Personally, I believe (!) in a causal chain like this: Poor people dream smaller (hopelessness,knowledge) -> less ambition (in school, career, wealth) -> less motivation (e.g. in IQ tests) -> envy -> aggression against wealthy people
Also what does "poverty" mean here? "Lack of basic resources", then practically nobody is poor in Germany due to our welfare system. Statistics use "less than 60% of average income" or something like that. Then we will never eliminate poverty, anyways.
To "solve" poverty I believe the big question is how to inspire people that it is possible to improve their situation? How to provide hope to poor people? In Germany I think it is intellectually realistic that anybody can improve, but people do not believe it. Essentially, (in the wealthy western world) poverty is not a technical problem, but rather an emotional one.
I do not care about IQ much. I do not know my own IQ. Since I am currently pursuing a PhD I am probably above average, but who really cares? Studies show that IQ predicts academic success, so it means something for high-education jobs. For creative tasks it's useless. Effectively, the IQ of a child only provides a hint about future career choices, but not about success or wealth.