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:

- Why should Pythagoras and his followers be credited with (or blamed for) some of the methodology of the "new" mathematics?
- How do modern algebras (plural) generalize the "common garden variety"?
- What single modern concept makes it possible to conceive in a nutshell of
*all*geometries plain and fancy—Euclidean, non-Euclidean, affine, projective, inversive, etc.? - What is the nature of the universal language initiated by a thirteenth-century Catalan mystic, actually formulated b Leibniz, and improved by Boole an De Morgan?
- How did Omar Khayy´m solve certain cubic equations?
- What are the common features of an boy's "engagement problem," the geishas' pantomime of baseball, and modern engineering decisions?
- Who are the "Leonardos" of modern mathematics?
- How did Queen Dido set a precedent for mathematicians and physicists?
- Why should isomorphism, homomorphism, and homeomorphism be an intrinsic part of the vocabulary of every mathophile?
- How did Maxwell's "demon" make the irreversible reversible?
- How did the mere matter of counting socks lead a millionaire mathematical genius to renounce mathematics in favor of finance?
- What are the beautiful "ideals" formulated by Richard Dedekind and advanced by Emmy Noether?

**Contents**

- From Babylonian Beginnings to Digital Computers
- Mathematical Method and Main Streams Are Launched
- Mathematical Reasoning from Eudoxus to Lobachevsky
- Algebra from Hypatia to Hamilton
- Equations, Human and Inhuman
- A Universal Language
- Forefathers of Modern Mathematics and Their Legacy
- A Calculus for Heaven and Earth
- Determinism and Its Creators
- The Elements of Strategy in War and Peace
- Probabilistic Models, Great Expectations, and Randomized Strategies
- General Games and Statistical Decision Theory
- From Dice to Quantum Theory and Quality Control
- Realm of Random Variables
- Demons, Energy, maxwell, and Gibbs
- Sweet Manuscript of Youth
- The Unification of Geometry
- A Special Group and Its Application
- Geometry for Universe-Builders
- Post-Relativity Geometry
- East Meets West in the Higher Arithmetic
- The Reformation of Analysis
- Royal Roads to Functional Analysis
- Infinite Hierarchy
- Angelic Geometry
- The Leonardos of Modern Mathematics
- Twentieth-Century Vistas—Analysis
- Twentieth-Century Vistas—Algebra
- Twentieth-Century Vistas—Logic and Foundations
- Retrospect and Prospect