In my experience, proof is the gym reps that allows you to harness strong intuition elsewhere.
In practice as an engineer, intuition is far more useful, eg, being able to “feel” when something is off in our reasoning — but proofs are where I train those same sensibilities on “harder” problems, (eg) details about how to model identity, equality, and equivalence in a formal model.
In my experience, proof is the gym reps that allows you to harness strong intuition elsewhere.
In practice as an engineer, intuition is far more useful, eg, being able to “feel” when something is off in our reasoning — but proofs are where I train those same sensibilities on “harder” problems, (eg) details about how to model identity, equality, and equivalence in a formal model.