I have a Ph.D. in Statistics and have always been interested in pure mathematics, but never had a chance to really pursue it. My mathematics background includes real analysis, linear algebra, functional analysis, and measure theory. These were taken at the graduate mathematics Ph.D. level. I am wondering how many classes are necessary for me to take in pure mathematics in order to do research in pure mathematics. Does it require me to go back to school or are there certain areas of pure mathematics that would be easier for someone like me to dive into? Thanks in ahead.