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'At the stroke of midnight, your brother will be hurtling sideways at an altitude of 150 meters' is a regular physics prediction about your nonmagical trebuchet, whereas 'you are cursed to build a brother-launching trebuchet' falls out of the Lagrangian.
A lot of math involves just moving things around until the problem is easier. It's just a bunch of tricks that work for relatively simple reasons. But you just memorize them to make it easier.
Statistics is more like magic than other kinds of math. Like when you have more than 30 random unbiased selections from a population you can start guessing at the composition of the whole, no matter how large it is. The explanations require someone who really knows what's going on.
Then you have modern LLMs that use statistics to produce the next word in a sentence. They can be so complex the designers don't really know why they do what they do. It's just trial and error testing the outcomes.