Yes.
No, not with respect to the maths examples. If we see them in the context of something we would find reasonably trustworthy and have before (as we would – they would not just be floating around somewhere¹), say a lay level scientific magazine, that is not ignorance. That is faith in a source.
Sets of co-instants with objective meaning implicitly tying them together² obviate the rest of your examples. Jim’s delightful example of how God can pleasingly care for his children in his providence is not one of those and indeed the meaning was not as clearly and objectively described by the circumstances as are the multiple discrete and otherwise dissociated events in the groupings I cite.
¹ETA: And if we did trip over one in isolation, we would not necessarily impute meaningfulness to it immediately, but we certainly might suspect that it did have meaning. And we would not be wrong. (Like Jim’s examples.)
²ETA: Jim had a thread connecting the events in his examples – maybe not a cable, but still a thread.