Like I said, I think there are not-necessarily-wrong ways to understand virtually everything as "socially constructed." But I think we need to either maintain careful conversational hygiene or use new terms if we're going to be talking about cultural stuff in the same breath
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."
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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
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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.
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FWIW I just don't think one's understanding of what math is has to imply anything about social ideology