The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order. Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.

    Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men.  Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.  This absorbing narrative of people, science and ideas  chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it.  Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

    In this unconventional introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind's enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    Breaking down the symbols themselves, they pose a series of questions: What is energy? What is mass? What has the speed of light got to do with energy and mass? In answering these questions, they take us to the site of one of the largest scientific experiments ever conducted. Lying beneath the city of Geneva, straddling the Franco-Swiss boarder, is a 27 km particle accelerator, known as the Large Hadron Collider. Using this gigantic machine—which can recreate conditions in the early Universe fractions of a second after the Big Bang—Cox and Forshaw will describe the current theory behind the origin of mass.Alongside questions of energy and mass, they will consider the third, and perhaps, most intriguing element of the equation: 'c' - or the speed of light. Why is it that the speed of light is the exchange rate? Answering this question is at the heart of the investigation as the authors demonstrate how, in order to truly understand why E=mc2, we first must understand why we must move forward in time and not backwards and how objects in our 3-dimensional world actually move in 4-dimensional space-time. In other words, how the very fabric of our world is constructed. A collaboration between two of the youngest professors in the UK, Why Does E=mc2? promises to be one of the most exciting and accessible explanations of the theory of relativity in recent years.

     In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone.Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

    It’s time we stand face-to-digital-face with the true powers and limitations of the algorithms that already automate important decisions in healthcare, transportation, crime, and commerce. Hello World is indispensable preparation for the moral quandaries of a world run by code, and with the unfailingly entertaining Hannah Fry as our guide, we’ll be discussing these issues long after the last page is turned.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    Such systems--whether political parties, stock markets, or ant colonies--present some of the most intriguing theoretical and practical challenges confronting the social sciences. Engagingly written, and balancing technical detail with intuitive explanations, Complex Adaptive Systems focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It provides a detailed introduction to concepts such as emergence, self-organized criticality, automata, networks, diversity, adaptation, and feedback. It also demonstrates how complex adaptive systems can be explored using methods ranging from mathematics to computational models of adaptive agents. John Miller and Scott Page show how to combine ideas from economics, political science, biology, physics, and computer science to illuminate topics in organization, adaptation, decentralization, and robustness. They also demonstrate how the usual extremes used in modeling can be fruitfully transcended.

    The book drives to the heart of the exciting debate on the origins of life and maintenance of order in complex biological systems. It focuses on the concept of self-organization: the spontaneous emergence of order that is widely observed throughout nature Kauffman argues that self-organization plays an important role in the Darwinian process of natural selection. Yet until now no systematic effort has been made to incorporate the concept of self-organization into evolutionary theory. The construction requirements which permit complex systems to adapt are poorly understood, as is the extent to which selection itself can yield systems able to adapt more successfully. This book explores these themes. It shows how complex systems, contrary to expectations, can spontaneously exhibit stunning degrees of order, and how this order, in turn, is essential for understanding the emergence and development of life on Earth. Topics include the new biotechnology of applied molecular evolution, with its important implications for developing new drugs and vaccines; the balance between order and chaos observed in many naturally occurring systems; new insights concerning the predictive power of statistical mechanics in biology; and other major issues. Indeed, the approaches investigated here may prove to be the new center around which biological science itself will evolve. The work is written for all those interested in the cutting edge of research in the life sciences.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    . . . The subject of complexity is vital and controversial. This book is important and beautifully done."—Stephen Jay Gould"[Complexity] is that curious mix of complication and organization that we find throughout the natural and human worlds: the workings of a cell, the structure of the brain, the behavior of the stock market, the shifts of political power. . . . It is time science . . . thinks about meaning as well as counting information. . . . This is the core of the complexity manifesto. Read it, think about it . . . but don't ignore it."—Ian Stewart, NatureThis second edition has been brought up to date with an essay entitled "On the Edge in the Business World" and an interview with John Holland, author of Emergence: From Chaos to Order.

    In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    The stories show that, as James Gleick puts it in the foreword, "inspiration strikes willy-nilly." One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a "bathroom sink epiphany" and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge."Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the "conspiracy" of the title); consider whether math is the universal language of nature (allowing for "a unified theory of randomness"); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question "Is mathematics good for you?"ContributorsAriel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie WolchoverCopublished with Quanta Magazine