It can be proven, in broadly the same sense as all of the atoms in your body can simultaneously "decide" to exist an inch to the right due to quantum field theory.
It is not practical to prove correctness for the vast majority of programs, and there are programs that are demonstrably incorrect, cannot be made correct, and yet are useful and still function anyway (e.g., closing TCP connections cannot be done "correctly").
It can be proven, in broadly the same sense as all of the atoms in your body can simultaneously "decide" to exist an inch to the right due to quantum field theory.
It is not practical to prove correctness for the vast majority of programs, and there are programs that are demonstrably incorrect, cannot be made correct, and yet are useful and still function anyway (e.g., closing TCP connections cannot be done "correctly").