The Heritage of Thales

1. Front Matter

   Pages i-x

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • W. S. Anglin, J. Lambek

      Pages 1-3

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3. Topics in the History and Philosophy of Mathematics

   1. Front Matter

      Pages 5-5

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   2. Egyptian Mathematics

      • W. S. Anglin, J. Lambek

      Pages 7-10

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   3. Scales of Notation

      • W. S. Anglin, J. Lambek

      Pages 11-14

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   4. Prime Numbers

      • W. S. Anglin, J. Lambek

      Pages 15-19

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   5. Sumerian-Babylonian Mathematics

      • W. S. Anglin, J. Lambek

      Pages 21-24

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   6. More about Mesopotamian Mathematics

      • W. S. Anglin, J. Lambek

      Pages 25-28

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   7. The Dawn of Greek Mathematics

      • W. S. Anglin, J. Lambek

      Pages 29-32

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   8. Pythagoras and His School

      • W. S. Anglin, J. Lambek

      Pages 33-36

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   9. Perfect Numbers

      • W. S. Anglin, J. Lambek

      Pages 37-40

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   10. Regular Polyhedra

       • W. S. Anglin, J. Lambek

       Pages 41-45

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   11. The Crisis of Incommensurables

       • W. S. Anglin, J. Lambek

       Pages 47-51

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   12. From Heraclitus to Democritus

       • W. S. Anglin, J. Lambek

       Pages 53-57

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   13. Mathematics in Athens

       • W. S. Anglin, J. Lambek

       Pages 59-65

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   14. Plato and Aristotle on Mathematics

       • W. S. Anglin, J. Lambek

       Pages 67-69

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   15. Constructions with Ruler and Compass

       • W. S. Anglin, J. Lambek

       Pages 71-77

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   16. The Impossibility of Solving the Classical Problems

       • W. S. Anglin, J. Lambek

       Pages 79-82

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   17. Euclid

       • W. S. Anglin, J. Lambek

       Pages 83-87

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This is intended as a textbook on the history, philosophy and foundations of mathematics, primarily for students specializing in mathematics, but we also wish to welcome interested students from the sciences, humanities and education. We have attempted to give approximately equal treatment to the three subjects: history, philosophy and mathematics. History We must emphasize that this is not a scholarly account of the history of mathematics, but rather an attempt to teach some good mathematics in a historical context. Since neither of the authors is a professional historian, we have made liberal use of secondary sources. We have tried to give ref­ cited facts and opinions. However, considering that this text erences for developed by repeated revisions from lecture notes of two courses given by one of us over a 25 year period, some attributions may have been lost. We could not resist retelling some amusing anecdotes, even when we suspect that they have no proven historical basis. As to the mathematicians listed in our account, we admit to being colour and gender blind; we have not attempted a balanced distribution of the mathematicians listed to meet today's standards of political correctness. Philosophy Both authors having wide philosophical interests, this text contains perhaps more philosophical asides than other books on the history of mathematics. For example, we discuss the relevance to mathematics of the pre-Socratic philosophers and of Plato, Aristotle, Leibniz and Russell. We also have vi Preface presented some original insights.

• History of Mathematics
• Renaissance
• education
• mathematics
• philosophy of mathematics
• physics
• proposition

• Department of Mathematics and Statistics, McGill University, Montreal, Canada

  W. S. Anglin, J. Lambek

Policies and ethics