Softcover ISBN:  9781470474607 
Product Code:  MPRIZE.S 
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AMS Member Price:  $27.20 
eBook ISBN:  9781470476014 
Product Code:  MPRIZE.E 
List Price:  $35.00 
MAA Member Price:  $31.50 
AMS Member Price:  $28.00 
Softcover ISBN:  9781470474607 
eBook: ISBN:  9781470476014 
Product Code:  MPRIZE.S.B 
List Price:  $69.00 $51.50 
MAA Member Price:  $62.10 $46.35 
AMS Member Price:  $55.20 $41.20 
Softcover ISBN:  9781470474607 
Product Code:  MPRIZE.S 
List Price:  $34.00 
MAA Member Price:  $30.60 
AMS Member Price:  $27.20 
eBook ISBN:  9781470476014 
Product Code:  MPRIZE.E 
List Price:  $35.00 
MAA Member Price:  $31.50 
AMS Member Price:  $28.00 
Softcover ISBN:  9781470474607 
eBook ISBN:  9781470476014 
Product Code:  MPRIZE.S.B 
List Price:  $69.00 $51.50 
MAA Member Price:  $62.10 $46.35 
AMS Member Price:  $55.20 $41.20 

Book Details2006; 165 ppMSC: Primary 00; Secondary 01; 11; 14; 35; 57; 03; 81
Guided by the premise that solving some of the world's most important mathematical problems will advance the field, this book offers a fascinating look at the seven unsolved Millennium Prize problems. This work takes the unprecedented approach of describing these important and difficult problems at the professional level.
In announcing the seven problems and a US$7 million prize fund in 2000, the Clay Mathematics Institute emphasized that mathematics still constitutes an open frontier with important unsolved problems. The descriptions in this book serve the Institute's mission to “further the beauty, power and universality of mathematical thinking.”
Separate chapters are devoted to each of the seven problems: the Birch and SwinnertonDyer Conjecture, the Hodge Conjecture, the Navier–Stokes Equation, the P versus NP Problem, the Poincaré Conjecture, the Riemann Hypothesis, and Quantum Yang–Mills Theory.
An essay by Jeremy Gray, a wellknown expert in the history of mathematics, outlines the history of prize problems in mathematics and shows how some of mathematics' most important discoveries were first revealed in papers submitted for prizes. Numerous photographs of mathematicians who shaped mathematics as it is known today give the text a broad historical appeal. Anyone interested in mathematicians' continued efforts to solve important problems will be fascinated with this text, which places into context the historical dimension of important achievements.
A copublication of the AMS and the Clay Mathematics Institute (Cambridge, MA).
ReadershipAnyone interested in the Millennium Prizes, especially graduate students.

Table of Contents

Front Cover

Contents

Introduction

Landon T. Clay

Statement of the Directors and the Scientific Advisory Board

A History of Prizes in Mathematics

1. Introduction

2. The Academic Prize Tradition in the 18th Century

3. The Academic Prize Tradition in the 19th Century

4. The Hilbert Problems

5. Some Famous Retrospective Prizes

Bibliography

The Birch and SwinnertonDyer Conjecture

1. Early History

2. Recent History

3. Rational Points on HigherDimensional Varieties

Bibliography

The Hodge Conjecture

1. Statement

2. Remarks

3. The Intermediate Jacobian

4. Detecting Hodge Classes

5. Motives

6. Substitutes and Weakened Forms

Bibliography

Existence and Smoothness of the Navier–Stokes Equation

Bibliography

The Poincar´e Conjecture

1. Introduction

2. Early Missteps

3. Higher Dimensions

4. The Thurston Geometrization Conjecture

5. Approaches through Differential Geometry and Differential Equations

Bibliography

The P versus NP Problem

1. Statement of the Problem

2. History and Importance

3. The Conjecture and Attempts to Prove It

Appendix: Definition of Turing Machine

Acknowledgments

Bibliography

The Riemann Hypothesis

1. The Problem

2. History and Significance of the Riemann Hypothesis

3. Evidence for the Riemann Hypothesis

4. Further Evidence: Varieties Over Finite Fields

5. Further Evidence: The Explicit Formula

Bibliography

Quantum Yang–Mills Theory

1. The Physics of Gauge Theory

2. Quest for Mathematical Understanding

3. Quantum Fields

4. The Problem

5. Comments

6. Mathematical Perspective

Bibliography

Rules for the Millennium Prizes

Authors’ Biographies

Picture Credits

Back Cover


Additional Material

Reviews

Given the interest generated by the Millennium Problems, this book should be in every mathematics library ...
MAA Reviews


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Guided by the premise that solving some of the world's most important mathematical problems will advance the field, this book offers a fascinating look at the seven unsolved Millennium Prize problems. This work takes the unprecedented approach of describing these important and difficult problems at the professional level.
In announcing the seven problems and a US$7 million prize fund in 2000, the Clay Mathematics Institute emphasized that mathematics still constitutes an open frontier with important unsolved problems. The descriptions in this book serve the Institute's mission to “further the beauty, power and universality of mathematical thinking.”
Separate chapters are devoted to each of the seven problems: the Birch and SwinnertonDyer Conjecture, the Hodge Conjecture, the Navier–Stokes Equation, the P versus NP Problem, the Poincaré Conjecture, the Riemann Hypothesis, and Quantum Yang–Mills Theory.
An essay by Jeremy Gray, a wellknown expert in the history of mathematics, outlines the history of prize problems in mathematics and shows how some of mathematics' most important discoveries were first revealed in papers submitted for prizes. Numerous photographs of mathematicians who shaped mathematics as it is known today give the text a broad historical appeal. Anyone interested in mathematicians' continued efforts to solve important problems will be fascinated with this text, which places into context the historical dimension of important achievements.
A copublication of the AMS and the Clay Mathematics Institute (Cambridge, MA).
Anyone interested in the Millennium Prizes, especially graduate students.

Front Cover

Contents

Introduction

Landon T. Clay

Statement of the Directors and the Scientific Advisory Board

A History of Prizes in Mathematics

1. Introduction

2. The Academic Prize Tradition in the 18th Century

3. The Academic Prize Tradition in the 19th Century

4. The Hilbert Problems

5. Some Famous Retrospective Prizes

Bibliography

The Birch and SwinnertonDyer Conjecture

1. Early History

2. Recent History

3. Rational Points on HigherDimensional Varieties

Bibliography

The Hodge Conjecture

1. Statement

2. Remarks

3. The Intermediate Jacobian

4. Detecting Hodge Classes

5. Motives

6. Substitutes and Weakened Forms

Bibliography

Existence and Smoothness of the Navier–Stokes Equation

Bibliography

The Poincar´e Conjecture

1. Introduction

2. Early Missteps

3. Higher Dimensions

4. The Thurston Geometrization Conjecture

5. Approaches through Differential Geometry and Differential Equations

Bibliography

The P versus NP Problem

1. Statement of the Problem

2. History and Importance

3. The Conjecture and Attempts to Prove It

Appendix: Definition of Turing Machine

Acknowledgments

Bibliography

The Riemann Hypothesis

1. The Problem

2. History and Significance of the Riemann Hypothesis

3. Evidence for the Riemann Hypothesis

4. Further Evidence: Varieties Over Finite Fields

5. Further Evidence: The Explicit Formula

Bibliography

Quantum Yang–Mills Theory

1. The Physics of Gauge Theory

2. Quest for Mathematical Understanding

3. Quantum Fields

4. The Problem

5. Comments

6. Mathematical Perspective

Bibliography

Rules for the Millennium Prizes

Authors’ Biographies

Picture Credits

Back Cover

Given the interest generated by the Millennium Problems, this book should be in every mathematics library ...
MAA Reviews