There are definitely states of systems(like mind) which are not quantifiable. For mathematics to work in principle, we need states which are quantifiable or measurable. So, does this go to show that complete description of reality in mathematical terms not possible?
David Chalmers argue the nature of consciousness, which is responsible for subjective experience, is something innate to the universe. An example he often cites is Mary a neuroscientist who knows everything, that is to know physically, about the colour red will still not know colour red when she first experiences it.
Also, Wittgenstein in Tractatus argues that
A logical picture of facts is a thought.
A thought is a proposition with a sense.
But it is generally agreed upon that this leaves a lot which can be claimed non-sense in Wittgenstein. As he himself acknowledges in his last proposition
Whereof one cannot speak, one must be silent.
So, if there are states of the world which cannot be appropriately expressed even in language, how can mathematics describe such states?
So, a further question is whether reality logical?