One, Two, Three ... Infinity: Facts & Speculations of Science

By George Gamow | Go to book overview

CHAPTER II
Natural and Artificial Numbers

1. THE PUREST MATHEMATICS

MATHEMATICS is usually considered, especially by mathematicians, the Queen of all Sciences and, being a queen, it naturally tries to avoid morganatic relations with other branches of knowledge. Thus, for example, when David Hilbert, at a "Joint Congress of Pure and Applied Mathematics," was asked to deliver an opening speech that would help to break down the hostility that, it was felt, existed between the two groups of mathematicians, he began in the following way:

"We are often told that pure and applied mathematics are hostile to each other. This is not true. Pure and applied mathematics are not hostile to each other. Pure and applied mathematics have never been hostile to each other. Pure and applied mathematics will never be hostile to each other. Pure and applied mathematics cannot be hostile to each other because, in fact, there is absolutely nothing in common between them."

But although mathematics likes to be pure and to stand quite apart from other sciences, other sciences, especially physics, like mathematics, and try to "fraternize" with it as much as possible. In fact, almost every branch of pure mathematics is now being put to work to explain one or another feature of the physical universe. This includes such disciplines as the theory of abstract groups, noncommutable algebra, and non-Euclidian geometry, which have always been considered most pure and incapable of any application whatever.

One large system of mathematics, however, has up to now managed to remain quite useless for any purpose except that of stimulating mental gymnastics, and thus can carry with honor the "crown of purity." This is the so-called "theory of numbers" (meaning integer numbers), one of the oldest and most intricate products of pure mathematical thought.

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One, Two, Three ... Infinity: Facts & Speculations of Science
Table of contents

Table of contents

  • Other Books by George Gamow ii
  • Title Page iii
  • Preface v
  • Contents vii
  • Illustrations viii
  • Part I - Playing with Numbers 1
  • Chapter I - Big Numbers 3
  • Chapter II - Natural and Artificial Numbers 24
  • Part II - Space, Time: & Einstein 39
  • Chapter III - Unusual Properties of Space 41
  • Chapter IV - The World of Four Dimensions 64
  • Chapter V - Relativity of Space and Time 84
  • Part III - Microcosmos 113
  • Chapter VI - Descending Staircase 115
  • Chapter VII - Modern Alchemy 149
  • Chapter VIII - The Law of Disorder 192
  • Chapter IX - The Riddle of Life 231
  • Part IV - Macrocosmos 267
  • Chapter X - Expanding Horizons 269
  • Chapter XI - The Days of Creation 298
  • Index 336
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