The Infinite in the Finite

By Alistair Macintosh Wilson | Go to book overview

PREFACE

I have never read prefaces to books. As a student I came to believe that prefaces are the places where authors, relieved finally of the burden of their books, parade their stables of pet hobby-horses. The purpose of this preface is therefore not to bore the reader with my views on the teaching of elementary mathematics or its history. It is simply to tell a few stories about how I came to write this book, and to thank the people without whose help it would never have come into existence.

In the mid- 1950s, I was very interested, like most children my age, in atomic bombs. Having read some of the popular accounts of the day, and seen some of the propaganda films of various 'ban-the-bomb' organizations, I was dissatisfied. I wanted to know how a nuclear weapon 'really' worked. I asked my cousin Michael, at the time manfully struggling through the Cambridge Mathematics Tripos. Michael told me that to understand how an atom bomb worked I would have to learn a lot of mathematics. After attempting unsuccessfully to teach me calculus, he suggested I started with trigonometry. He gave me E. T. Bell Men of mathematics to read. I loved the stories of the great mathematicians, but found I couldn't learn any mathematics from this book.

When I returned to school (Bedales) I went to the library to find a book on trigonometry. Being very small for my age, I remember how huge the library doors seemed. I emerged from the Bedales library with no knowledge of trigonometry, but clutching one fact which I have never forgotten; a radian is 57°17′44.8″. I had no idea why mathematicians should choose to measure angles in terms of this strange unit. Further trips to the library unearthed another book which I enjoyed; W. W. Sawyer Mathematicians delight.

By then my ideas on how I wanted to learn mathematics had begun to take concrete form. I wanted to learn mathematics as a story. Since no book that I could find presented the subject in this way, I rejected them all with the ferocity of childhood as 'a pack of trash'. I very quickly convinced myself that I was no good at mathematics. At the same time, however, I believed that behind the courses I sat through with rising irritation and incomprehension, there was a 'real' mathematics out of whose living force came the problems and solutions which seemed to me to appear at random.

-vii-

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The Infinite in the Finite
Table of contents

Table of contents

  • Title Page iii
  • Preface vii
  • Contents xi
  • 1 - Symphonies of Stone 1
  • 2 - The Pyramid Builders 19
  • 3 - The Theban Mysteries 42
  • 4 - Babylon 53
  • 5 - The Middle Kingdom 72
  • 6 - The Achaeans 105
  • 7 - A World Made of Numbers 112
  • 8 - The Thoughts of Zeus 132
  • 9 - The Philosopher's Criticism 163
  • 10 - The Elements of Euclid 206
  • 11 - An Island Interlude 239
  • 12 - Proportion 252
  • 13 - The Divine Archimedes 278
  • 14 - Apollonius the Great Geometer 324
  • 15 - The Science of Numbers 366
  • 16 - The School of Alexandria 388
  • 17 - The Dark Sub­ Continent of India 426
  • 18 - The Contribution of Islam 461
  • Bibliography 509
  • Index 515
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