I am like this as well for the most part. I'm going to need a lot of paper in order to do complex math (and I was a math minor in college), none of it in my head except the derivative of e^x^.
That said, on rare occasions -- twice in my half a century life -- my brain has instantly popped out the answer to a math puzzle and I was correct. But do I know how I arrived at that answer? Nope. My brain told me and that's all there is that I'm consciously aware of. One of those instances was the winning point for my team in a Math Olympics type competition.
In general, my rule of thumb is how it is stored at the grocers is how you should store it at home.
In a plastic bag in refrigeration at the grocer's? Same at home. Room temp and naked at the grocer's? Same at home. Etc.