader, a detailed portrait of the genius who invented an astonishing way of describing our complex universe from the inside. Everett's mathematical model (called the "universal wave function") treats all possible events as "equally real," and concludes that countless copies of every person and thing exist in all possible configurations spread over an infinity of universes: many worlds. Afflicted by depression and addictions, Everett strove to bring rational order to the professional realms in which he played historically significant roles. In addition to his famous interpretation of quantum mechanics, Everett wrote a classic paper in game theory; created computer algorithms that revolutionized military operations research; and performed pioneering work in artificial intelligence for top secret government projects. He wrote the original software for targeting cities in a nuclear hot war; and he was one of the first scientists to recognize the danger of nuclear winter. As a Cold Warrior, he designed logical systems that modeled "rational" human and machine behaviors, and yet he was largely oblivious to the emotional damage his irrational personal behavior inflicted upon his family, lovers, and business partners. He died young, but left behind a fascinating record of his life, including correspondence with such philosophically inclined physicists as Niels Bohr, Norbert Wiener, and John Wheeler. These remarkable letters illuminate the long and often bitter struggle to explain the paradox of measurement at the heart of quantum physics. In recent years, Everett's solution to this mysterious problem-the existence of a universe of universes-has gained considerable traction in scientific circles, not as science fiction, but as an explanation of physical reality.

    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.

    With the Big Bang, it went from a state of unimaginable density to an all-encompassing cosmic fireball to a simmering fluid of matter and energy, laying down the seeds for everything from dark matter to black holes to one rocky planet orbiting a star near the edge of a spiral galaxy that happened to develop life. But what happens at the end of the story? In billions of years, humanity could still exist in some unrecognizable form, venturing out to distant space, finding new homes and building new civilizations. But the death of the universe is final. What might such a cataclysm look like? And what does it mean for us? Dr. Katie Mack has been contemplating these questions since she was eighteen, when her astronomy professor first informed her the universe could end at any moment, setting her on the path toward theoretical astrophysics. Now, with lively wit and humor, she unpacks them in The End of Everything, taking us on a mind-bending tour through each of the cosmos’ possible finales: the Big Crunch; the Heat Death; Vacuum Decay; the Big Rip; and the Bounce. In the tradition of Neil DeGrasse’s bestseller Astrophysics for People in a Hurry, Mack guides us through major concepts in quantum mechanics, cosmology, string theory, and much more, in a wildly fun, surprisingly upbeat ride to the farthest reaches of everything we know.

    On the bloody battlefield of Waterloo, the Emperor Napoleon and his hastily formed legions clashed with the Anglo-Allied armies led by the Duke of Wellington -- the only time the two greatest military strategists of their age faced each other in combat.With precision and elegance, Andrew Roberts sets the political, strategic, and historical scene, providing a breathtaking account of each successive stage of the battle while also examining new evidence that reveals exactly how Napoleon was defeated. Illuminating, authoritative, and engrossing, Waterloo is a masterful work of history.

    He shows how oxygen underpins the origin of biological complexity, the birth of photosynthesis, the sudden evolution of animals, the need for two sexes, the accelerated aging of cloned animals like Dolly the sheep, and the surprisingly long lives of bats and birds. Drawing on this grand evolutionary canvas, Oxygen offers fresh perspectives on our own lives and deaths, explaining modern killer diseases, why we age, and what we can do about it. Advancing revelatory new ideas, following chains of evidence, the book ranges through many disciplines, from environmental sciences to molecular medicine. The result is a captivating vision of contemporary science and a humane synthesis of our place in nature. This remarkable book will redefine the way we think about the world.

    And it is ignorance--not knowledge--that is the true engine of science.Most of us have a false impression of science as a surefire, deliberate, step-by-step method for finding things out and getting things done. In fact, says Firestein, more often than not, science is like looking for a black cat in a dark room, and there may not be a cat in the room. The processis more hit-or-miss than you might imagine, with much stumbling and groping after phantoms. But it is exactly this not knowing, this puzzling over thorny questions or inexplicable data, that gets researchers into the lab early and keeps them there late, the thing that propels them, the verydriving force of science. Firestein shows how scientists use ignorance to program their work, to identify what should be done, what the next steps are, and where they should concentrate their energies. And he includes a catalog of how scientists use ignorance, consciously or unconsciously--aremarkable range of approaches that includes looking for connections to other research, revisiting apparently settled questions, using small questions to get at big ones, and tackling a problem simply out of curiosity. The book concludes with four case histories--in cognitive psychology, theoreticalphysics, astronomy, and neuroscience--that provide a feel for the nuts and bolts of ignorance, the day-to-day battle that goes on in scientific laboratories and in scientific minds with questions that range from the quotidian to the profound.Turning the conventional idea about science on its head, Ignorance opens a new window on the true nature of research. It is a must-read for anyone curious about science.

    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.

    Whatever your experience level, you'll find something here to delight you!

    The books published on the subject are so technical that only a person trained in pure physics and higher mathematics is able to fully understand them. In order to make a popular explanation of this far-reaching theory available, the present book is published.

    These weren't simply variations on apes, but upright-walking humans who lived side by side, competing, cooperating, sometimes even mating with our direct ancestors. Why did the line of ancient humans who eventually evolved into us survive when the others were shown the evolutionary door? Chip Walter draws on new scientific discoveries to tell the fascinating tale of how our survival was linked to our ancestors being born more prematurely than others, having uniquely long and rich childhoods, evolving a new kind of mind that made us resourceful and emotionally complex; how our highly social nature increased our odds of survival; and why we became self aware in ways that no other animal seems to be. Last Ape Standing also profiles the mysterious "others" who evolved with us-the Neanderthals of Europe, the "Hobbits" of Indonesia, the Denisovans of Siberia and the just-discovered Red Deer Cave people of China who died off a mere eleven thousand years ago. Last Ape Standing is evocative science writing at its best-a witty, engaging and accessible story that explores the evolutionary events that molded us into the remarkably unique creatures we are; an investigation of why we do, feel, and think the things we do as a species, and as people-good and bad, ingenious and cunning, heroic and conflicted.

    The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

    Inside these pages some of the biggest (and smallest) mysteries of the natural world are explained in essays by real working scientists, which are then illustrated by artists given free rein to be as literal or as imaginative as they like. The result is a celebration of the wonder that inspires every new discovery. Featuring work by such contemporary luminaries as Lisa Congdon, Jen Corace, Neil Farber, Susie Ghahremani, Jeremyville, and many more, this is a work of scientific and artistic exploration to pique the interest of both the intellectually and imaginatively curious.

    Mathematics: The Loss of Certainty refutes that myth.