> The question is, how is consciousness different from that
A consciousness experiences perceptions, if you don't, I won't be able to describe this to you. If you do, it should be clear what I mean by that.
We have no evidence that either a camera or a GPU executing an LLM experiences perception. Certainly they react to physical stimuli, but so does an atom, physical reaction is not the definition of experience I am referring to when I say perception. We also have no evidence that they do not, except for the lack of evidence to the contrary.
We have some reason to believe that other people do experience perception, in that they spontaneously describe experiencing things that our similar to our experiences, and it's surprising they do that if they don't also experience things*. When I say "we", I really mean "I", but I'm assuming that you have the same experience I do.
> What prevents any of this to be fully mathematically described?
There's nothing that says you can't, in principle, create an entirely accurate mathematical description of perception (in the experiencing and not the reacting sense) where you define that certain abstract variables correspond to certain perceptions and can entirely predict them. The model would still be that, a model that predicts what perceptions occur, not the perceptions themselves. The same way mathematically describing a particle of hydrogen doesn't create a particle of hydrogen. The common concrete example is that mathematically describing what color someone perceives when looking at something, while basically possible, gives absolutely no insight in to what that experience is like (apart from saying "it's similar to had by the same consciousness").
* See my other comment in this thread for why this argument does not apply to GPUs running LLMs.