I think you are confusing "memory" with strategies based on memorisation. Yes memorising (ie putting things into memory) is always involved in learning in some way, but that is too general and not what is discussed here. "Compression is understanding" possibly to some extent, but understanding is not just compression; that would be a reduction of what understanding really is, as it involves a certain range of processes and contexts in which the understanding is actually enacted rather than purely "memorised" or applied, and that is fundamentally relational. It is so relational that it can even go deeply down to how motor skills are acquired or spatial relationships understood. It is no surprise that tasks like mental rotation correlates well with mathematical skills.
Current research in early mathematical education now focuses on teaching certain spatial skills to very young kids rather than (just) numbers. Mathematics is about understanding of relationships, and that is not a detached kind of understanding that we can make into an algorithm, but deeply invested and relational between the "subject" and the "object" of understanding. Taking the subject and all the relations with the world out of the context of learning processes is absurd, because that is in the exact centre of them.
Current research in early mathematical education now focuses on teaching certain spatial skills to very young kids rather than (just) numbers. Mathematics is about understanding of relationships, and that is not a detached kind of understanding that we can make into an algorithm, but deeply invested and relational between the "subject" and the "object" of understanding. Taking the subject and all the relations with the world out of the context of learning processes is absurd, because that is in the exact centre of them.