This is something I have been thinking about for some time. What I study is pretty much on the edge between applied and pure math. Specifically, I am interested in stochastic dynamics including SPDEs. Thus I have been investing a lot of time into stochastic analysis, really enjoy the subject, and am looking into some new ideas in my "spare time". I say my spare time because right now I am really productive on the more applied side where I am looking at stochastic dynamics in developmental biology and numerical methods for stochastic systems (I have a few publications I will be able to push out before advancement).
There is some trade-off here. My adviser strongly thinks I should drop all other activities because I am already building a solid foundation in the applied math / systems biology direction, and going 100% in it would make me have a higher chance of being a top candidate in the field come graduation. However, I kind of think that incorporating more "theoretical" stochastic analysis into my studies/research will lead to stronger results further down the line, but in the short term will inevitably be a hindrance. If I am thrown in the same pool as other applied mathematicians (who tend to publish more than pure math) and judged in the same manner for productivity, it seems that the extra time it takes for pure math results would most likely be detrimental to my chances of getting a post-doc.
I assume I am not the only person in academia who has faced this kind of decision. Is this something to come back to as a post-doc, or tackle now? How did you handle it? How did your colleagues handle it? How did it turn out? Do you think you made the right decision?
I do want to emphasize that right now I am doing quite well, and I think that matters a lot in this decision. However, since I will have a good amount of publications pre-advancement (based off of my own ideas), have fellowships, and will have a masters in both math and bio: does it make sense to take the time to diversify my personal portfolio? [Currently I am thinking of doing like 75% applied 25% pure, trying to spend less time optimizing code and using the down time as theory time.]