Is mathematics something inherent to nature, or is it a purely human construct?
I prefer to frame this question as such: “Is mathematics something inherent to a universe void of beings that possess self-consciousness, or is it a purely an emergent behavior borne surreptitiously of a self-conscious beings language abilities?”. Either way, I tend towards the latter. I have the mindset that, although we have discovered/invented/evolved a certain flavor of math as humans (and other living species have likewise created (seemingly) less robust languages of math), there could be another universe with a similar paradigm as cause & effect in which a similar flavor of math could be invented/discovered/evolved. These disparate flavors of math I believe would be children of a higher mathematics. I wonder if this relates to Goedel’s proof that there are truths in math that are unprovable. If nothing exists as the vesicle by which mathematics emerges, is there mathematics? I don’t think so. I think at the core of math is observation. Would nature still exist? Sure, there just wouldn’t be a specific type of language to talk about it without the talkers.

Why do you think math is so effective in describing the physical world around us?
I believe that mathematics is very effective in describing the world around us for a few main reasons: its roots in the empirical, the rigor by which it is practiced, the proof building methodology that strengthens its incremental findings, and the continual abstractions that allow for more complex proof building on top of previous work. To me it seems to be the most extensive language we have developed to speak about the Physical world, so in that regard, it should be very effective at describing it certain aspects of it.