VI. The Universe and Beyond: The Existence of the Hypercosmic

Chapters in this book

1. Frontmatter I
2. Preface V
3. Preface to the Second Edition VII
4. Contents IX
5. I. The Human Worth of Rigorous Thinking 1
6. II. The Human Significance of Mathematics 25
7. III. The Humanization of the Teaching of Mathematics 60
8. IV. The Walls of the World; or Concerning the Figure and the Dimensions of the Universe of Space 80
9. V. Mathematical Emancipations: Dimensionality and Hyperspace 100
10. VI. The Universe and Beyond: The Existence of the Hypercosmic 120
11. VII. The Axiom of Infinity: A New Presupposition of Thought 137
12. VIII. The Permanent Basis of a Liberal Education 161
13. IX. Graduate Mathematical Instruction for Graduate Students Not Intending to Become Mathematicians 173
14. X. The Source and Functions of a University 197
15. XI. Research in American Universities 204
16. XII. Principia Mathematica 215
17. XIII. Concerning Multiple Interpretations of Postulate Systems and the " Existence" of Hyperspace 228
18. XIV. Mathematical Productivity in the United States 251
19. XV. Mathematics 265
20. XVI. Man and Men 308
21. XVII. Educational Ideals That Are Most Worthy of Loyalty 315
22. Index of Authors 321