Are people genetically predisposed to being interested in specific fields/ideas? How does specialization occur?
I think the concept you are looking for is the one of heritability.

In short, heritability represents the part of the variance for a trait that is caused by the genetic variance only. For more information, you can refer to this, this, this or this post or to wiki.

This wikipedia article talks about the heritability of IQ in human. It has been measured to be around 0.7.

Of course, heritability in IQ is not the same as heritability of "interests". But I don't know about any measure concerning the heritability of "interests". Such measure will be highly dependent on how you classify interests together. Does a mathematician specialist of probability theory have the same interests than a mathematician specialist of non-linear algebra? Does a Mathematician have the same interests than a chemist? and of a engineer? and of an electrician? Does a butcher have the same interests than a backer? and of a waiter? and of a bricklayer? .. Does anyone who work in business have the same interests? The fewer groups you make, the higher will the correlation between parents and offsprings and the higher is the part of the genetic variance that explain the variance in interests choice.