eBook ISBN:  9780821894262 
Product Code:  PSPUM/28.2.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9780821894262 
Product Code:  PSPUM/28.2.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 28; 1976; 318 ppMSC: Primary 00
In May 1974, the American Mathematical Society sponsored a special symposium on the mathematical consequences of the Hilbert problems, held at Northern Illinois University, DeKalb, Illinois. The central concern of the symposium was to focus upon areas of importance in contemporary mathematical research which can be seen as descended in some way from the ideas and tendencies put forward by Hilbert in his speech at the International Congress of Mathematicians in Paris in 1900. The Organizing Committee's basic objective was to obtain as broad a representation of significant mathematical research as possible within the general constraint of relevance to the Hilbert problems. The Committee consisted of P. R. Bateman (secretary), F. E. Browder (chairman), R. C. Buck, D. Lewis, and D. Zelinsky.
This twopart volume contains the proceedings of that symposium and includes papers corresponding to all the invited addresses with one exception: Part 2 contains the address of Professor B. Stanpacchia, which he could not deliver at the symposium because of health problems.
The volume includes photographs of the speakers (by the courtesy of Paul Halmos) and a translation of the text of the Hilbert Problems as published in the Bulletin of the American Mathematical Society of 1903. The papers are published in the order of the problems to which they are filiated, and not in the alphabetical order of their authors.
An additional unusual feature of the volume is the article in Part 1 entitled “Problems of present day mathematics” which appears immediately after the text of Hilbert's article. The development of this material was initiated by Jean Dieudonné through correspondence with a number of mathematicians throughout the world. The resulting problems, as well as others obtained by the editor, appear in the form in which they were suggested.
This item is also available as part of a set: 
Table of Contents

Articles

J. Tate — Problem 9: The general reciprocity law [ MR 0429839 ]

Martin Davis, Yuri Matijasevič and Julia Robinson — Hilbert’s tenth problem: Diophantine equations: positive aspects of a negative solution [ MR 0432534 ]

O. T. O’Meara — Hilbert’s eleventh problem: The arithmetic theory of quadratic forms

R. P. Langlands — Some contemporary problems with origins in the Jugendtraum (Hilbert’s problem 12) [ MR 0437500 ]

G. G. Lorentz — The 13th problem of Hilbert [ MR 0507425 ]

David Mumford — Hilbert’s fourteenth problem–the finite generation of subrings such as rings of invariants [ MR 0435076 ]

Steven L. Kleiman — Problem 15: rigorous foundation of Schubert’s enumerative calculus [ MR 0429938 ]

Albrecht Pfister — Hilbert’s seventeenth problem and related problems on definite forms

J. Milnor — Hilbert’s problem 18: on crystallographic groups, fundamental domains, and on sphere packing [ MR 0430101 ]

James Serrin — The solvability of boundary value problems (Hilbert’s problem 19) [ MR 0427784 ]

Enrico Bombieri — Variational problems and elliptic equations (Hilbert’s problem 20) [ MR 0425740 ]

Nicholas M. Katz — An overview of Deligne’s work on Hilbert’s twentyfirst problem

Lipman Bers — On Hilbert’s 22nd problem

Guido Stampacchia — Hilbert’s twentythird problem: extensions of the calculus of variations [ MR 0428150 ]


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In May 1974, the American Mathematical Society sponsored a special symposium on the mathematical consequences of the Hilbert problems, held at Northern Illinois University, DeKalb, Illinois. The central concern of the symposium was to focus upon areas of importance in contemporary mathematical research which can be seen as descended in some way from the ideas and tendencies put forward by Hilbert in his speech at the International Congress of Mathematicians in Paris in 1900. The Organizing Committee's basic objective was to obtain as broad a representation of significant mathematical research as possible within the general constraint of relevance to the Hilbert problems. The Committee consisted of P. R. Bateman (secretary), F. E. Browder (chairman), R. C. Buck, D. Lewis, and D. Zelinsky.
This twopart volume contains the proceedings of that symposium and includes papers corresponding to all the invited addresses with one exception: Part 2 contains the address of Professor B. Stanpacchia, which he could not deliver at the symposium because of health problems.
The volume includes photographs of the speakers (by the courtesy of Paul Halmos) and a translation of the text of the Hilbert Problems as published in the Bulletin of the American Mathematical Society of 1903. The papers are published in the order of the problems to which they are filiated, and not in the alphabetical order of their authors.
An additional unusual feature of the volume is the article in Part 1 entitled “Problems of present day mathematics” which appears immediately after the text of Hilbert's article. The development of this material was initiated by Jean Dieudonné through correspondence with a number of mathematicians throughout the world. The resulting problems, as well as others obtained by the editor, appear in the form in which they were suggested.

Articles

J. Tate — Problem 9: The general reciprocity law [ MR 0429839 ]

Martin Davis, Yuri Matijasevič and Julia Robinson — Hilbert’s tenth problem: Diophantine equations: positive aspects of a negative solution [ MR 0432534 ]

O. T. O’Meara — Hilbert’s eleventh problem: The arithmetic theory of quadratic forms

R. P. Langlands — Some contemporary problems with origins in the Jugendtraum (Hilbert’s problem 12) [ MR 0437500 ]

G. G. Lorentz — The 13th problem of Hilbert [ MR 0507425 ]

David Mumford — Hilbert’s fourteenth problem–the finite generation of subrings such as rings of invariants [ MR 0435076 ]

Steven L. Kleiman — Problem 15: rigorous foundation of Schubert’s enumerative calculus [ MR 0429938 ]

Albrecht Pfister — Hilbert’s seventeenth problem and related problems on definite forms

J. Milnor — Hilbert’s problem 18: on crystallographic groups, fundamental domains, and on sphere packing [ MR 0430101 ]

James Serrin — The solvability of boundary value problems (Hilbert’s problem 19) [ MR 0427784 ]

Enrico Bombieri — Variational problems and elliptic equations (Hilbert’s problem 20) [ MR 0425740 ]

Nicholas M. Katz — An overview of Deligne’s work on Hilbert’s twentyfirst problem

Lipman Bers — On Hilbert’s 22nd problem

Guido Stampacchia — Hilbert’s twentythird problem: extensions of the calculus of variations [ MR 0428150 ]