[dragonwriter]

> Do genes really matter all that much?

Yes.

> Judging from a few of the latest pop-sci books

That's not really much better than “judging from my newspaper horoscope”.

> I was under the impression that culture and nurture play a much greater role: high quality medicine, food rich in nutrients, good education available to all.

Those play a huge role in whether genetic potential will be reached, genetics play a huge role in the actual outcome given similar environment.

> When you read the biographies of the many of the brightest academics of the USSR, many of them are descendants of a typical peasant family. Some of their parents weren't able to read or write, had a lot of children, etc. This "genetic handicap"

You describe an socioeconomic handicap, not a genetic one, so it doesn't really say anything about the effects of genetics.