Mathematicians and Their Times (eBook)

Front Cover 1
Mathematicians and Their Times: History of Mathematics and Mathematics of History 4
Copyright Page 5
Contents 10
Preface 6
INTRODUCTION 12
Part I: Generalities 12
1. The non-mathematical framework 12
2. The trained observer 14
3. The embellishment of truth 15
4. The intrusion of personal feelings 17
5. Some rules of critical analysis 20
Part II: Early History 24
6. The historical significance of mathematics 24
7. The meaning of mathematics 27
8. The distant past 30
9. The Greek school of mathematics 33
10. The destructive bends 43
11. The miraculous preservation 48
Part III: The Slow Renaissance 50
12. Dismal prospects in Western Europe 50
13. The pioneers who came too soon 52
14. The leadership that could not last 60
Part IV: The New Beginning 67
15. The beginnings of analysis 67
16. Newton 83
17. Preparing for bankruptcy 100
18. Euler 114
19. The rise of mathematics in Paris 125
CHAPTER I. The Romantic Period 135
20. The flouting of arithmetic 135
21. The founding of the Ecole Polytechnique 141
22. Gauss 153
23. The first romantics 166
24. Riemann and Weierstrass 198
25. Between two worlds 215
CHAPTER II. The Dream of a Conceptual Age, and Hard Reality of Struggle for Existence 227
26. The unprized heritage 227
27. The significance of Plato for mathematics 233
28. Cantor and Sets 237
29. Goettingen 244
CHAPTER III. The Age of Contradictions and of the Great Question Marks 260
30. The art of the possible 260
31. The expansion of mathematics 266
32. Cambridge 277
33. The Hardy-Littlewood era 286
34. The battleground of ideas 306
35. The uncertain further blooming 324
36. The other side of catastrophe 333
INDEX 350