>> Algebraic and topological structures seem to manifest themselves readily within nature. I should think infinities provide greater concern.

So basically what you are saying is that, we can't be so certain that we humans invented math. Math is there, structures were there to be discovered ? Why is there such a thing as monster group ? We named those things, but if we didn't exists, it would still be there in the abstract world ? This is what is bugging me lately, I can't decide if math was invented or not. Some parts may be invented, but some parts may be discovered.