the "becoming" sounds just like a dynamic process, which is a usual mathematical object. i should say that i don't know the precise definition of "becoming" so my claim is merely a speculation.

math does not always rely on quantities. for example, its "model theory" analyzes languages ("truth", "axioms", "proofs", etc) rigorously. also a part of topology (Mr. Beggar's favorite topic, i presume) does not rely on numbers.