When I was 5 years old (I was born in 1980), I decided to become a theoretical physicist. After finishing the school I joined the physics faculty of a university, but after the first year of study moved to math faculty out-of-sight. I learned about 5 years and left the university unfinished. (I am not going to explain here why I have not finished study.) Now I work as a programmer.
In the interim I developed a completely new theory in the field of general topology:
See the above link for the research monograph I've written. My own opinion may be biased but it looks like for me that this my monograph is worth highest math awards.
But when I finished writing this book, I found that I am unable to add anything new to it. I have neither new concept ideas nor ideas how to prove my open problems formulated in this book. My book sparkled and extinguished like a meteor.
Because of this now I think about switching to a new research field. I remember little of what I studied in the university and need to learn anew.
I feel that I should try functional analysis research.
As such, what would you suggest me? Take into account that I am probably relatively weak in theorem proving, my strong side is probably the ability to discover new concepts and definitions. Is functional analysis a right research area for me, taking in account these my weak and strong sides?
What else except of functional analysis would you suggest (taking into account my dislike of number theory and combinatorics and preference for analysis and algebra)?
Maybe you'll also suggest me some particular books? (free e-books would be preferred)