>...suspected somebody is trying to make fun of me...
I think that too, "Futamura projections" are important but they are very very far from "complex mathematical machinery" as you may hear it. They are indeed very simple (even mathematically trivial) and require no special background to understand.
What do you mean by "trained mathematician"? I ask this because I always think that mathematicians are simply people do research in mathematics, if not they aren't mathematician. So no need to add "trained", what is an "untrained mathematician" btw?
I saw some people claimed on their twitter/blog that they are "trained mathematician" but I cannot find any single published contribution of them in mathematics.
And everyone I know who do research in math seems to agree all that "math is hard".
Yes, static disassembling is well known undecidable, data and code are indistinguishable in general. The reason is very simple (it's actually just an exercice), consider an assembly code:
jmp rax
...some binary data...
Where the value of "rax" depends on some input, so the disassembler can never be sure that "some binary data" is actually "data" or "code".
I think that too, "Futamura projections" are important but they are very very far from "complex mathematical machinery" as you may hear it. They are indeed very simple (even mathematically trivial) and require no special background to understand.