side comment to q, not answers (as the q is not for me): isn't engineering about creating a solution that mostly works, based on mostly formal rules and mostly

side comment to q, not answers (as the q is not for me): isn't engineering about creating a solution that mostly works, based on mostly formal rules and mostly proven facts, test it, start using it in production, and then MAYBE, if you have the need and/or resources actually formally proving that it will keep working in most cases or discover the cases where it will not and ad some hacks for them? (there's actually 2 main approaches to engineering: the science/proof/theory based one and the empirical one that also uses science/proofs/theory but as a scaffolding and as a compass to realize we don't waste resources trying to do something "really" impossible)