Devlin’s Angle: The First Arithmetic Textbook in the Western World

Liber abbaci, completed in 1202, was the first comprehensive description of modern arithmetic (using the Hindu-Arabic numerals, decimal place-value representations of numbers, and the basic arithmetic algorithms we all learn in school) in the western world.

via Devlin’s Angle: The First Arithmetic Textbook in the Western World.

About Irfan

I am an independent researcher and blogger interested in everything under the sun, but more so in the philosophy and history of education and education reform generally, and specifically in the so-called post colonial contexts

4 Responses to “Devlin’s Angle: The First Arithmetic Textbook in the Western World”

  1. Isn’t it ironic that these most influential books of all time, which introduced modern arithmetic to Western Europe, was actually derived and translated from the work of well known Muslim mathematician Al Khawarizmi?

  2. It is not to deny that introduction of decimal numeration system to the western world in 13th century led to an enormous revolution in the western world that was still concentric to the Roman representation of numbers. The author of this post Keith Devlin referred Leonardo of Pisa, who is known for his contribution for introducing Hindi/Arabic numerals to the western world, as The Man of Numbers in his recent book and acknowledged him as an ‘overlooked genius’ and ‘competent mathematician’ which is, my view, quite misleading.

    Though I have not explored the history of mathematics much but, through my meager knowledge, I know that Leonardo was not the pioneer in any respected field of number system. He had learned the Hind/Arabic number system when he traveled to North Africa with his father, a customs agent. He witnessed its advantage over roman numeral system and that motivated him to write a book Liber abbaci in which he mentioned how to replace roman numbers by the digits 1,2,3,4,5,6,7,8,9 and 0. He only translated his knowledge into his native language without adding any innovative ideas of his own and followed the same representation of numbers used by Arabs. According to Wikipedia, “Al-Khwarizmi’s work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world. The term “algorithm” is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both “algorithm” and “algorism” are derived from the Latinized forms of al-Khwarizmi’s name, Algoritmi and Algorismi, respectively.” Therefore I refuse to accept Leonardo as a genuine mathematician like Muslim Mathematician Al-Khwarizmi and other western mathematicians Euler, Gauss, Leibniz and many others. Devlin wrote himself in his book that “Leonardo’s role was to ‘package’ and ‘sell’ the new method to the world” and “Leonardo was more a salesperson of modern arithmetic rather than its inventor.”

    Leonardo is best known for introducing the infamous Fibonacci sequence to the western world, though known to Indian mathematicians since approximately 200 BC. Few years back, I also studied Fibonacci numbers, its pattern and several results in detail. And I derived some of its result on my own. Later I came to know that these results had been proved earlier. However this exercise, at least, made me realize that these results were quite straight forward as compared to the other major results in other disciplines of mathematics. Moreover these results have negligible effect and scope in a broader spectrum of mathematics as compared to substantial scope of solution of, say, quadratic equation offered by Al-Khwarizmi.

    • Thank you for writing this longer comment Saima. Very enlightening. There are also stories of a long and sometimes bitter debates within the European intellectual circles over whether to adopt the arabic numeration system. It was easy to use and much more efficient, and talking in the same numerical language made trade with the Arabs much more convenient. So the then ‘progressives’ wanted it, and the ‘conservatives’ fought for the preservation of the Roman numeration system An interesting story indeed of the struggle between the forces of ‘change’ and ‘continuity’. We are going to the similar struggles now with reference to what are hurled at us now as Western discourses.
      Thanks again.

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