Well I didn't actually see the Matrix but I've seen other movies where with similar sorts of themes.

There are considerable mysteries surrounding the strange values that Nature's actual particles have for their mass and charge. For example, there is the unexplained 'fine structure constant' ... governing the strength of electromagnetic interactions.

our present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake up

I would say the universe has a purpose. It's not there just somehow by chance.

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

Consciousness ... is the phenomenon whereby the universe's very existence is made known.

Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.