Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The language of symbols and infinitely large (and small) regions of mathematics should be rendered with clarity for the general reader.

    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.

    Your head hurts. You're mildly annoyed as you get the kids ready for school and dress for work yourself. Meanwhile, an epic war is being fought, just below your skin. Millions are fighting and dying for you to be able to complain as you head out the door.So what, exactly, is your immune system?Second only to the human brain in its complexity, it is one of the oldest and most critical facets of life on Earth. Without it, you would die within days. In Immune, Philipp Dettmer, the brains behind the most popular science channel on YouTube, takes readers on a journey through the fortress of the human body and its defenses. There is a constant battle of staggering scale raging within us, full of stories of invasion, strategy, defeat, and noble self-sacrifice. In fact, in the time you've been reading this, your immune system has probably identified and eradicated a cancer cell that started to grow in your body.Each chapter delves into an element of the immune system, including defenses like antibodies and inflammation as well as threats like bacteria, allergies, and cancer, as Dettmer reveals why boosting your immune system is actually nonsense, how parasites sneak their way past your body's defenses, how viruses work, and what goes on in your wounds when you cut yourself.Enlivened by engaging graphics and immersive descriptions, Immune turns one of the most intricate, interconnected, and confusing subjects—immunology—into a gripping adventure through an astonishing alien landscape. Immune is a vital and remarkably fun crash course in what is arguably, and increasingly, the most important system in the body.

    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.

    Indeed, many physicists today believe that there are other dimensions beyond the four of our space-time, and that a unified vision of the various forces of nature can be achieved, if we consider that everything we see around us, from the trees to the stars are nothing but vibrations in hyperspace. Hyperspace theory - and its more recent derivation, superstring theory - is the eye of this revolution. In this book, Michio Kaku shows us a fascinating panorama, which completely changes our view of the cosmos, and takes us on a dazzling journey through new dimensions: wormholes connecting parallel universes, time machines, "baby universes" and more. Similar wonders are emerging in some pages in which everything is explained with elegant simplicity and where the mathematical formulation is replaced by imaginative illustrations that allow the problems to be visualized. The result is a very entertaining and surprising book, which even leaves behind the greatest fantasies of the old science fiction authors.

    The story of information begins in a time profoundly unlike our own, when every thought and utterance vanishes as soon as it is born. From the invention of scripts and alphabets to the long-misunderstood talking drums of Africa, Gleick tells the story of information technologies that changed the very nature of human consciousness. He provides portraits of the key figures contributing to the inexorable development of our modern understanding of information: Charles Babbage, the idiosyncratic inventor of the first great mechanical computer; Ada Byron, the brilliant and doomed daughter of the poet, who became the first true programmer; pivotal figures like Samuel Morse and Alan Turing; and Claude Shannon, the creator of information theory itself. And then the information age arrives. Citizens of this world become experts willy-nilly: aficionados of bits and bytes. And we sometimes feel we are drowning, swept by a deluge of signs and signals, news and images, blogs and tweets. The Information is the story of how we got here and where we are heading.

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    You might even be worried that these lapses in memory could be an early sign of Alzheimer's or dementia. In reality, for the vast majority of us, these examples of forgetting are completely normal. Why? Because while memory is amazing, it is far from perfect. Our brains aren't designed to remember every name we hear, plan we make, or day we experience. Just because your memory sometimes fails doesn't mean it's broken or succumbing to disease. Forgetting is actually part of being human. In Remember, neuroscientist and acclaimed novelist Lisa Genova delves into how memories are made and how we retrieve them. You'll learn whether forgotten memories are temporarily inaccessible or erased forever and why some memories are built to exist for only a few seconds (like a passcode) while others can last a lifetime (your wedding day). You'll come to appreciate the clear distinction between normal forgetting (where you parked your car) and forgetting due to Alzheimer's (that you own a car). And you'll see how memory is profoundly impacted by meaning, emotion, sleep, stress, and context. Once you understand the language of memory and how it functions, its incredible strengths and maddening weaknesses, its natural vulnerabilities and potential superpowers, you can both vastly improve your ability to remember and feel less rattled when you inevitably forget. You can set educated expectations for your memory, and in doing so, create a better relationship with it. You don't have to fear it anymore. And that can be life-changing.

    Darrell Huff runs the gamut of every popularly used type of statistic, probes such things as the sample study, the tabulation method, the interview technique, or the way the results are derived from the figures, and points up the countless number of dodges which are used to fool rather than to inform.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    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.

    What should we do, or leave undone, in a day or a lifetime? How much messiness should we accept? What balance of new activities and familiar favorites is the most fulfilling? These may seem like uniquely human quandaries, but they are not: computers, too, face the same constraints, so computer scientists have been grappling with their version of such issues for decades. And the solutions they've found have much to teach us.In a dazzlingly interdisciplinary work, acclaimed author Brian Christian and cognitive scientist Tom Griffiths show how the algorithms used by computers can also untangle very human questions. They explain how to have better hunches and when to leave things to chance, how to deal with overwhelming choices and how best to connect with others. From finding a spouse to finding a parking spot, from organizing one's inbox to understanding the workings of memory, Algorithms to Live By transforms the wisdom of computer science into strategies for human living.