Agree with this and would also add: in addition to being able to do algebra fast and have it be second-nature, at higher levels it helps if you are able to do it 100% accurately. 5 nines isn't enough.
I didn't appreciate this until I was a graduate physics student and was frequently frustrated by minor algebra errors in long, complex problems.
I didn't appreciate this until I was a graduate physics student and was frequently frustrated by minor algebra errors in long, complex problems.