In my understanding (diffeq in college), the singularity in black holes and futurology are both special cases of the relatively old concept of a "singularity" i

In my understanding (diffeq in college), the singularity in black holes and futurology are both special cases of the relatively old concept of a "singularity" in a function, which is (technically) something like a spot where the function stops being expressible as a series. The most interesting kind is where that happens because it went infinite, but IIRC it can also just not be defined there. Point is, neither Einstein nor Vinge nor especially Kurzweil invented it. :)