Their sciences, then, lie midway between verified disciplines that yield no benefit—we seek refuge in God from knowledge that is of no use—and false conjectures in which no confidence can be placed, for “indeed, some conjecture is sin” (Q 49:12). By the first they mean the mathematical sciences; by the second, what they assert in matters of divinity, judicial astrology, and the like.

Reasons that entice people to occupy themselves with mathematics and similar fields:

The soul may take pleasure in such study just as it enjoys other pursuits. A person delights in learning what he did not previously know and hearing what he had not heard before, so long as he is not pre-engaged with something he considers of greater importance. In the same way he may find enjoyment in various activities that amount to diversion and play.

Moreover, habitual engagement with these studies accustoms the soul to sound knowledge, truthful propositions, and straight reasoning; thereby the mind and its perceptions are refined, and the soul is trained to recognize the truth and articulate it, using that habit as an aid to reach knowledge that is higher than this.

For that reason it is said that the earliest philosophers began their children’s education with mathematics. Many of their senior masters, too, spent their final years absorbed in it: after examining their own methods and those of their opponents among the practitioners of false dialectic and finding no solid truth therein, they diverted themselves with mathematics. The same occurred with leading philosophers such as Ibn Wāṣil and others.

Likewise, many of our later scholars occupy their idle hours with the science of inheritance, arithmetic, algebra and restoration, geometry, and the like, because it refreshes the soul and is a sound discipline into which error does not intrude.