The Millennium Prize Problems

The Millennium Prize Problems

Author: James Carlson

Publisher: American Mathematical Society, Clay Mathematics Institute

Published: 2023-09-14

Total Pages: 185

ISBN-13: 1470474603

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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.


The Millennium Problems

The Millennium Problems

Author: Keith J. Devlin

Publisher: Granta Books

Published: 2005

Total Pages: 237

ISBN-13: 9781862077355

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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.


The Millennium Prize Problems

The Millennium Prize Problems

Author: James A. Carlson

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 192

ISBN-13: 9780821836798

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"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.


The Poincare Conjecture

The Poincare Conjecture

Author: Donal O'Shea

Publisher: Bloomsbury Publishing USA

Published: 2009-05-26

Total Pages: 306

ISBN-13: 0802718949

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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.


Poincare's Prize

Poincare's Prize

Author: George G. Szpiro

Publisher: Penguin

Published: 2008-07-29

Total Pages: 324

ISBN-13: 1440634289

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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.


What's Happening in the Mathematical Sciences

What's Happening in the Mathematical Sciences

Author: Barry Cipra

Publisher: American Mathematical Soc.

Published:

Total Pages: 108

ISBN-13: 9780821890431

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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.


The Great Mathematical Problems

The Great Mathematical Problems

Author: Ian Stewart

Publisher: Profile Books

Published: 2013-03-07

Total Pages: 468

ISBN-13: 1847653510

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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.


Introduction to Cosmology

Introduction to Cosmology

Author: Jayant V. Narlikar

Publisher: Cambridge University Press

Published: 1993-03-11

Total Pages: 431

ISBN-13: 9780521412506

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This introductory textbook describes modern cosmology at a level suitable for advanced undergraduates who are familiar with mathematical methods and basic theoretical physics. An introductory survey of the large scale structure of the universe is followed by an outline of general relativity. This is then used to construct the standard models of the universe. The very early and early stages of the Big Bang are described, and this includes primordial nucleosynthesis, grand unified theories, primordial black holes, and the era of quantum cosmology. The problem of the formation of structure in the universe is then addressed. This textbook concludes with brief outlines of alternative cosmologies. It includes 400 problems for students to solve, and is accompanied by numerous worked examples.


Stalking the Riemann Hypothesis

Stalking the Riemann Hypothesis

Author: Dan Rockmore

Publisher: Vintage

Published: 2006-05-09

Total Pages: 306

ISBN-13: 0375727728

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For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.


Elliptic Tales

Elliptic Tales

Author: Avner Ash

Publisher: Princeton University Press

Published: 2012

Total Pages: 277

ISBN-13: 0691151199

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Describes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture.