The Convergence of Judaism and Islam. Religious, Scientific, and Cultural Dimensions

Al-Khwarizmi’s Mathematical Doctrines in Ibn-Ezra’s Biblical Commentary r 185

For from it emerged every sum and every sum will be found in it for

it is the foundation. And here this, the first commandment that the

revered God spoke, includes all precepts of the heart, the tongue

and the deed. For he who does not believe in his heart in God, on

him there is no precept.... And I already explained that the first

commandment is the foundation and on it are all constructs of the

precepts.]

Ibn-Ezra speaks here about facets of objects. Researchers have found,
he says, ten such facets (quality, quantity, etc.), and they all relate to the
first one, presumably the object itself (the other nine merely describing
various attributes). Thus, he maintains, we have here the like of the num-
ber 1. Here he returns to arithmetic, our concern; specifically to the notion
of the number 1 as the foundation of all numbers. Similarly, he tells us,
the first commandment is the basis of all precepts, for you won’t follow
God’s rules and obey His instructions if you don’t believe in Him. Thus
the first commandment is the essence of religious observance just as the
first number is the essence of arithmetic.
We note that here too al-Khwarizmi’s influence cannot be ignored. The
italicized words in the bracketed paragraph above echo the words of al-
Khwarizmi in the following paragraph.
From the Latin Translation of Book of Hindu Calculus:

Et iam patefeci in libro algebr et almucabalah... quod uniueresus nu-

merus sit compositus et quod uniuersus numerus componatur super

unum. Unum ergo inuenitur in uniuerso numero.

English translation by André Allard:

I’ve already told in a book about al-jabr and al-muqabala... that

any number is a compound and that any number is formed in the

unit. The unit is thus in any number.^14

Concluding Remarks and Story

Over the years Ibn-Ezra’s approach was challenged from both the re-
ligious and the scientific points of view. Religious critics argued that it
belittles God to have the glory of His name rest on numerical consider-
ations. More relevant to our work here are the following mathematical
observations: