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Learn from the Masters

1 rating: 3.0
A book by Frank Swetz

This book is for high school and college teachers who want to know how they can use the history of mathematics as a pedagogical tool to help their students construct their own knowledge of mathematics. Often, a historical development of a particular … see full wiki

Author: Frank Swetz
Publisher: The Mathematical Association of America
1 review about Learn from the Masters

A fitting tribute to Niels Henrik Abel

  • Feb 23, 2000
It is well-known that using clichés is considered poor form in writing. However, there is often a fine, essentially nonexistent line between a cliché and an old truism with a great deal of wisdom. The title of this book is one form of what is perhaps the best of all the words of wisdom, namely to be the best, you must learn from the best. No one knew this better than Niels Henrik Abel, Norway's greatest mathematician. He wrote the following in the margin of one of his notebooks,

"It appears to me that if one wants to make progress in mathematics one should study the masters."

This book is a publication of some of the papers presented at an international conference on the History of Mathematics held in Kristiansand, Norway in 1988. It is fitting that Abel lived in that area for some time.
Reading about the actions of the masters is always refreshing and helps to improve your self-esteem. To know that even the great ones struggled and made colossal errors reminds us that mathematical progress is not linear, but extremely chaotic. If a chart could be made of the development of mathematics, it would exhibit a gross upward movement. However, if one was to perform an expansion transformation, the local behavior would resemble Brownian motion. It is also sad to be informed about some of the spiteful actions that even geniuses are capable of.
The range of topics covered in this collection of papers is wide and includes some of the applied mathematical motivations in the development of new areas of mathematics. It is reasonable to argue that most of the development of mathematics throughout history originated in "simple" problems that had to be solved. Problems from the simplification of calculations to the trajectories of cannonballs to a set of bridges in the old city of Konigsberg all served as the impetus that led to the creation of new mathematics. Many of the papers also present problems that can be used in college classes. It is good for us all to occasionally revisit the historical origins of the topics that we present and re-present in class after class. Looking at it from the perspective of those who created it is sometimes the best way to get new insights into the material, and many such items are found in this book.

Published in Journal of Recreational Mathematics, reprinted with permission.

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