Is it better to focus on relearning mathematics fundamentals or learn material as needed to understand research papers? I am working toward a PhD degree and my major involves lot of mathematics. The problem is that my basis of math is not very strong but after putting a lot of time I can understand the theorems, lemmas, corollaries in the published papers. Sometime I wonder should I start learning the basics again or should I read the research papers only to make my math strong. If I start from the basics then it may consume lot of time however it may help me understanding things better and in applying accepted ideas to more general problems. On the other hand if I learn through research papers then my knowledge will be limited to only the problem I am working on and new ideas of solving the problem may not fluently come into my mind. 

In essence which of the following strategy is better in your opinion


Start learning from basics.
Learn through published research papers during the literature review.
It will not be very easy to learn a broad subject in mathematics by reading research papers.  Books which cover the subject starting from the basics will be more cohesive (for instance, regarding notation and terminology) and will leave you with more approaches to solve problems. If your major requires a lot of mathematics, hopefully you can identify a specific area (like analysis, geometry, probability, etc.) that you need, and find a good text that synthesizes a lot of the research.