"Oh, of course no one ever really *does* it..." A compressed version of my own confusion as a maths student: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/ooasn01bfe
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So it really is handwaving all the way down? This sentiment is amusingly close to the stereotypical physicist's defense of a low-rigor derivation.
I think this is part of why I ended up moving to physics, at least they're honest about it!