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Depends on the kind of math desu. The real formalism autists nowadays are homotopy type theory people. This whole trend started with set theory being invented, but that turned out to be flawed and not totally useful. This is why you’ll often see professional mathematicians not be fully rigorous, since that would mostly be a waste of time for them - when you’re doing math for that long lots of things get chunked up conceptually and allow the people (I find analysis people most guilty of this) to think somewhat less informally, even though they think deep down “it can all be formalized with limits or whatever”. Thing is, they turn out to be right most of the time, because the way mathematics is formalized at some level doesn’t necessarily tell you about the next level up.
T. Model theorist