"A mind-bending jaunt ... that makes clear in fascinating detail how math is more than a sum of its parts" (Publishers Weekly) “Let no one ignorant of geometry enter here,” Plato warned would-be philosophers. Mathematician Karl Sigmund agrees. In The Waltz of Reason, he shows how mathematics and philosophy together have shaped our understanding of space, chance, logic, cooperation, voting, and the social contract. Sigmund shows how game theory is integral to moral philosophy, how statistics shaped the meaning of reason, and how the search for a logical basis for math leads to deep questions about the nature of truth itself. But this is no dry tome: Sigmund’s wit and humor shine as brightly as his erudition. The Waltz of Reason is an engrossing history of ideas as vibrant as a ballroom full of dancers, one that empowers as it entertains, following the complex and occasionally dizzying steps of the thinkers who have molded our thought and founded our world.
A dazzling group biography of the early twentieth-century thinkers who transformed the way the world thought about math and science Inspired by Albert Einstein's theory of relativity and Bertrand Russell and David Hilbert's pursuit of the fundamental rules of mathematics, some of the most brilliant minds of the generation came together in post-World War I Vienna to present the latest theories in mathematics, science, and philosophy and to build a strong foundation for scientific investigation. Composed of such luminaries as Kurt Gö 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.
Accessible, informative, and enjoyable treatment discusses the application of the ideas and methods of game theory and mathematical modeling to such areas as evolution, sex, animal behavior, and aggression. "Excellent." — Nature
An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. 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.
A mathematician reveals the hidden beauty, power, and—yes—fun of algebra What comes to mind when you think about algebra? For many of us, it’s memories of dull or frustrating classes in high school. Award-winning mathematics professor G. Arnell Williams is here to change that. Algebra the Beautiful is a journey into the heart of fundamental math that proves just how amazing this subject really is. Drawing on lessons from twenty-five years of teaching mathematics, Williams blends metaphor, history, and storytelling to uncover algebra’s hidden grandeur. Whether you’re a teacher looking to make math come alive for your students, a parent hoping to get your children engaged, a student trying to come to terms with a sometimes bewildering subject, or just a lover of mathematics, this book has something for you. With a passion that’s contagious, G. Arnell Williams shows how each of us can grasp the beauty and harmony of algebra.
A pioneer in evolutionary game theory looks at selfishness and cooperation How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the "invisible hand" that should turn selfish efforts into public benefit is not always at work. The Calculus of Selfishness looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation. Focusing on some of the best-known social and economic experiments, including games such as the Prisoner's Dilemma, Trust, Ultimatum, Snowdrift, and Public Good, Sigmund explores the conditions leading to cooperative strategies. His approach is based on evolutionary game dynamics, applied to deterministic and probabilistic models of economic interactions. Exploring basic strategic interactions among individuals guided by self-interest and caught in social traps, The Calculus of Selfishness analyzes to what extent one key facet of human nature—selfishness—can lead to cooperation.
SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Nicolas Bourbaki, whose mathematical publications began to appear in the late 1930s and continued to be published through most of the twentieth century, was a direct product as well as a major force behind an important revolution that took place in the early decades of the twentieth century that completely changed Western culture. Pure mathematics, the area of Bourbaki's work, seems on the surface to be an abstract field of human study with no direct connection with the real world. In reality, however, it is closely intertwined with the general culture that surrounds it. Major developments in mathematics have often followed important trends in popular culture; developments in mathematics have acted as harbingers of change in the surrounding human culture. The seeds of change, the beginnings of the revolution that swept the Western world in the early decades of the twentieth century -- both in mathematics and in other areas -- were sown late in the previous century. This is the story both of Bourbaki and the world that created him in that time. It is the story of an elaborate intellectual joke -- because Bourbaki, one of the foremost mathematicians of his day -- never existed.
This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
NEW YORK TIMES BESTSELLER • “A meditation on sense-making when there’s no sense to be made, on letting go when we can’t hold on, and on being unafraid even when we’re terrified.”—Lucy Kalanithi “Belongs on the shelf alongside other terrific books about this difficult subject, like Paul Kalanithi’s When Breath Becomes Air and Atul Gawande’s Being Mortal.”—Bill Gates NAMED ONE OF THE BEST BOOKS OF THE YEAR BY REAL SIMPLE Kate Bowler is a professor at Duke Divinity School with a modest Christian upbringing, but she specializes in the study of the prosperity gospel, a creed that sees fortune as a blessing from God and misfortune as a mark of God’s disapproval. At thirty-five, everything in her life seems to point toward “blessing.” She is thriving in her job, married to her high school sweetheart, and loves life with her newborn son. Then she is diagnosed with stage IV colon cancer. The prospect of her own mortality forces Kate to realize that she has been tacitly subscribing to the prosperity gospel, living with the conviction that she can control the shape of her life with “a surge of determination.” Even as this type of Christianity celebrates the American can-do spirit, it implies that if you “can’t do” and succumb to illness or misfortune, you are a failure. Kate is very sick, and no amount of positive thinking will shrink her tumors. What does it mean to die, she wonders, in a society that insists everything happens for a reason? Kate is stripped of this certainty only to discover that without it, life is hard but beautiful in a way it never has been before. Frank and funny, dark and wise, Kate Bowler pulls the reader deeply into her life in an account she populates affectionately with a colorful, often hilarious retinue of friends, mega-church preachers, relatives, and doctors. Everything Happens for a Reason tells her story, offering up her irreverent, hard-won observations on dying and the ways it has taught her to live. Praise for Everything Happens for a Reason “I fell hard and fast for Kate Bowler. Her writing is naked, elegant, and gripping—she’s like a Christian Joan Didion. I left Kate’s story feeling more present, more grateful, and a hell of a lot less alone. And what else is art for?”—Glennon Doyle, #1 New York Times bestselling author of Love Warrior and president of Together Rising
