16 years later, the French Ambassador Hugues de Terlon secretly unearthed Descartes' bones & transported them to France. Why would this devoutly Catholic official care so much about the remains of a philosopher who was hounded from country to country on charges of atheism? Why would Descartes' bones take such a strange, serpentine path over the next 350 years—a path intersecting some of the grandest events imaginable: the birth of science, the rise of democracy, the mind-body problem, the conflict between faith & reason? Their story involves people from all walks of life—Louis XIV, a Swedish casino operator, poets & playwrights, philosophers & physicists, as these people used the bones in scientific studies, stole them, sold them, revered them as relics, fought over them, passed them surreptitiously from hand to hand. The answer lies in Descartes’ famous phrase: Cogito ergo sum—"I think, therefore I am." In his deceptively simple 78-page essay, Discourse on the Method, this small, vain, vindictive, peripatetic, ambitious Frenchman destroyed 2000 years of received wisdom & laid the foundations of the modern world. At the root of Descartes’ method was skepticism: "What can I know for certain?" Like-minded thinkers around Europe passionately embraced the book--the method was applied to medicine, nature, politics & society. The notion that one could find truth in facts that could be proved, & not in reliance on tradition & the Church's teachings, would become a turning point in human history. In an age of faith, what Descartes was proposing seemed like heresy. Yet Descartes himself was a good Catholic, who was spurred to write his incendiary book for the most personal of reasons: He'd devoted himself to medicine & the study of nature, but when his beloved daughter died aged 5, he took his ideas deeper. To understand the natural world one needed to question everything. Thus the scientific method was created & religion overthrown. If the natural world could be understood, knowledge could be advanced, & others might not suffer as his child did. The great controversy Descartes ignited continues to our era: where Islamic terrorists spurn the modern world & pine for a culture based on unquestioning faith; where scientists write bestsellers that passionately make the case for atheism; where others struggle to find a balance between faith & reason. Descartes’ Bonesis a historical detective story about the creation of the modern mind, with twists & turns leading up to the present day—to the science museum in Paris where the philosopher’s skull now resides & to the church a few kilometers away where, not long ago, a philosopher-priest said a mass for his bones.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    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"

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    Why is the universe expanding at an ever faster rate? What is the nature of the "dark matter" that makes up almost a quarter of the universe? Why does the universe appear fine-tuned for life? Are there others besides our own? Ananthaswamy soon finds himself at the ends of the earth--in remote and sometimes dangerous places. Take the Atacama Desert in the Chilean Andes, one of the coldest, driest places on the planet, where not even a blade of grass can survive. Its spectacularly clear skies and dry atmosphere allow astronomers to gather brilliant images of galaxies billions of light-years away. Ananthaswamy takes us inside the European Southern Observatory's Very Large Telescope on Mount Paranal, where four massive domes open to the sky each night "like dragons waking up."He also takes us deep inside an abandoned iron mine in Minnesota, where half-mile-thick rock shields physicists as they hunt for elusive dark matter particles. And to the East Antarctic Ice Sheet, where engineers are drilling 1.5 miles into the clearest ice on the planet. They're building the world's largest neutrino detector, which could finally help reconcile quantum physics with Einstein's theory of general relativity.The stories of the people who work at these and other dramatic research sites--from Lake Baikal in Siberia to the Indian Astronomical Observatory in the Himalayas to the subterranean lair of the Large Hadron Collider--make for a compelling new portrait of the universe and our quest to understand it. An atmospheric, engaging, and illuminating read, "The Edge of Physics" depicts science as a human process, bringing cosmology back down to earth in the most vivid terms.

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.