His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Taking us on a journey through every fundamental field of science, as well as the history of civilization, art, moral values, and the theory of political institutions, Deutsch tracks how we form new explanations and drop bad ones, explaining the conditions under which progress—which he argues is potentially boundless—can and cannot happen. Hugely ambitious and highly original, The Beginning of Infinity explores and establishes deep connections between the laws of nature, the human condition, knowledge, and the possibility for progress.

    Like you, the elements have lives: personalities and attitudes, talents and shortcomings, stories rich with meaning. You may think of them as the inscrutable letters of the periodic table but you know them much better than you realise. Welcome to a dazzling tour through history and literature, science and art. Here you'll meet iron that rains from the heavens and noble gases that light the way to vice. You'll learn how lead can tell your future while zinc may one day line your coffin. You'll discover what connects the bones in your body with the Whitehouse in Washington, the glow of a streetlamp with the salt on your dinner table. From ancient civilisations to contemporary culture, from the oxygen of publicity to the phosphorus in your pee, the elements are near and far and all around us. Unlocking their astonishing secrets and colourful pasts, Periodic Tales will take you on a voyage of wonder and discovery, excitement and novelty, beauty and truth. Along the way, you'll find that their stories are our stories, and their lives are inextricable from our own.

    The main message i absorbed from it was a set of conditions required for success in mathematics: talent, yes; single-mindedness, almost as obvious; sense of humour, essential when the going gets tough; and love, yes that is the right word - you must love mathematics, and that means all the ingredients, passion, pain and loyalty." The Mathematical Gazette#1"The book is written in a very personal, but plain and honest way, result of reflected experience and mature self-assessment of a wise man. It avoids palliation as well as exaggerated modesty.- It should be a document for history and sociology of science." (R. Fischer) Zentralblatt für Mathematik#2

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    She explains ideas at the cutting-edge of scientific enquiry, making them comprehensible and accessible to the layperson.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    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.

    As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone--from those who fumble over fractions to those who solve complex equations in their heads--winds up marveling at what numbers can do.Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach them.

    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.

    There's a wonderful mix of science, history and wit, all in bite-sized chapters on a broad range of topics.Urgent and essential, Numbers Don't Lie inspires readers to interrogate what they take to be true in these significant times. Smil is on a mission to make facts matter, because after all, numbers may not lie, but which truth do they convey?'The best book to read to better understand our world. Once in a while a book comes along that helps us see our planet more clearly. By showing us numbers about science, health, green technology and more, Smil's book does just that. It should be on every bookshelf!' Linda Yueh, author of The Great Economists'He is rigorously numeric, using data to illuminate every topic he writes about. The word "polymath" was invented to describe people like him' Bill Gates 'Important' Mark Zuckerberg, on Energy 'One of the world's foremost thinkers on development history and a master of statistical analysis . . . The nerd's nerd' Guardian 'There is perhaps no other academic who paints pictures with numbers like Smil' Guardian 'In a world of specialized intellectuals, Smil is an ambitious and astonishing polymath who swings for fences . . . They're among the most data-heavy books you'll find, with a remarkable way of framing basic facts' Wired 'He's a slayer of bullshit' David Keith, Gordon McKay Professor of Applied Physics & Professor of Public Policy, Harvard UniversityVaclav Smil is Distinguished Professor Emeritus at the University of Manitoba. He is the author of over forty books on topics including energy, environmental and population change, food production and nutrition, technical innovation, risk assessment and public policy. No other living scientist has had more books (on a wide variety of topics) reviewed in Nature. A Fellow of the Royal Society of Canada, in 2010 he was named by Foreign Policy as one of the Top 100 Global Thinkers. This is his first book for a more general readership.

    Pi-or ? as it is symbolically known-is infinite and, in The Joy of pi, it proves to be infinitely intriguing. With incisive historical insight and a refreshing sense of humor, David Blatner explores the many facets of pi and humankind's fascination with it-from the ancient Egyptians and Archimedes to Leonardo da Vinci and the modern-day Chudnovsky brothers, who have calculated pi to eight billion digits with a homemade supercomputer.The Joy of Pi is a book of many parts. Breezy narratives recount the history of pi and the quirky stories of those obsessed with it. Sidebars document fascinating pi trivia (including a segment from the 0. J. Simpson trial). Dozens of snippets and factoids reveal pi's remarkable impact over the centuries. Mnemonic devices teach how to memorize pi to many hundreds of digits (or more, if you're so inclined). Pi-inspired cartoons, poems, limericks, and jokes offer delightfully "square" pi humor. And, to satisfy even the most exacting of number jocks, the first one million digits of pi appear throughout the book.A tribute to all things pi, The Joy of pi is sure to foster a newfound affection and respect for the big number with the funny little symbol.

    Mysteries don't lose their poetry because they are solved: the solution often is more beautiful than the puzzle, uncovering deeper mysteries. With the wit, insight, and spellbinding prose that have made him a best-selling author, Dawkins takes up the most important and compelling topics in modern science, from astronomy and genetics to language and virtual reality, combining them in a landmark statement of the human appetite for wonder. This is the book Richard Dawkins was meant to write: a brilliant assessment of what science is (and isn't), a tribute to science not because it is useful but because it is uplifting.

    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.

    From the death of Archimedes at the hands of an irritated Roman soldier to the concoction of a superconducting witches' brew at the close of the twentieth century, the stories in Eurekas and Euphorias pour out, told with wit and relish by Walter Gratzer. Open this book at random and you may chance on the clumsy chemist named Sapper who broke a thermometer in a reaction vat and made the discovery that launched the modern dyestuff industry. Or the physicist who dissolved his gold Nobel Prize medal in acid to prevent it from falling into the hands of the Nazis. We meet mathematicians and physicists in prison cells, and even in a madhouse, making important advances in their field. And we witness the careers, sometimes tragic, sometimes carefree, of the great women scientists, from Hypatia of Alexandria, to Sophie Germain and Sonia Kovalevskaya, to Marie Curie and her relentless battle with the French Academy. A glorious parade unfolds to delight the reader, with stories to astonish, to instruct, and most especially, to entertain.