It is nice to notice someone suggesting that I present something "clearly" here. You asked and I answered.
Sure it seems to be a case that once a "new area" of math appears in culture the world can sublimly become descripted to "conform to some mathematical laws" even though a collective "we" of the world are not aware of (it) or not.
I would just see that as one stage in the ever expanding "tool set" of mathematicians as to when it might become true that some other math is developed that can do a better job of informing the same formation of lawlike behavior at a second remove.
I am actively thinking of how transcedental numbers can gain say the patterns findable in evoluiontary theory but as of yet there are no "laws" even though the math already exists. If I was to write these applications the older math of "parents" as expressed in population genetics would walk the rope of finer line so constructed. In that future, I might be aware of subjective elements that pass for nothing but a stage in my personal horizon only later to be upbraided (if true in your sense).
When I THOUGHT the product I thought of it NOT as I FIRST LEARNED IT, as a rote table but as something with a potential sense in population thinking and thus "abstract" but via an application rather than a formal 'table' instantiated in a form that might also be analogous no matter the application but as the application was about homology the math and the bio-physical sense were seperated as to the normal form the logic of it would detail.
Using my own ideas is not going to be useful as this does depend on the factual truth which only the math and not my thought of it depends. One could of course say something different if one was refering specifically and only to past episodes in the mathematical history. That is what I meant by giving it a harder and second thought not this explanation of my first thought or sequence from a given thought.
Math is the one part of doing science that is as clear cut as I suggest.
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