The Universal History of Numbers : From Prehistory to the Invention of the Computer by Georges Ifrah
This is a book I read because I am trying to make a math curriculum for my daughter. I am not happy with how they are teaching math in school and many of the homeschool math books are not to fun either.
This is a deep and fairly heavy book and not really fun though it would be a great reference work to do that.
Now this book traces the deep origins of numbers: How various cultures counted using fingers and other parts of the body. The use of physical marks or markers for counting. Many cultures couldn't count past 3 or 4 and to do that they used a bowl of pebbles or tally sticks to keep track of the number of sheep and stuff. It is amazing that rural France still used tally sticks to track how much bread was delivered to each home and for balancing the books.
The most amazing part of the book is that he found that our "Arabic" number system isn't Arabic at all, rather it is from India. A major historical date is Monday 25 August 458 A.D. The exact date of the Lokavibhaga (The Parts of the Universe), the Jaina cosmological text; the oldest known Indian text to use zero and the place value system with word symbols. Obviously this is based on early uses of the number system but this is the earliest preserved work we have found. This is utterly fascinating.
The Indian number system slowly worked its way West into the Arab countries and eventually into Europe through Spain.
The best story is the Legend of Sessa, where the king wants to reward inventor of chess, who asks for 1 grain of wheat on the first square of the chessboard, 2 grains on the second, 4 on the third, 8 on the fourth and so on. That sound innocuous enough at first but it gets completely out of hand halfway across the board. He would end up with 10^64 grains of wheat or enough to stretch the diameter of the orbit of the Earth around the Sun.
Another great story is that during the Renaissance multiplication and division were so hard it required traveling to Italian universities for what amounted to a Ph.D. to pull it off. The sad thing is that some schools are going back to those methods, throwing away hundreds of years of mathematical development.
There is a lot of heft to this book, so it is better to skimming over the massive evolutions of various number systems and skipping to the good stuff.
I rather liked it.