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.

    Gut, an international bestseller, gives the alimentary canal its long-overdue moment in the spotlight. With quirky charm, rising science star Giulia Enders explains the gut’s magic, answering questions like: Why does acid reflux happen? What’s really up with gluten and lactose intolerance? How does the gut affect obesity and mood? Communication between the gut and the brain is one of the fastest-growing areas of medical research—on par with stem-cell research. Our gut reactions, we learn, are intimately connected with our physical and mental well-being. Enders’s beguiling manifesto will make you finally listen to those butterflies in your stomach: they’re trying to tell you something important.

    Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    In How to Create a Mind, Kurzweil presents a provocative exploration of the most important project in human-machine civilization—reverse engineering the brain to understand precisely how it works and using that knowledge to create even more intelligent machines.Kurzweil discusses how the brain functions, how the mind emerges from the brain, and the implications of vastly increasing the powers of our intelligence in addressing the world’s problems. He thoughtfully examines emotional and moral intelligence and the origins of consciousness and envisions the radical possibilities of our merging with the intelligent technology we are creating.Certain to be one of the most widely discussed and debated science books of the year, How to Create a Mind is sure to take its place alongside Kurzweil’s previous classics which include Fantastic Voyage: Live Long Enough to Live Forever and The Age of Spiritual Machines.

    But more than this, there was gravity. After that, all hell broke loose… In A Universe from Nothing, Krauss revealed how our entire universe could arise from nothing. Now, he reveals what that something—reality—is. And, reality is not what we think or sense—it’s weird, wild, and counterintuitive; it’s hidden beneath everyday experience; and its inner workings seem even stranger than the idea that something can come from nothing. In a landmark, unprecedented work of scientific history, Krauss leads us to the furthest reaches of space and time, to scales so small they are invisible to microscopes, to the birth and rebirth of light, and into the natural forces that govern our existence. His unique blend of rigorous research and engaging storytelling invites us into the lives and minds of the remarkable, creative scientists who have helped to unravel the unexpected fabric of reality—with reason rather than superstition and dogma. Krauss has himself been an active participant in this effort, and he knows many of them well. The Greatest Story challenges us to re-envision ourselves and our place within the universe, as it appears that “God” does play dice with the universe. In the incisive style of his scintillating essays for The New Yorker, Krauss celebrates the greatest intellectual adventure ever undertaken—to understand why we are here in a universe where fact is stranger than fiction.

    It can be microscopic, yet also accounts for the largest organisms ever recorded, living for millennia and weighing tens of thousands of tonnes. Its ability to digest rock enabled the first life on land, it can survive unprotected in space, and thrives amidst nuclear radiation.In this captivating adventure, Merlin Sheldrake explores the spectacular and neglected world of fungi: endlessly surprising organisms that sustain nearly all living systems. They can solve problems without a brain, stretching traditional definitions of ‘intelligence’, and can manipulate animal behaviour with devastating precision. In giving us bread, alcohol and life-saving medicines, fungi have shaped human history, and their psychedelic properties, which have influenced societies since antiquity, have recently been shown to alleviate a number of mental illnesses. The ability of fungi to digest plastic, explosives, pesticides and crude oil is being harnessed in break-through technologies, and the discovery that they connect plants in underground networks, the ‘Wood Wide Web’, is transforming the way we understand ecosystems. Yet they live their lives largely out of sight, and over ninety percent of their species remain undocumented.Entangled Life is a mind-altering journey into this hidden kingdom of life, and shows that fungi are key to understanding the planet on which we live, and the ways we think, feel and behave. The more we learn about fungi, the less makes sense without them.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Along the way he provides an engaging and witty commentary while introducing the lay reader to both classic and cutting-edge concepts in physics, including:What Superman's strength can tell us about the Newtonian physics of force, mass, and accelerationHow Iceman's and Storm's powers illustrate the principles of thermal dynamicsThe physics behind the death of Spider-Man's girlfriend Gwen StacyWhy physics professors gone bad are the most dangerous evil geniuses!

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.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 hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Today, that taboo is dead. The causal revolution, instigated by Judea Pearl and his colleagues, has cut through a century of confusion and established causality -- the study of cause and effect -- on a firm scientific basis. His work explains how we can know easy things, like whether it was rain or a sprinkler that made a sidewalk wet; and how to answer hard questions, like whether a drug cured an illness. Pearl's work enables us to know not just whether one thing causes another: it lets us explore the world that is and the worlds that could have been. It shows us the essence of human thought and key to artificial intelligence. Anyone who wants to understand either needs The Book of Why.

    The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved but one that baffles mathematicians to this day.Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting-edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.

    But in recent decades, these claims have eroded, or even been disproven outright, by a revolution in the study of animal cognition. Take the way octopuses use coconut shells as tools; elephants that classify humans by age, gender, and language; or Ayumu, the young male chimpanzee at Kyoto University whose flash memory puts that of humans to shame. Based on research involving crows, dolphins, parrots, sheep, wasps, bats, whales, and of course chimpanzees and bonobos, Frans de Waal explores both the scope and the depth of animal intelligence. He offers a firsthand account of how science has stood traditional behaviorism on its head by revealing how smart animals really are, and how we’ve underestimated their abilities for too long.People often assume a cognitive ladder, from lower to higher forms, with our own intelligence at the top. But what if it is more like a bush, with cognition taking different forms that are often incomparable to ours? Would you presume yourself dumber than a squirrel because you’re less adept at recalling the locations of hundreds of buried acorns? Or would you judge your perception of your surroundings as more sophisticated than that of a echolocating bat? De Waal reviews the rise and fall of the mechanistic view of animals and opens our minds to the idea that animal minds are far more intricate and complex than we have assumed. De Waal’s landmark work will convince you to rethink everything you thought you knew about animal—and human—intelligence.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.

    An impassioned critique of K 12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. "Measurement "offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can do the math in a way that brings emotional and aesthetic rewards. "Measurement" is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work."