How Euler Did It, by C. Edward Sandifer, The Mathematical Association of America, Washington, D. C., 2007. 304 pp., $51.95 (Hardbound). ISBN 978-0-88385-563-8.
Leonhard Euler was arguably the most prolific mathematician of all time, the breadth of his coverage is the most impressive aspect of his work. He literally created several new areas of mathematics and mathematicians continue to expand and refine his work.
Yet, there is still the question of how he actually proved the results that so many mathematicians have committed to memory. This book is a collection of annotated reproductions of some of the most memorable of Euler’s results. The 40 items all appeared in the column “How Euler Did It” that was published in the MAAOnline column between November, 2003 and February, 2007.
The columns are organized into four groups: geometry, number theory, combinatorics and analysis. Even if you were already astounded at Euler’s accomplishments, that emotional state will be expanded even further. For in reading these columns, you are often faced with the question, “How did Euler ever think to do that?”
When you are faced with the question in the title, the simplistic response is “Euler was a genius in math.” True and obvious, but not descriptive. In this book you are privileged to see that genius in action, where you see some of the thought processes that led to the “Voila” moment in the reader when the proof is complete.
This book was made available for free for review purposes