easy for their minds to grasp its proofs. Thus the evidences for affirming the Maker, His oneness, and the signs and proofs of prophethood are exceedingly numerous, and the avenues by which people come to know them are likewise many. A large share of those avenues are unnecessary for most people; they are required only by someone who has learned no other method or who has turned away from simpler ones.

There are individuals for whom the more intricate, subtle, and multi-premised the argument—and the longer its chain—the more useful it is, because their minds have become accustomed to prolonged reflection on fine points. When the proof contains few premises or is plainly obvious, they find no satisfaction in it. With such people one may therefore employ theological–dialectical or logical demonstrations and the like, not because knowledge of the desired conclusion is in itself contingent upon them, but simply because these approaches accord with their habitual mode of inquiry. Indeed, there are some who, if they know only what the general public knows, or what people of average intelligence can grasp, do not feel distinguished by any special knowledge; for them it becomes necessary to learn hidden, subtle matters that rest on many premises, and to them this path is tailored.

Moreover, engaging with the more exacting sciences opens and nourishes the intellect, strengthening it for the pursuit of knowledge. It is like frequent practice with the bow or constant horseback riding: both sharpen one’s skill in shooting and riding even when no battle is imminent. This is a praiseworthy aim.

For that reason many scholars of the Sunnah were eager to study sound and precise disciplines such as algebra (al-jabr wa’l-muqābalah), the intricate aspects of the laws of inheritance, wills, and cyclical estate problems, in order to sharpen their minds; these are valid sciences in their own right and, for that reason, are called “mathematical” (riyāḍī). The term riyāḍah (exercise) is used in three ways: exercise of the body through movement and walking, as physicians and others mention; exercise of the soul through balanced virtues and praiseworthy manners; and exercise of the intellect through mastering subtle knowledge and investigating obscure questions.

It is narrated that ʿUmar ibn al-Khaṭṭāb—may Allah be pleased with him—said:

“Whenever you entertain yourselves, do so with archery, and when you converse, converse about the laws of inheritance.”

He meant that if they occupy themselves with an activity for diversion, let it be an activity that benefits them in their religion—namely archery—and if they seek diversion through speech, let that speech likewise be of benefit to them.