Despite the controversy around this topic, Ashkenazim Jews are smarter than other European ethnic groups. We have the numbers. The average IQ of Ashkenazim Jews is 115, compared to 100 for other European groups. Given the normal distribution of the bell curve, this means that there are 23 in 1000 Ashkenazim Jews with IQs over 140, as compared to 4 in 1000 Europeans with IQs over 140 in a given population. We also have countless examples of high achieving Jewish scientists and scholars, including Einstein. Proportionally, Ashkenazim Jews account for a vastly higher number of doctors, Nobel prize winners, chess champions, or creative geniuses than their small population (.25 of the world's population) would predict.
Some theorists have offered explanations for higher Jewish intelligence. First of all, this intellectual trend is found in Ashkenazim Jews, not Jews worldwide. Who are the Ashkenazim Jews? Ashkenazim Jews refer to groups that migrated to Northern France and the Rhineland in Germany, and Central and Northern Europe in general from the year 800 AD to the Middle Ages. Over the centuries the Jews experienced varied levels of religious prosecution and cultural restrictions. In general, Jews were not allowed to join the guilds in Germany and France, nor were they allowed to own land. Other than mastering a trade, or farming, there were few other ways to make a living. Hence the Jews primarily became the money lenders during the Middle Ages, and were restricted to this occupation for 900 years.
Given these historical factors, some theorists postulate that higher cognitive skills such as numeracy, literacy, and critical reasoning became highly selective for Jewish survival. And because of low intermarriage with other groups for centuries, due to religious and ethnic differences, these cognitive skills were passed on through generations. Another interesting fact is that Ashkenazim Jews suffer a high incidence of metabolic and sphingolipid diseases such as Tay-Sachs and Gaucher's Disease. Apparently, these diseases have as a side effect a likelihood of higher intelligence, because they are related to chemicals affecting neuron growth. Is it possible these diseases (despite their clear negative effects) have persisted in the Ashkenazim population because higher cognitive abilities proved to be highly selective for survival?
There are debates as to whether intelligence is even an inheritable trait. Is intelligence largely genetics, or established by environmental factors? In my opinion, it's likely a combination of both, with genetics playing more of a role than we would like to accept. It seems reasonable that the trend of higher intelligence in Ashkenazim Jews is due to a combination of strong cultural factors, as well as genetics.