As I understand, this is an unsolved problem.
But that aside, it's such a shame that many drinking the AI Kool-Aid aren't even aware of the theoretical limits of a computer's capabilities.
Computers are finite machines. There is a theorem that although a machine with finite memory can add, multiplication requires unbounded memory. Somehow we muddle along and use computers for multiplication anyway.
More to your point there is a whole field of people who write useful programs using languages in which every program must be accompanied by a proof that it halts on all inputs.
(See for example https://lean-lang.org/ or David Turner's work on Total Functional Programming from about 20 years ago.)
Other examples are easy to find. The simplex algorithm for linear optimization requires exponential time in general, and the problem it solves is NP-hard, but in practice works well on problems of interest and is widely used. Or consider the dynamic programming algorithms for problems like subset-sum.
Theory is important, but engineering is also important.
"Somewhat easier than an impossible task" is not a particularly strong claim about when (or whether) this problem will be solved, though.
Those were written by humans, and don't involve unsolved mathematics.
Is your claim tht you just need to solve comprehensibility of LLMs?
Figuring out epistemology and cognition to have a chance to reason about the outputs of a LLM seems to me way harder that traditional attempts to reason directly about algorithms.
"is this implementation/code actually aligned with what i want to do?"
humanic responsibility's focus will move entirely from implementing code to deciding whether it should be implemented or not.
u probably mean unsolved as in "not yet able to be automated", and that's true.
if pull-request checks verifying that tests are conforming to the spec are automated, then we'd have AGI.