Doesn't your observation that most successful autodidacts come from financially stable backgrounds SUPPORT the hypothesis that intelligent individuals from low-income backgrounds are prevented from becoming successful?

With the facts you've highlighted, two conclusions may be drawn: either most poor people are stupid, or the aforementioned "starving farmers" don't have the time or the resources to educate themselves or "[bang] out some impressive proofs," on account of the whole "I'm starving and need to grow some food" thing. I don't see how such people would be able to afford books to learn from or time to spend reading them.