[jholman]

Yes, exactly. And "this code has a mathematical error in it" is often interesting, often non-trivial, and often has probability 1 (and often probability 0).

And these things are exactly the sort of thing that "differ from [trivialities about triangles] only in degree of complexity".

Note that "all triangles have 3 sides" is probably an axiom, but "all triangles have less than 11 sides" is a trivial theorem.