I think you've hit the nail on the head, particularly with a mathematician as opposed to an arithmetist (love that invented word!). Spontaneously inventing long division is rather unlikely, even for Terry Tao.
I think this is true. Early exposure to reading is much more common for preschoolers than math, and it's not as easy to take off on. My son as a preschooler understood conceptually multiplication, division, fraction operations etc. You could give him word problems and he'd solve them in his head. But if shown a word problem on paper or mathematical notation, he would have been lost and possibly not tested much ahead. While in reading, the reading doesn't necessarily need to line up with other skills for kids to be able to "show their stuff". He's doing algebra as a 4th grader after I stalled him the past couple years while his writing skills came to the level where he could carry out multi step problems on paper.
