The mechanic who repairs the cars knows how the engine works.

The telco that manages loads and allocates networks knows how voice compression works.

The farmers and supermarkets know how the supply chain works.

None of your questions show why mathematics should include blobs of incomprehensible gloop, where no mathematician, no logician, no philosopher, no man on the street can make sense of said gloop, or use it in any way to further human knowledge.

When it's been decomposed down we can discuss this further, but now it's like saying red is red, just because.