[auggierose]

I've studied mathematics, too. Yes, formal logic is an afterthought when you do mathematics. But formal logic is just an explicit representation of what goes on internally in a mathematician. Or at least that's how I approach formal logic (most logicians don't). I would describe these internal processes inside a mathematician (and outside, when used for communication) as intuition + "logic to keep intuition in check". Sounds like ML + logic to me.