But how do I know if something works if I don't know how it works? By testing (literally) all use cases, every single permutation of of variables? For complex programs there might not be enough time and energy in the universe to do that.

If I know what addition is, I can look at at a line that does addition and reason about it. If I just check "if it works", for all I know, the actual code is something like

    if (thing == 17)
    {
      shit_the_bed();
    }
    else
    {
      thing += other_thing;
    }

Sure, I can use an LLM to check on the first LLM, and then a third LLM to check on the second, and so on ad infinitum, but none of that, at no point, can give me what "knowing what addition is" gives me.

It's kinda like cheap/fake concrete: If you know something about concrete and what concrete is being used, you can roughly tell if it will last, what it will withstand. If you just go by "seems to work", "looks good", you get collapsing bridges and buildings after a few years, during heavy rainfall etc.