[davidktr]

But do "we" really ignore the tacit knowledge? I think you are wrong that "scientific literature" pretends those things.

The issue of "context of discovery" vs "context of justification" is a hundred years old. And modern accounts of measurement and modeling make it quite clear that there is much more going on than simply writing down numbers. Theories/hypotheses can come from anywhere, I don't think that is even disputed.

However, when doing science, maths, engineering, the question is often what people are even saying, and what counts as evidence that something works. You cannnot do this without abstractions, and at some point we'll have to agree what those abstractions are. Should we leave it to individual experience if LK-99 is a superconductor?

You don't need formal maths training to raise a barn or build a kayak because there is brutal feedback if you are wrong. You'll need maths training to learn how to be right about things that will not give you any feedback.