The same is true of computers, in fact it has been mathematically proven that it is impossible to answer the general question if a computer program is correct.
But that hasn't stopped the last 40 years from happening because computers made fewer mistakes than the next best alternative. The same needs to be true of LLMs.
That is not true at all. You do not need to generate a spec. All you need to do is prove a property. This can be done in many ways.
For example, many things can be proven about the following program without having to solve any general problem at all:
echo “hello world”
Similarly for quick sort, merge sort, and all sort of things. The degree of formality doesn’t have to go to formal methods which are only a very small part of the whole field
What you’re saying is equivalent to throwing out all of mathematics due to the incompleteness theorem and start praying to fried egg jellyfish on full moon
But that hasn't stopped the last 40 years from happening because computers made fewer mistakes than the next best alternative. The same needs to be true of LLMs.