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Book Synopsis The Millennium Prize Problems by : James Carlson
Download or read book The Millennium Prize Problems written by James Carlson and published by American Mathematical Society, Clay Mathematics Institute. This book was released on 2023-09-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: On August 8, 1900, at the second International Congress of Mathematicians in Paris, David Hilbert delivered his famous lecture in which he described twenty-three problems that were to play an influential role in mathematical research. A century later, on May 24, 2000, at a meeting at the Collège de France, the Clay Mathematics Institute (CMI) announced the creation of a US$7 million prize fund for the solution of seven important classic problems which have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution. The Millennium Prize Problems were selected by the founding Scientific Advisory Board of CMI—Alain Connes, Arthur Jaffe, Andrew Wiles, and Edward Witten—after consulting with other leading mathematicians. Their aim was somewhat different than that of Hilbert: not to define new challenges, but to record some of the most difficult issues with which mathematicians were struggling at the turn of the second millennium; to recognize achievement in mathematics of historical dimension; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; and to emphasize the importance of working towards a solution of the deepest, most difficult problems. The present volume sets forth the official description of each of the seven problems and the rules governing the prizes. It also contains an essay by Jeremy Gray on the history of prize problems in mathematics.
Book Synopsis The Millennium Prize Problems by : James A. Carlson
Download or read book The Millennium Prize Problems written by James A. Carlson and published by American Mathematical Soc.. This book was released on 2006 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "On May 24, 2000, at a meeting at the Collège de France, the Clay Mathematics Institute announced the creation of a US$7 million prize fund for the solution of seven important classic problems that have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution. The Millennium Prize problems gives the official description of each of the seven problems and the rules governing the prizes"--Information screen.
Book Synopsis The Millennium Problems by : Keith J. Devlin
Download or read book The Millennium Problems written by Keith J. Devlin and published by Granta Books. This book was released on 2005 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2000, the Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1million in prize money. They encompass many of the most fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. Keith Devlin describes here what the seven problems are, how they came about, and what they mean for mathematics and science. In the hands of Devlin, each Millennium Problem becomes a fascinating window onto the deepest questions in the field.
Book Synopsis The Poincare Conjecture by : Donal O'Shea
Download or read book The Poincare Conjecture written by Donal O'Shea and published by Bloomsbury Publishing USA. This book was released on 2009-05-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.
Book Synopsis Losing the Nobel Prize: A Story of Cosmology, Ambition, and the Perils of Science's Highest Honor by : Brian Keating
Download or read book Losing the Nobel Prize: A Story of Cosmology, Ambition, and the Perils of Science's Highest Honor written by Brian Keating and published by W. W. Norton & Company. This book was released on 2018-04-24 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Riveting."—Science A Forbes, Physics Today, Science News, and Science Friday Best Science Book Of 2018 Cosmologist and inventor of the BICEP (Background Imaging of Cosmic Extragalactic Polarization) experiment, Brian Keating tells the inside story of the mesmerizing quest to unlock cosmology’s biggest mysteries and the human drama that ensued. We follow along on a personal journey of revelation and discovery in the publish-or-perish world of modern science, and learn that the Nobel Prize might hamper—rather than advance—scientific progress. Fortunately, Keating offers practical solutions for reform, providing a vision of a scientific future in which cosmologists may finally be able to see all the way back to the very beginning.
Book Synopsis Prime Obsession by : John Derbyshire
Download or read book Prime Obsession written by John Derbyshire and published by Joseph Henry Press. This book was released on 2003-04-15 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.
Book Synopsis The Great Mathematical Problems by : Ian Stewart
Download or read book The Great Mathematical Problems written by Ian Stewart and published by Profile Books. This book was released on 2013-03-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincaré Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.
Book Synopsis The Mathematical Monthly by : John Daniel Runkle
Download or read book The Mathematical Monthly written by John Daniel Runkle and published by . This book was released on 1860 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A complete catalogue of the writings of Sir John Herschel": v. 3, p. 220-227.
Book Synopsis Discovering Prices by : Paul Milgrom
Download or read book Discovering Prices written by Paul Milgrom and published by Columbia University Press. This book was released on 2017-05-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional economic theory studies idealized markets in which prices alone can guide efficient allocation, with no need for central organization. Such models build from Adam Smith’s famous concept of an invisible hand, which guides markets and renders regulation or interference largely unnecessary. Yet for many markets, prices alone are not enough to guide feasible and efficient outcomes, and regulation alone is not enough, either. Consider air traffic control at major airports. While prices could encourage airlines to take off and land at less congested times, prices alone do just part of the job; an air traffic control system is still indispensable to avoid disastrous consequences. With just an air traffic controller, however, limited resources can be wasted or poorly used. What’s needed in this and many other real-world cases is an auction system that can effectively reveal prices while still maintaining enough direct control to ensure that complex constraints are satisfied. In Discovering Prices, Paul Milgrom—the world’s most frequently cited academic expert on auction design—describes how auctions can be used to discover prices and guide efficient resource allocations, even when resources are diverse, constraints are critical, and market-clearing prices may not even exist. Economists have long understood that externalities and market power both necessitate market organization. In this book, Milgrom introduces complex constraints as another reason for market design. Both lively and technical, Milgrom roots his new theories in real-world examples (including the ambitious U.S. incentive auction of radio frequencies, whose design he led) and provides economists with crucial new tools for dealing with the world’s growing complex resource-allocation problems.
Download or read book The Mathematical Monthly written by and published by . This book was released on 1859 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Prime Numbers and the Riemann Hypothesis by : Barry Mazur
Download or read book Prime Numbers and the Riemann Hypothesis written by Barry Mazur and published by Cambridge University Press. This book was released on 2016-04-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Book Synopsis Poincare's Prize by : George G. Szpiro
Download or read book Poincare's Prize written by George G. Szpiro and published by Penguin. This book was released on 2008-07-29 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
Download or read book Max's Math written by Kate Banks and published by Macmillan. This book was released on 2015-03-10 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max and his brothers drive to Shapeville and Count Town searching for problems, and are able to use their skills in arithmetic and sleuthing to help get things ready for a rocket launch.
Book Synopsis Challenging Problems in Algebra by : Alfred S. Posamentier
Download or read book Challenging Problems in Algebra written by Alfred S. Posamentier and published by Courier Corporation. This book was released on 2012-05-04 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
Download or read book Mathematical monthly written by and published by . This book was released on 1860 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Chess-monthly written by and published by . This book was released on 1884 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Scottish Book by : R. Daniel Mauldin
Download or read book The Scottish Book written by R. Daniel Mauldin and published by Birkhäuser. This book was released on 2015-11-26 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such areas as functional and real analysis, group theory, measure and set theory, probability, and topology. Finding solutions to the problems they proposed has been ongoing since World War II, with prizes offered in many cases to those who are successful. In the 35 years since the first edition published, several more problems have been fully or partially solved, but even today many still remain unsolved and several prizes remain unclaimed. In view of this, the editor has gathered new and updated commentaries on the original 193 problems. Some problems are solved for the first time in this edition. Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac, Antoni Zygmund, Paul Erdös, and Andrzej Granas that provide amazing insights into the mathematical environment of Lwów before World War II and the development of The Scottish Book. Also new in this edition are a brief history of the University of Wrocław’s New Scottish Book, created to revive the tradition of the original, and some selected problems from it. The Scottish Book offers a unique opportunity to communicate with the people and ideas of a time and place that had an enormous influence on the development of mathematics and try their hand on the unsolved problems. Anyone in the general mathematical community with an interest in the history of modern mathematics will find this to be an insightful and fascinating read.
