I can't tell if this a troll attempt or not.

If your definition of "algorithm" is "list of instructions", then there is nothing surprising. It's very obvious. The "algorithm" isn't perfect, but a mapping with an error exists.

If your definition of "algorithm" is "error free equivalent of the equations", then the analytical equations do not map to "algorithms". "Algorithms" do not exist.

I mean, your objection is kind of like questioning how a construction material could hold up a building when it is inevitably bound to decay and therefore result in structural collapse. Is it actually holding the entire time or is it slowly collapsing the entire time?