Is it possible to pursue two distinct research interests in the same discipline? Is it possible or legitimate to pursue two distinct research interests in the same discipline in the context of an advanced academic career (PhD and beyond that)?

For example, can I  have two research interests the one concerning History of Economics and the other concerning Mathematical &amp; Computational Economics in a PhD program in an Economics department where there are always professors that have these but usually not the same person?

Or for example, can I  have two research interests the one concerning Political Theory/Philosophy and the other concerning Mathematical &amp; Computational Social Sciences(Political Science) in a PhD program in Political Science department where there are always professors that have these but usually not the same person?

Just for the record, I have postgraduate academic education from prestigious universities both in Computer Science &amp; Applied Mathematics and in Social Sciences(mainly Economics) &amp; Philosophy. For this reason, I want to maintain both my strong qualitative and quantitative skills and have these, two in each case essentially, quite distinct research interests.
For example, can I have two research interests the one concerning History of Economics and the other concerning Mathematical &amp; Computational Economics in a PhD program in an Economics department where there are always professors that have these but usually not the same person?


Practically speaking, your PhD topic will need to be on one topic, so you will need to choose to some extent. Relatedly, you will also need one (and usually exactly one) advisor - you can have the other person as a member of your committee, or sympathies permitting, just as an unofficial mentor and collaborator, but typically the formal advisor will need to be one specific person.

However, this should not prevent you from conducting research on both your interests. Typically, there are two ways to go about this:


Find a topic that naturally integrates your interests. For instance, you may write a thesis in political sciences, but with a healthy dose of econ (which almost automatically also includes plenty of applied maths), or you may write a thesis in economics, but with a focus on political implications of economic theory. In this example, both versions sound completely reasonable to me. Of course, if your actual interests are farther apart, this becomes less reasonable.
Choose one of your interests as thesis topic, and work on the other as side topic. This you can do in most cases, as long as there is some understanding between the disciplines (and your advisor is generally in favour of side projects, which apparently not everybody is). This course of action has the disadvantage that ultimately, you will lose time to work on your thesis, and your thesis may accordingly take longer to complete or be less compelling than if you worked 100% on it.


That all being said, a common advice given to students is to remain somewhat narrow in their academic interests early in their career, and only start to branch out and diversify once one is strongly established in one particular aspect of a field or discipline.