This question has been puzzling me lately. In my view because the most "raw" understanding we have of the world is our experience, which isn't mathematical (color, feelings, etc) which means that the world cannot be purely mathematical. I think then what we have is a "materialistic" world which can be described as mathematics. The maths isn't what is really happening, but it helps us in manipulation. Kind of like moving an desktop icon to the bin on your screen is just a metaphor for execution of code inside the computer. It would be a mistake to assume how the computer really works is icons on some screen, even if it helps us in manipulation.
Furthermore what makes me believe this more, is that sometimes scientific discoveries can have multiple interpretations. Quantum mechanics has like 4,and all of them are valid logically. Which one you chose depends more on your preference then anything. If that wasn't the case, you wouldn't have scientist debating the exact same theory. You may say one is more clean or beautiful or intuitive, but previous scientific discoveries did not care about that. Some weren't symmetrical as people wanted or intuitive, some were. So it's just speculation.
Where this bothers me though is simulations. Assume we model a person inside a computer by describing every particle in him through code. Would he "think"? Obviously I expect him to behave a certain way like a human do, but so would a simulated model of a tree, even if it wasn't really a tree. It does not mean the simulated person thinks. He just fools us, but has no understanding of the world himself.
What even gets me more confused is the fact that thoughts, as in consciousness and direct experience play a role in our behaviour. We all know the famous experiment of brain activity appearing milliseconds before a person is conscious of moving his finger, but this wasn't the only thing found. Consciousness can also cancel that movement as it desires. actually in practice the complexity, free will or how you want to call what makes humans unique is a reason why it is impossible with current understanding to predict human behaviour. Game theory only works if you assume people as psychopaths and shallow husk only interested in playing the game the game theorist made up. This makes the idea of unconscious mathematical digital human being the same as a regular human bit wonky, yet because I can't point to from where consciousness emerges, my position is wonPost too long. Click here to view the full text.