Unsolved Problems on Mathematics for the 21st Century PDF Download

Author: Kiyoshi Iseki
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 344

View

Book Description

Author: Satyan Devadoss
Publisher: MIT Press
ISBN: 0262542757
Category : Mathematics
Languages : en
Pages : 117

View

Book Description
Sixteen of today's greatest unsolved mathematical puzzles in a story-driven, illustrated volume that invites readers to peek over the edge of the unknown. Most people think of mathematics as a set of useful tools designed to answer analytical questions, beginning with simple arithmetic and ending with advanced calculus. But, as Mage Merlin's Unsolved Mathematical Mysteries shows, mathematics is filled with intriguing mysteries that take us to the edge of the unknown. This richly illustrated, story-driven volume presents sixteen of today's greatest unsolved mathematical puzzles, all understandable by anyone with elementary math skills. These intriguing mysteries are presented to readers as puzzles that have time-traveled from Camelot, preserved in the notebook of Merlin, the wise magician in King Arthur's court. Our guide is Mage Maryam (named in honor of the brilliant young mathematician, the late Maryam Mirzakhani), a distant descendant of Merlin. Maryam introduces the mysteries--each of which is presented across two beautifully illustrated pages--and provides mathematical and historical context afterward. We find Merlin confronting mathematical puzzles involving tinker toys (a present for Camelot's princesses from the sorceress Morgana), cake-slicing at a festival, Lancelot's labyrinth, a vault for the Holy Grail, and more. Each mystery is a sword awaiting removal from its stone, capturing the beauty and power of mathematics.

Author: John Forbes Nash, Jr.
Publisher: Springer
ISBN: 3319321625
Category : Mathematics
Languages : en
Pages : 543

View

Book Description
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Author: Keith J. Devlin
Publisher: Granta Books
ISBN: 9781862077355
Category : Mathematical recreations
Languages : en
Pages : 237

View

Book Description
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.

Author: Piergiorgio Odifreddi
Publisher: Princeton University Press
ISBN: 0691128057
Category : Mathematics
Languages : en
Pages : 224

View

Book Description
The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century, Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details. Odifreddi opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four most important open mathematical problems of the twenty-first century. In presenting the thirty problems at the heart of the book he devotes equal attention to pure and applied mathematics, with applications ranging from physics and computer science to biology and economics. Special attention is dedicated to the famous "23 problems" outlined by David Hilbert in his address to the International Congress of Mathematicians in 1900 as a research program for the new century, and to the work of the winners of the Fields Medal, the equivalent of a Nobel prize in mathematics. This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics.

Author: Richard Guy
Publisher: Springer Science & Business Media
ISBN: 0387266771
Category : Mathematics
Languages : en
Pages : 455

View

Book Description
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.

Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Category : Science
Languages : en
Pages : 446

View

Book Description
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.

Author: J. Barwise
Publisher: Cambridge University Press
ISBN: 1107168252
Category : Mathematics
Languages : en
Pages : 912

View

Book Description
This book brings together several directions of work in model theory between the late 1950s and early 1980s.

Author: Ian Stewart
Publisher: Profile Books
ISBN: 1847653510
Category : Mathematics
Languages : en
Pages : 340

View

Book Description
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 Poincar 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.

Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821890431
Category : Science
Languages : en
Pages : 108

View

Book Description
Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.