Honors Class : Hilbert's Problems and Their Solvers

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Honors Class : Hilbert's Problems and Their Solvers

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  • A K Peters Ltd(2003/12発売)
  • 外貨定価 US$ 42.95
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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 436 p.
  • 言語 ENG
  • 商品コード 9781568812168
  • DDC分類 510.904

Full Description

This eminently readable book focuses on the people of mathematics and draws the reader into their fascinating world. In a monumental address, given to the International Congress of Mathematicians in Paris in 1900, David Hilbert, perhaps the most respected mathematician of his time, developed a blueprint for mathematical research in the new century. Jokingly called a natural introduction to thesis writing with examples, this collection of problems has indeed become a guiding inspiration to many mathematicians, and those who succeeded in solving or advancing their solutions form an Honors Class among research mathematicians of this century. In a remarkable labor of love and with the support of many of the major players in the field, Ben Yandell has written a fascinating account of the achievements of this Honors Class, covering mathematical substance and biographical aspects.

Table of Contents

Acknowledgments                                    ix
Introduction: The Origin of the Coordinates 1 (22)
Introduction 3 (2)
Advice: How to Read This Book 5 (2)
The Origin of the Coordinates 7 (16)
The Foundation Problems 1,2,10 23 (92)
Set Theory, Anyone? 25 (12)
I Am Lying (Mathematics Is Consistent) 37 (22)
The Perfect Spy: How Many Real Numbers 59 (26)
Are There?
Can't We Do This with a Computer? 85 (30)
The Foundations of Specific Areas 3,4,5,6 115(48)
In the Original 117(20)
Distance 137(6)
Something for Nothing 143(16)
On Again, Off Again: Physics and Math 159(4)
Number Theory 7,8,9,11,12 163(96)
First, State the Tune 165(6)
Transcending Local Conditions 171(32)
The Inordinate Allure of the Prime Numbers 203(10)
Castles of Air 213(46)
Algebra and Geometry: A Miscellany 259(34)
What Is Algebra? 261(8)
Schubert's Variety Show 269(6)
Graph That Curve 275(4)
How Many Kinds of Crystals Are There, and 279(14)
Does the Grocer Know How to Stack Oranges?
The Analysis Problems 13,19,20,21,22,23 293(90)
Analysis Takes at Least Seven Years 295(2)
How Famous Can a Function Theorist Be? 297(34)
Schools Amid Turbulence 331(34)
Past Chernaya Rechka, to 61 Savushkina 365(8)
Work on It 373(10)
We Come to Our Census 383(4)
Census 385(2)
Appendix 387(2)
Mathematical Problems 389(36)
Notes 425(28)
Selected Bibliography 453(20)
Index 473