Agnes Scott College

Edna E. Kramer

The Nature and Growth of Modern Mathematics
Hawthorn Books, Inc., New York, 1970


Preface (Excerpts)

The Nature and Growth of Modern Mathematics traces the development of the most important mathematical concepts from their inception to their present formulation. Although chief emphasis is placed on the explanation of mathematical ideas, nevertheless, mathematical content, history, lore, and biography are integrated in order to offer an overall, unified picture of the mother science. The work presents a discussion of major notions and the general settings in which they were conceived, with particular attention to the lives and thoughts of some of the most creative mathematical innovators. It provides a guide to what is still important in classical mathematics, as well as an introduction to many significant recent developments.

Answers to questions like the following are simple and will be found in this book:


  1. From Babylonian Beginnings to Digital Computers
  2. Mathematical Method and Main Streams Are Launched
  3. Mathematical Reasoning from Eudoxus to Lobachevsky
  4. Algebra from Hypatia to Hamilton
  5. Equations, Human and Inhuman
  6. A Universal Language
  7. Forefathers of Modern Mathematics and Their Legacy
  8. A Calculus for Heaven and Earth
  9. Determinism and Its Creators
  10. The Elements of Strategy in War and Peace
  11. Probabilistic Models, Great Expectations, and Randomized Strategies
  12. General Games and Statistical Decision Theory
  13. From Dice to Quantum Theory and Quality Control
  14. Realm of Random Variables
  15. Demons, Energy, maxwell, and Gibbs
  16. Sweet Manuscript of Youth
  17. The Unification of Geometry
  18. A Special Group and Its Application
  19. Geometry for Universe-Builders
  20. Post-Relativity Geometry
  21. East Meets West in the Higher Arithmetic
  22. The Reformation of Analysis
  23. Royal Roads to Functional Analysis
  24. Infinite Hierarchy
  25. Angelic Geometry
  26. The Leonardos of Modern Mathematics
  27. Twentieth-Century Vistas—Analysis
  28. Twentieth-Century Vistas—Algebra
  29. Twentieth-Century Vistas—Logic and Foundations
  30. Retrospect and Prospect