The whole tirade on rigorous proofs and colonial mindset puzzles me. From my understanding (I am European ...), rigorous proofs were increasingly seen as a need because as things like calculus progressed, any loose definition had a tendency to become a minefield. Think of the definition of derivatives, continuity. Also, at a time where things were getting mechanize because we could and it was a gain, it was natural t…
I've just finished reading Feyerabend's Tyranny of Science which goes down a very similar path to OP's interview: >In this wide-ranging and accessible book Feyerabend challenges some modern myths about science, including the myth that ‘science is successful’. He argues that some very basic assumptions about science are simply false and that substantial parts of scientific ideology were created on the basis of superfi…
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.