والعلم الرياضي: علم يتعلق بأمور يتوقف على مادة في الوجود دون التصور
Mathematics concerns things requiring matter for external existence but not for conceptualization.
In classical philosophical classification, riyāḍiyyāt (mathematics) examines objects that can be understood independently of a particular material while their concrete external instances appear through a material bearer. A sphere, circle, or quantity helps illustrate the distinction.
In conception: one can investigate an ideal sphere without specifying wood, iron, or any other material.
In external instantiation: a ball placed before us exists as some concrete physical thing.
The point is the difference between requiring material in the concept itself and needing a material instance for a particular physical realization. It does not amount to denying either mathematical truth or concrete objects.