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Mathematics and the Mind

Hassan Tahiri
Publisher: 
Springer
Publication Date: 
2015
Number of Pages: 
76
Format: 
Paperback
Series: 
Springer Briefs in Philosophy
Price: 
54.99
ISBN: 
9783319252360
Category: 
Monograph
[Reviewed by
Charles Ashbacher
, on
03/28/2016
]

For nearly all people in the west, philosophy was invented by the ancient Greeks and, according to the creators, they were the only ones that could do it. Epicurus is quoted as saying, “only Greeks philosophize.” The sequence of scholars and some of the work of Socrates, Plato and Aristotle are known to every person that has taken a course in philosophy.

Students of history, especially the area of mathematics, know that much of this learning was lost to Europe during the time period known as the Dark Ages. Fortunately, much of what the Greeks accomplished was saved and expanded by the Arabic-Islamic scholars. Ibn Sῑna (known in the west as Avicenna) was born in 980 CE and did a great deal to extend Greek philosophy, specifically in the treatment of numbers.

One of the most interesting and revealing historical points in this book is a quote from Ibn Sῑna found on page 9 of this book: “ … when I reached the age of ten I had finished the Quran and many works of literature… Then he [my father] send me to a vegetable seller who used Indian arithmetic.” His father was indeed wise, for this gave Ibn Sῑna knowledge of the new way of representing numbers that we still use today.

As is explained in chapter three, Ibn Sῑna then went on to make substantial alterations to the Greek views as to what numbers are, a direction of thought that was aided by the new notation that he learned from that merchant. Chapter four has the title “Ibn Sῑna’s Basic Theory of Knowledge” and chapter five is “The Logico-Epistemic Construction of Numbers.”

This book is loaded with detailed footnotes; on some pages there is more space devoted to footnotes than there is to the text itself. There are also four pages of references in small print at the end of the book. If you have an interest in Islamic scholarship that preserved and expanded the achievements of the ancient Greeks, this book is an excellent place to start. 


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 the publisher's webpage.

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