Mason  🏃‍♂️ ✂️

I don't think engineers, etc, usually care what mathematicians think. They like that it gives them useful tools to solve problems. If Dr. Tai's method has a flaw because he didn't prove its error bounds or that it converges, it doesn't matter. True != useful.

I think we're approaching an impasse, if you see no strong relationship between truth and usefulness in e.g. math/physics/engineering. I don't even really know what you *can* mean by "useful" if it bears no relationship to ground truths about the world.

Because for the most part, like with software engineering, whether or not code is formally verified or some biologist's method of integration is proved to converge often has little bearing on whether either method is used. What ground truth is there?

AFAICT your statement and your question are non sequiturs. I'm not sure where to go from here, because I seem to be saying "squares are rectangles" and you seem to be saying "plenty of rectangles aren't squares" — in order to defend the claim that squares aren't a real thing

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