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Probably should define intelligence, because if you are talking about IQ, which is objective measurable quality by Standard-Binet IQ test, and the test score goes up with education level (linear relationship), but intelligence is not just IQ, there is EQ as well in terms of performance.

And achievements, depends on the person of course, but also there is some luck involved as well i think, meeting the right people in the right time, etc. But of course, someone who is proactive is more likely to succeed than say, someone that stays in the basement all day without the chance to make certain connections (academically, business, or socially)