Consider a game of Chess. Or cards. The very existence of the game depends on some pattern-conservation rules (imagine trying to play Chess if pieces kept exchanging forms, and the number of squares on the board kept changing!

Human beings are in a 'game' of life in this Universe which has necessary pattern conservations (you call symmetries, maths) as part of the very integrity and existence of the 'game' itself.

Humans have freedom to make many kinds of moves. Self-responsibility is what existence appears to be about- freedom and liberty. God = Existence.

The question of God 'intervening' appears to be based on misunderstanding how it works. You don't 'take over' someone's vote in a free election- that would mean there was no vote of their's. Humans are created as free moral agents; time to stop running from responsibility and take responsibility as much as we can for our choices.

Human beings- we have to wake up to the fact of what we are capable of. In my opinion we are capable of recalling infant-knowledge related to built-in abilities like teleportation and telepathy that protect us from harm.

The Universe looks like it 'goes by itself through math' because self-determination, being, and letting be (love) is what Existence (God) is apparantly about.

God does not coerce us; he lets us BE.