"Culture" is an empty explanation. The question is: were your odds of getting married and having children as a Medieval Ashkenazi Jew better if you were smarter?

I'm descended from these people and I don't know.

Over that time period is it more likely to be selective pressure or a founder effect?

A founder effect doesn't require continuous selective pressure, it just requires a population with a small group of founders from whom the entire population is descended. For instance, a group that splits off from a larger group, or passes through a population bottleneck. In this situation a set of genes -- inherited from the founder who is the common ancestor of the entire population -- can very rapidly become dominant in a population, not because they are beneficial but because there are no alternatives.

So in other words, if there is an Ashakenzi 'smart gene' it may not be a matter of the selective pressures of the Jewish condition over the last few hundred years, it might just be a matter of descending from a single very smart person.

That could be, but with a founder effect in a population whose European contribution came from a small number of females, we then have to expect either:

* The intelligence came from the European converted-in founder females. In which case, how come we don't see similar intelligence averages in similar European populations?

* Or, the intelligence came from the male Jewish founders. In which case, how come we don't see similar intelligence averages in other Jewish populations?

Both questions can, of course, be accompanied by, "OR DO WE!?!?!?! dun dun duuuun".

The founder effect gives two possible answers:

1. The gene or gene suite originated with one of the founders. Novel mutation or assemblage of uncommon preexisting mutations.

2. The proposed smart gene is not adaptive. Being smart is cool, but only one facet of fitness. The smart gene would then be weeded out of the larger population through selection pressure, but survive in the smaller population through the founder effect.