Algorithmic correctness? Unit tests are great for quickly poking holes in obviously algorithmically incorrect code, but far from good enough to ensure correctness. Passing unit tests is necessary, not sufficient.

Syntactic correctness is more or less a solved problem, as you say. Doesn't matter if the author is a human or an LLM.

It depends on the algorithm of course. If your code is trying to prove P=NP, of course you can't test for it.

But it's disingenuous to claim that even the majority of code written in the world is so difficult algorithmically that it can't be unit-tested to a sufficient degree.

Suppose you're right and the "majority of code" is fully specified by unit testing (I doubt it). The remaining body of code is vast, and the comments in this thread seem to overlook that.