I have a master in physics and philosophy and have a keen interest in mathematics. Currently I am doing a PhD in philosophy. On a personal level, however, I cherish the interdisciplinary ideal of combining mathematics, physics and philosophy. I am well aware that realizing this ideal requires an enormous amount of work and talent – and that very likely I cannot 'completely' realize it.
On a structural level, I suppose this is an unfortunate side-effect of the level of specialization in academia today. On a subjective level, however, I feel the need to “revolt” against such over-specialization. It a shame that some "philosophers of science" in my branch haven't solved one differential equation in their life; yet they intend to reflect on what physicists do. I am convinced that combining different disciplines is a worthy thing to do. I suspect many people would agree with me, but the competitive reality of academia makes it very hard to realize.
The time one invests in a secondary area of interest (i.e. mathematics, physics) takes away time to do research in one's main area (i.e. philosophy). The reduced time would (on the short-term) make me less productive and successful. However, in the long-term, it might allow me to produce work of more value and depth.
(1) Is it wise for a PhD student, somewhere below on the academic ladder, to gamble already on long-term investments, or should one give in to the short-term safety and (over)specialize in one area?
(2) Is there some middle-way between the two extremes?
(3) Is it more useful in later stages of one's career to have a broad skill-set or have more publications in one (limited) area?