As a grad student in math, i would say that determination still plays a important role. For me, there have often been periods where you lose motivation and dont see why you are doing what you are doing, and then sometimes there are moments of clarity. (someone aptly compared this to mountain climbing). I imagine this happens in lots of other fields,(music, to pick a random example) where there is a prequisite of learning lots of arbitary things before understanding/creativity happens. Determination, is what you might need to to go through these phases.
I agree. I had a problem with this specific claim by PG:
"Most people would agree it's more admirable to be good at math than memorizing long strings of digits, even though the latter depends more on natural ability."
Surely determination plus the right mnemonics can help anyone memorise long sequences of digits. I would have thought that reasoning creatively, carefully, and abstractly - i.e., mathematics - requires more natural talent, or at least a predisposition, than wanting to memorise digits.
I agree with you about PG's claim. Memorization might appear to depend on natural ability as much as success depending on intelligence. To me, PG's one statement there contradicts the rest of the essay.
As for creativity, reasoning, abstract mathematics, I don't think those have innate factors. If anything, the only thing stopping people from becoming exceptional in those fields is the belief that they cannot improve (== lack of determination).
I certainly hope you are right. I am just starting my own graduate studies in math, but having limited apparant innate abilities in mathematics I am counting on practice and study to correct that deficiency.
