But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

    Not just a collection of anecdotes but a fair, reasoned appraisal of eccentric theory, it is unique in recognizing the scientific, philosophic, and sociological-psychological implications of the wave of pseudoscientific theories which periodically besets the world.To this second revised edition of a work formerly titled In the Name of Science, Martin Gardner has added new, up-to-date material to an already impressive account of hundreds of systematized vagaries. Here you will find discussions of hollow-earth fanatics like Symmes; Velikovsky and wandering planets; Hörbiger, Bellamy, and the theory of multiple moons; Charles Fort and the Fortean Society; dowsing and the other strange methods for finding water, ores, and oil. Also covered are such topics as naturopathy, iridiagnosis, zone therapy, food fads; Wilhelm Reich and orgone sex energy; L. Ron Hubbard and Dianetics; A. Korzybski and General Semantics. A new examination of Bridey Murphy is included in this edition, along with a new section on bibliographic reference material.

    Included in this edition is a new chapter on the revolutionary topic of quantum computing.

    Niels Bohr's dictum bears witness to the bewildering impact of quantum theory, flying in the face of classical physics and dramatically transforming scientists' outlook on our relationship with the material world. In this book Paul Davies interviews eight physicists involved in debating and testing the theory, with radically different views of its significance.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    But when Feynman said he didn’t understand quantum mechanics, he didn’t mean that he couldn’t do it – he meant that’s all he could do. He didn’t understand what the maths was saying: what quantum mechanics tells us about reality.Over the past decade or so, the enigma of quantum mechanics has come into sharper focus. We now realise that quantum mechanics is less about particles and waves, uncertainty and fuzziness, than a theory about information: about what can be known and how.This is more disturbing than our bad habit of describing the quantum world as ‘things behaving weirdly’ suggests. It calls into question the meanings and limits of space and time, cause and effect, and knowledge itself.The quantum world isn’t a different world: it is our world, and if anything deserves to be called ‘weird’, it’s us. This exhilarating book is about what quantum maths really means – and what it doesn’t mean.

    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.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Enjoy a thrilling intergalactic tour as Andrew Thomas redefines the force of gravity and introduces a brave new view of the universe!

    In the past, discoveries often had to wait for the rise of the next generation to see questions in a new light and let go of old truisms. Today, in a world that is defined by a rapid rate of change, staying on the cutting edge has as much to do with shedding outdated notions as adopting new ones. In this spirit, John Brockman, publisher of the online salon Edge.org ("the world's smartest website"—The Guardian), asked 175 of the world's most influential scientists, economists, artists, and philosophers: What scientific idea is ready for retirement?Jared Diamond explores the diverse ways that new ideas emerge * Nassim Nicholas Taleb takes down the standard deviation * Richard Thaler and novelist Ian McEwan reveal the usefulness of "bad" ideas * Steven Pinker dismantles the working theory of human behavior * Richard Dawkins renounces essentialism * Sherry Turkle reevaluates our expectations of artificial intelligence * Physicist Andrei Linde suggests that our universe and its laws may not be as unique as we think * Martin Rees explains why scientific understanding is a limitless goal * Alan Guth rethinks the origins of the universe * Sam Harris argues that our definition of science is too narrow * Nobel Prize winner Frank Wilczek disputes the division between mind and matter * Lawrence Krauss challenges the notion that the laws of physics were preordained * plus contributions from Daniel Goleman, Mihaly Csikszentmihalyi, Nicholas Carr, Rebecca Newberger Goldstein, Matt Ridley, Stewart Brand, Sean Carroll, Daniel C. Dennett, Helen Fisher, Douglas Rushkoff, Lee Smolin, Kevin Kelly, Freeman Dyson, and others.

    It is the basis of our understanding of atoms, radiation, and so much else, from elementary particles and basic forces to the behaviour of materials. But for a century it has also been the problem child of science, plagued by intense disagreements between its intellectual giants, from Albert Einstein to Stephen Hawking, over the strange paradoxes and implications that seem like the stuff of fantasy. Whether it's Schr�dinger's cat--a creature that is simultaneously dead and alive--or a belief that the world does not exist independently of our observations of it, quantum theory is what challenges our fundamental assumptions about our reality. In Einstein's Unfinished Revolution, globally renowned theoretical physicist Lee Smolin provocatively argues that the problems which have bedeviled quantum physics since its inception are unsolved for the simple reason that the theory is incomplete. There is more, waiting to be discovered. Our task--if we are to have simple answers to our simple questions about the universe we live in--must be to go beyond it to a description of the world on an atomic scale that makes sense. In this vibrant and accessible book, Smolin takes us on a journey through the basics of quantum physics, introducing the stories of the experiments and figures that have transformed the field, before wrestling with the puzzles and conundrums that they present. Along the way, he illuminates the existing theories about the quantum world that might solve these problems, guiding us toward his own vision that embraces common sense realism. If we are to have any hope of completing the revolution that Einstein began nearly a century ago, we must go beyond quantum mechanics as we know it to find a theory that will give us a complete description of nature. In Einstein's Unfinished Revolution, Lee Smolin brings us a step closer to resolving one of the greatest scientific controversies of our age.

    Here Lawrence M. Krauss, himself a theoretical physicist and best-selling author, offers a unique scientific biography: a rollicking narrative coupled with clear and novel expositions of science at the limits. An immensely colorful persona in and out of the office, Feynman revolutionized our understanding of nature amid a turbulent life. Krauss presents that life—from the death of Feynman’s childhood sweetheart during the Manhattan Project to his reluctant rise as a scientific icon—as seen through the science, providing a new understanding of the legacy of a man who has fascinated millions. An accessible reflection on the issues that drive physics today, Quantum Man captures the story of a man who was willing to break all the rules to tame a theory that broke all the rules.

    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.

    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.

    From the minds of the world's leading physicists there flowed a river of ideas that would transport mankind to the pinnacle of wonderment and to the very depths of human despair. This was a century that began with the certainties of absolute knowledge and ended with the knowledge of absolute uncertainty. It was a century in which physicists developed weapons with the capacity to destroy our reality, whilst at the same time denying us the possibility that we can ever properly comprehend it.Almost everything we think we know about the nature of our world comes from one theory of physics. This theory was discovered and refined in the first thirty years of the twentieth century and went on to become quite simply the most successful theory of physics ever devised. Its concepts underpin much of the twenty-first century technology that we have learned to take for granted. But its success has come at a price, for it has at the same time completely undermined our ability to make sense of the world at the level of its most fundamental constituents.Rejecting the fundamental elements of uncertainty and chance implied by quantum theory, Albert Einstein once famously declared that 'God does not play dice'. Niels Bohr claimed that anybody who is not shocked by the theory has not understood it. The charismatic American physicist Richard Feynman went further: he claimed that nobody understands it.This is quantum theory, and this book tells its story.Jim Baggott presents a celebration of this wonderful yet wholly disconcerting theory, with a history told in forty episodes -- significant moments of truth or turning points in the theory's development. From its birth in the porcelain furnaces used to study black body radiation in 1900, to the promise of stimulating new quantum phenomena to be revealed by CERN's Large Hadron Collider over a hundred years later, this is the extraordinary story of the quantum world.Oxford Landmark Science books are 'must-read' classics of modern science writing which have crystallized big ideas, and shaped the way we think.