I like the way you expressed the matter in your essay "What You'll Wish You'd Known" (January 2005).
http://paulgraham.com/hs.html
"Don't think that you can't do what other people can. And I agree you shouldn't underestimate your potential. People who've done great things tend to seem as if they were a race apart. And most biographies only exaggerate this illusion, partly due to the worshipful attitude biographers inevitably sink into, and partly because, knowing how the story ends, they can't help streamlining the plot till it seems like the subject's life was a matter of destiny, the mere unfolding of some innate genius. In fact I suspect if you had the sixteen year old Shakespeare or Einstein in school with you, they'd seem impressive, but not totally unlike your other friends.
"Which is an uncomfortable thought. If they were just like us, then they had to work very hard to do what they did. And that's one reason we like to believe in genius. It gives us an excuse for being lazy. If these guys were able to do what they did only because of some magic Shakespeareness or Einsteinness, then it's not our fault if we can't do something as good.
"I'm not saying there's no such thing as genius. But if you're trying to choose between two theories and one gives you an excuse for being lazy, the other one is probably right."
We are NOT sure, on the basis of research, what anyone's upper limit of ability is. We have no idea about the extent of the "reaction range" constrained by the shuffle of genes a person obtains before a person is born, but we are absolutely sure that the reaction range is a RANGE, exquisitely sensitive to environmental influences. The discordance of identical twins for all human behavioral characteristics amply proves that. So, yes, let's say determination can matter as much or more than inborn ability. There are ample examples of that in today's world.
EDIT AFTER SEEING stiff's COMMENT AT THIS LEVEL:
Yes, many children bail out of further study of mathematics because they assume school lessons should be easy, and so they think "they have no talent" for subjects that become hard. A series of FAQs I have written about mathematics learning,
"Problems versus Exercises"
http://www.epsiloncamp.org/ProblemsversusExercises.php
"Repetition and Practice"
http://www.epsiloncamp.org/RepetitionPractice.php
"Resources about Learning Mathematics"
http://www.epsiloncamp.org/LearningMathematics.php
"Courage in the Face of Stupidity"
http://www.epsiloncamp.org/CourageandStupidity.php
were written to encourage learners to be willing to challenge themselves when they feel stuck learning mathematics. Most professional mathematicians feel stuck a lot of the time when they do their daily research work, but they keep going.