Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

    He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather.Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship.The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.'A wonderful book . . . Moving, sometimes comic, sometimes infinitely sad, and goes to the roots of what we mean by truth in science.' Lord Waldegrave, Daily Telegraph

    This authoritative yet accessible study is the ultimate astronomy lesson. Combining fascinating and often alarming scenarios that seem plucked from science fiction with the latest research and opinions, Plait illustrates why outer space is not as remote as most people think. Each chapter explores a different phenomenon, explaining it in easy-to-understand terms, and considering how life on earth and the planet itself would be affected should the event come to pass. Rather than sensationalizing the information, Plait analyzes the probability of these catastrophes occurring in our lifetimes and what we can do to stop them. With its entertaining tone and enlightening explanation of unfathomable concepts, Death from the Skies! will appeal to science buffs and beginners alike.

    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.

    As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    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.

    This idea is considered a foundation of modern physics, but what if it is wrong? Theoretical physicist Magueijo presents the idea that light traveled faster in the early universe than it does today. The varying speed of light theory solves some of the most intractable problems in cosmology, and could have major implications for the study of physics.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    In Peter Woit's view, superstring theory is just such an idea. In Not Even Wrong , he shows that what many physicists call superstring "theory" is not a theory at all. It makes no predictions, even wrong ones, and this very lack of falsifiability is what has allowed the subject to survive and flourish. Not Even Wrong explains why the mathematical conditions for progress in physics are entirely absent from superstring theory today and shows that judgments about scientific statements, which should be based on the logical consistency of argument and experimental evidence, are instead based on the eminence of those claiming to know the truth. In the face of many books from enthusiasts for string theory, this book presents the other side of the story.

    Richard Gott leads time travel out of the world of H. G. Wells and into the realm of scientific possibility. Building on theories posited by Einstein and advanced by scientists such as Stephen Hawking and Kip Thorne, Gott explains how time travel can actually occur. He describes, with boundless enthusiasm and humor, how travel to the future is not only possible but has already happened, and he contemplates whether travel to the past is also conceivable. Notable not only for its extraordinary subject matter and scientific brilliance, Time Travel in Einstein’s Universe is a delightful and captivating exploration of the surprising facts behind the science fiction of time travel.

    Using the dialogue form, a genre common in classical philosophical works, Galileo masterfully demonstrates the truth of the Copernican system over the Ptolemaic one, proving, for the first time, that the earth revolves around the sun. Its influence is incalculable. The Dialogue is not only one of the most important scientific treatises ever written, but a work of supreme clarity and accessibility, remaining as readable now as when it was first published. This edition uses the definitive text established by the University of California Press, in Stillman Drake’s translation, and includes a Foreword by Albert Einstein and a new Introduction by J. L. Heilbron.

    But soon, Earth's isolation could come to an end. Over the past two decades, astronomers have discovered thousands of planets orbiting other stars. Some of these exoplanets may be mirror images of our own world. And more are being found all the time.Yet as the pace of discovery quickens, an answer to the universe's greatest riddle still remains just out of reach: Is the great silence and emptiness of the cosmos a sign that we and our world are somehow singular, special, and profoundly alone, or does it just mean that we’re looking for life in all the wrong places? As star-gazing scientists come closer to learning the truth, their insights are proving ever more crucial to understanding life’s intricate mysteries and possibilities right here on Earth.Science journalist Lee Billings explores the past and future of the "exoplanet boom" through in-depth reporting and interviews with the astronomers andplanetary scientists at its forefront. He recounts the stories behind their world-changing discoveries and captures the pivotal moments that drove them forward in their historic search for the first habitable planets beyond our solar system. Billings brings readers close to a wide range of fascinating characters, such as:FRANK DRAKE, a pioneer who has used the world’s greatest radio telescopes to conduct the first searches for extraterrestrial intelligence and to transmit a message to the stars so powerful that it briefly outshone our Sun.JIM KASTING, a mild-mannered former NASA scientist whose research into the Earth’s atmosphere and climate reveals the deepest foundations of life on our planet, foretells the end of life on Earth in the distant future, and guides the planet hunters in their search for alien life.SARA SEAGER, a visionary and iron-willed MIT professor who dreams of escaping the solar system and building the giant space telescopes required to discover and study life-bearing planets around hundreds of the Sun’s neighboring stars.Through these and other captivating tales, Billings traces the triumphs, tragedies, and betrayals of the extraordinary men and women seeking life among the stars. In spite of insufficient funding, clashing opinions, and the failings of some of our world’s most prominent and powerful scientific organizations, these planet hunters will not rest until they find the meaning of life in the infinite depths of space. Billings emphasizes that the heroic quest for other Earth-like planets is not only a scientific pursuit, but also a reflection of our own culture’s timeless hopes and fears.

    Space is the venue of physics; it's where things exist, where they move and take shape. Yet over the past few decades, physicists have discovered a phenomenon that operates outside the confines of space and time: nonlocality-the ability of two particles to act in harmony no matter how far apart they may be. It appears to be almost magical. Einstein grappled with this oddity and couldn't come to terms with it, describing it as "spooky action at a distance." More recently, the mystery has deepened as other forms of nonlocality have been uncovered. This strange occurrence, which has direct connections to black holes, particle collisions, and even the workings of gravity, holds the potential to undermine our most basic understandings of physical reality. If space isn't what we thought it was, then what is it? In Spooky Action at a Distance, George Musser sets out to answer that question, offering a provocative exploration of nonlocality and a celebration of the scientists who are trying to explain it. Musser guides us on an epic journey into the lives of experimental physicists observing particles acting in tandem, astronomers finding galaxies that look statistically identical, and cosmologists hoping to unravel the paradoxes surrounding the big bang. He traces the often contentious debates over nonlocality through major discoveries and disruptions of the twentieth century and shows how scientists faced with the same undisputed experimental evidence develop wildly different explanations for that evidence. Their conclusions challenge our understanding of not only space and time but also the origins of the universe-and they suggest a new grand unified theory of physics. Delightfully readable, Spooky Action at a Distance is a mind-bending voyage to the frontiers of modern physics that will change the way we think about reality.Long-listed for the 2016 PEN/E. O. Wilson Literary Science Writing Award“An important book that provides insight into key new developments in our understanding of the nature of space, time and the universe. It will repay careful study.” —John Gribbin, The Wall Street Journal “An endlessly surprising foray into the current mother of physics' many knotty mysteries, the solving of which may unveil the weirdness of quantum particles, black holes, and the essential unity of nature.” —Kirkus Reviews (starred review)

    But gravitational waves – ripples in the fabric of space and time – are unrelenting, passing through barriers that stop light dead.At the two 4-kilometre long LIGO observatories in the US, scientists developed incredibly sensitive detectors, capable of spotting a movement 100 times smaller than the nucleus of an atom. In 2015 they spotted the ripples produced by two black holes spiralling into each other, setting spacetime quivering.This was the first time black holes had ever been directly detected – and it promises far more for the future of astronomy. Brian Clegg presents a compelling story of human technical endeavour and a new, powerful path to understand the workings of the universe.Brian Clegg’s most recent books are The Reality Frame (Icon, 2017), What Colour is the Sun? (Icon, 2016) and Ten Billion Tomorrows (St Martin’s Press, 2016). His Dice World and A Brief History of Infinity were both longlisted for the Royal Society Prize for Science Books. He has also written Big Data for the Hot Science series. Brian has written for numerous publications including The Wall Street Journal, Nature, BBC Focus, Physics World, The Times and The Observer. Brian is editor of popularscience.co.uk and blogs at brianclegg.blogspot.com.