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Sourcebook in the Mathematics of Medieval Europe and North Africa

Victor J. Katz, Menso Folkerts, Barnabas Hughes, Roi Wagner, and J. Lennart Berggren, editors
Princeton University Press
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Charles Ashbacher
, on

This is a very deep and detailed dive into the mathematics of the medieval era, a time that superficial history claims was one where little learning took place (the “Dark Ages”). The actual years covered are roughly from 800 to 1450, when Islam and Christianity were struggling for political control of Africa, the Middle East and Europe. The Christian expeditionary forces known as the Crusades took place from 1095 to 1291.

In the years covered in this book, international commerce was reignited in the Mediterranean Sea, leading to the transfer of ideas between civilizations. Embedded within both the Christian and Islamic lands were the Jews, separate and unequal, but also a people that valued scholarship. The role that the Jews filled in the maintenance and advancement of learning during this time period is rarely examined.

That oversight is corrected in this book, at least in terms of mathematics. There are three main sections:

  • The Latin Mathematics of Medieval Europe
  • Mathematics in Hebrew in Medieval Europe
  • Mathematics in the Islamic World in Medieval Spain and North Africa

Translations of the original works are given. While some of them will be recognized by the casual student of math history, most will be known only to the scholar. The original form of the material is kept, which makes it difficult for the modern reader to work through. This was a time when the modern mathematical notation had yet to appear, so the statement and solutions to the problems are textual in nature. There is also the archaic usage of some of the terms to further confuse.

The emphasis is on the mathematics, so that there is very little ink spent in explaining the political situation. Yet, I found the most interesting passage in the book to be the two pages that described the difficulties the Jews in Spain faced when it was partitioned between the Christians and the Muslims. Even within the turmoil and persecution, Jewish scholars were able to advance mathematical knowledge.

This book is a poster child for the term “deep, scholarly work.” Even in the worst of times, there are people able to recover and advance mathematics and this book is a tribute to their skills and perseverance. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.

See the table of contents in pdf format.