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The AMS series What's Happening in the Mathematical Sciences distills the amazingly rich brew of current research in mathematics down to a few choice samples. This volume leads off with an update on the Poincaré Conjecture, a hundred-year-old problem that has apparently been solved by Grigory Perelman of St. Petersburg, Russia. So what did topologists do when the oldest and most famous problem about closed manifolds was vanquished? As the second chapter describes, they confronted a suite of problems concerning the 'ends' of open manifolds ... and solved those, too. Not to be outdone, number theorists accomplished several unexpected feats in the first five years of the new century, from computing a trillion digits of pi to finding arbitrarily long equally-spaced sequences of prime numbers. Undergraduates made key discoveries, as explained in the chapters on Venn diagrams and primality testing. In applied mathematics, the Navier-Stokes equations of fluid mechanics continued to stir up interest. One team proved new theorems about the long-term evolution of vortices, while others explored the surprising ways that insects use vortices to move around. The random jittering of Brownian motion became a little less mysterious. Finally, an old and trusted algorithm of computer science had its trustworthiness explained in a novel way. -- Back cover.
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"Everyone has heard the claim, "Correlation does not imply causation." What might sound like a reasonable dictum metastasized in the twentieth century into one of science's biggest obstacles, as a legion of researchers became unwilling to make the claim that one thing could cause another. Even two decades ago, asking a statistician a question like "Was it the aspirin that stopped my headache?" would have been like asking if he believed in voodoo, or at best a topic for conversation at a cocktail party rather than a legitimate target of scientific inquiry. Scientists were allowed to posit only that the probability that one thing was associated with another. This all changed with Judea Pearl, whose work on causality was not just a victory for common sense, but a revolution in the study of the world"--
Causation. --- Inference. --- Philosophy of nature --- Causation --- Inference --- Causalité --- Inférence. --- Causalité --- Inférence.
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Correlation does not imply causation.' This mantra was invoked by scientists for decades in order to avoid taking positions as to whether one thing caused another, such as smoking and cancer and carbon dioxide and global warming. But today, that taboo is dead. The causal revolution, sparked by world-renowned computer scientist Judea Pearl and his colleagues, has cut through a century of confusion and placed cause and effect on a firm scientific basis. Now, Pearl and science journalist Dana Mackenzie explain causal thinking to general readers for the first time, showing how it allows us to explore the world that is and the worlds that could have been. It is the essence of human and artificial intelligence. And just as Pearl's discoveries have enabled machines to think better, The Book of Why explains how we can think better
Causation --- Causation.
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De kunstmatige intelligentie baseert zich op het leggen van verbanden (correlaties). De auteurs beargumenteren dat de menselijke vaardigheid oorzakelijke denken (oorzaak en gevolg), eerst moet worden toegepast in kunstmatige intelligentie, voordat computers 'kunnen denken als een mens'.
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This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
Mathematics. --- Science. --- Natural science --- Science of science --- Sciences --- Math --- Science --- Mathematic --- Natural sciences --- Mathematics
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