Explaining Bell violations from a statistical / stochastic quantum interpretation Future states seem to have a mathematical relationship with past states. It might be because future states derive from applying mathematical laws or computations to those past states - that might be how the universe itself works. Or it might even be, as many physicists think, that time itself is an illusion, and future states and past states are all encoded together in one big mathematical object - and what we experience as the passing of time and the perception of casual chains might just be what it feels like to be inside that mathematical object.
But in the end it actually is a matter of likes and dislikes. It's not like there's a known objective answer to the true fundamental nature of our universe right now, so if you feel strongly that it can't be mathematical, which you seem to do, it's not because you have scientific proof that it can't be. It's because you don't like it, it's because there's some aspect of it that doesn't sit well with you, that goes against the grain of your intuitions about how the world works. It goes exactly with the grain of my intuitions, so I think it's a compelling idea.
The concept of Turing completeness provides the bedrock, for me, for the idea that we might be in a computational universe - that computation and/or mathematics are strongly analogous to the root nature of every thing and every event in this place. That makes sense to me.