Mason  🏃‍♂️ ✂️

Is integration that isn't proven correct integration? Even if they don't know what it is and lack the tools to know why it converges?

A child doesn't have to know what "weight" *is* — that it's a function (and measure) of gravity — in order to put it to use deciding whether they'll be able to pick something up. It's useful because of facts about the world unknown to the child. The map is not the territory.

Useful != true. It'll also be the case that most of the things they drop will appear to fall at a constant rate, and that air has no resistance, and so on.

As soon as they try to do anything where the reality of whether or not air creates resistance bears on the outcome, their predictions will start failing. Right up until then, "air has no resistance" will work fine. Maps can be accurate enough for some purposes and not others

The ground truth is a bunch of equations that wildly change each time, have different (experimentally observed) constants, and since Euclid have used wildly different mathematical tools with different axiomatic systems?

I think you're conflating the ground truth (if one exists?) of our physical universe with mathematics?

The two are linked via e.g. physics. The universe behaves according to certain rules, and math can both describe and predict features of those rules. Which we can then use to do interesting things with engineering. At no point here does consensus among experts change the rules.