How much should a mathematician confine themselves to a particular area if they are to be successful? My main discipline is PDE however, I have a heart for computer science too. I am wondering if I should work to get my knowledge in the ladder area up or continue what I am doing. My plan is to do research in PDE as a career, but is there possibly room for Computer Science in my research?
I guess, if I were to do both, the question boils down to if there exists such an occupation in which I could do both. Any other way, coding and computer science would be mere hobbies which I am fine with however, less satisfies with.
This question can be generalized to the cases of others too, though: What is more important, getting insights in your main discipline, or strengthening your knowledge in weaker, less familiar areas of mathematics that may be somewhat unaffiliated with what you already know?
A (most likely useless) tremendously vague and incomplete answer.
Have clear concrete short-term goals (depending on your definition of success). Work hard on these goals. This will: clarify what is your potential, your weaknesses, your motivation; speed up your capability of judging different career options/topics; force you to broaden your knowledge with purpose; meet professionals;...(many other benefits)
Keep an eye around you.
Make sure you're having fun.