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Math through the Ages: A Gentle History for Teachers and Others

William P. Berlinghoff and Fernando Q. Gouvêa
Oxton House
Publication Date: 
Number of Pages: 
[Reviewed by
Victor J. Katz
, on

Where does π come from? Why should we be interested in negative numbers, or square roots of negative numbers? How did people ever figure out the quadratic formula? The answers to these and many other similar questions asked by college and secondary teachers and their students can be found, in easily accessible form, in this wonderful little book by two faculty members at Colby College.

Although knowledge of the history of mathematics is an important tool for mathematics teachers at the secondary and college level, it is not always simple to find out about the history of a particular topic. There are many solid texts in the field, but often the history of the quadratic equation, for example, is spread among several chapters because it extends through many cultures and many centuries. In this book, on the other hand, the basic story can be found immediately by turning to chapter 10.

The authors call this book "a gentle history," and indeed it is. It very carefully gives the reader capsule histories of such topics as zero, symbols in algebra, solving cubic equations, the Pythagorean theorem, sines and cosines, and elementary statistics, among many others. Each short chapter discusses the history of a particular idea, often spanning centuries and civilizations, but always clearly and concisely. It is written so that a teacher can dip in wherever she wants, find the information she needs, and use the information in classes or answer questions of her students.

But if the teacher wants more than these capsule histories, the first section of the book, entitled "The History of Mathematics in a Large Nutshell," will help. Here, the authors treat the history of mathematics chronologically, from its beginnings in ancient Egypt and Mesopotamia up to the development of computers in the late twentieth century. This section thus provides a broad overview that will help the reader place the individual chapters in context.

And if the reader wants to go deeper into any particular subject, or into the history of mathematics as a whole, the authors again provide guidance, first with a suggested reference shelf of books to which to turn to find more information, then with a list of "fifteen historical books you ought to read" (in their entirety), and finally with a brief tour of historical sources on the Internet. Finally, the book contains a marvelous bibliography of other works referred to in the various chapters.

Math through the Ages is a very well-organized and thus a very user-friendly book. It will be a wonderful resource for teachers at all levels. And since it sells for a very reasonable price, it should be part of every teacher's personal library.

(See also the authors' web site for this book.)

Note: This review was solicited and written without the knowledge or participation of the editor of Read This! and MAA Reviews.

Victor J. Katz ( is professor of mathematics at the University of the District of Columbia and is Visiting Mathematician at the MAA this year.


History in the Mathematics Classroom

The History of Mathematics in a Large Nutshell

  • Beginnings
  • Greek Mathematics
  • Meanwhile, in India
  • Arabic Mathematics
  • Medieval Europe
  • The 15th and 16th Centuries
  • Algebra Comes of Age
  • Calculus and Applied Mathematics
  • Rigor and Professionalism
  • Abstraction, Computers, and New Applications
  • Mathematics Today


  1. Keeping Count
    Writing Whole Numbers
  2. Reading and Writing Arithmetic
    Where the Symbols Came From
  3. Nothing Becomes a Number
    The Story of Zero
  4. Broken Numbers
    Writing Fractions
  5. Something Less Than Nothing?
    Negative Numbers
  6. By Tens and Tenths
    Metric Measurement
  7. Measuring the Circle
    The Story of π
  8. The Cossic Art
    Writing Algebra with Symbols
  9. Linear Thinking
    Solving First Degree Equations
  10. A Square and Things
    Quadratic Equations
  11. Intrigue in Renaissance Italy
    Solving Cubic Equations
  12. A Cheerful Fact
    The Pythagorean Theorem
  13. A Marvelous Proof
    Fermat's Last Theorem
  14. On Beauty Bare
    Euclid's Plane Geometry
  15. In Perfect Shape
    The Platonic Solids
  16. Shapes by the Numbers
    Coordinate Geometry
  17. Impossible, Imaginary, Useful
    Complex Numbers
  18. Half Is Better
    Sine and Cosine
  19. Strange New Worlds
    The Non-Euclidean Geometries
  20. In the Eye of the Beholder
    Projective Geometry
  21. What's in a Game?
    The Start of Probability Theory
  22. Making Sense of Data
    Statistics Becomes a Science
  23. Machines that Think?
    Electronic Computers
  24. The Arithmetic of Reasoning
    Logic and Boolean Algebra
  25. Beyond Counting
    Infinity and the Theory of Sets

What to Read Next

  • The Reference Shelf
  • Fifteen Historical Books You Ought to Read
  • The Internet and Other Media