At the moment I'm in the final stages of my doctorate in mathematics. (My background is a BS in physics and an MS in mathematics.) My focus and interest have been in applied functional analysis in general and various kinds of abstract and concrete delay equations in particular. These are evolution equations which generate infinite dimensional (semi)dynamical systems. Like all doctorate candidates, I have acquired a certain amount of specialised knowledge and published certain results. I would very much enjoy continuing doing applied functional analysis and teaching in an academic environment, but sometimes I find the focus on delay equations rather narrow. Recently I have been drawn to the fields of control theory and continuum mechanics, and I would be quite curious to learn more about the functional analytic aspects as well as the physical foundation of at least one of these two. Although these fields may be considered more or less tangent to my own field, on the level of specialisation they are quite different. My question is: Have any of you, in a similar situation, pursued such a kind of new interest in an academic setting (e.g. as a post-doc) after the completion of your doctorate? How did that work out? Would you advise me to give in to my curiosity? Or is current research too specialised for such excursions and am I just wasting my time and past efforts? I thank you for any sensible comments.