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The Millennium Prize Problems
 
Edited by: James Carlson :  Clay Mathematics Institute, Cambridge, MA
Arthur Jaffe :  Harvard University, Cambridge, MA
Andrew Wiles :  Institute for Advanced Study, Princeton, NJ
A co-publication of the AMS and Clay Mathematics Institute
Softcover ISBN:  978-1-4704-7460-7
Product Code:  MPRIZE.S
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $27.20
eBook ISBN:  978-1-4704-7601-4
Product Code:  MPRIZE.E
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
Softcover ISBN:  978-1-4704-7460-7
eBook: ISBN:  978-1-4704-7601-4
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
Add to cart
Click above image for expanded view
The Millennium Prize Problems
Edited by: James Carlson :  Clay Mathematics Institute, Cambridge, MA
Arthur Jaffe :  Harvard University, Cambridge, MA
Andrew Wiles :  Institute for Advanced Study, Princeton, NJ
A co-publication of the AMS and Clay Mathematics Institute
Softcover ISBN:  978-1-4704-7460-7
Product Code:  MPRIZE.S
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $27.20
eBook ISBN:  978-1-4704-7601-4
Product Code:  MPRIZE.E
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
Softcover ISBN:  978-1-4704-7460-7
eBook ISBN:  978-1-4704-7601-4
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
Add to cart
  • Book Details
     
     
    2006; 165 pp
    MSC: 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 Swinnerton-Dyer 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 well-known 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 co-publication of the AMS and the Clay Mathematics Institute (Cambridge, MA).

    Readership

    Anyone 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 Swinnerton-Dyer Conjecture
    • 1. Early History
    • 2. Recent History
    • 3. Rational Points on Higher-Dimensional 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
2006; 165 pp
MSC: 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 Swinnerton-Dyer 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 well-known 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 co-publication of the AMS and the Clay Mathematics Institute (Cambridge, MA).

Readership

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 Swinnerton-Dyer Conjecture
  • 1. Early History
  • 2. Recent History
  • 3. Rational Points on Higher-Dimensional 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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