Mason  🏃‍♂️ ✂️

Math is integral to physics, engineering, etc. Not all mathematical concepts will be forced to contend with reality anytime soon, but when they do, nobody gets to say "my math was right, the rocket was wrong."

I think this gets to the heart of it then: most of the "ground truths" that those folks care about are algorithms that people find useful, mixed in with a huge array of experimentally derived "constants" and coefficients. That's pretty far from Matt's philosophy of math reference

One of my favorite math facts is that a biology paper got dozens of citations in top journals because it described how to find the area under the curve for metabolic studies. Math is a tool those folks reach to because it's useful, not a thing full of universal ground truths.

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?