Hi, I am a Software Developer in a company. I work on cutting edge technologies in System Software and High Performance Computing. But, I'm also interested in Pure Math and also Physics. I get excited about Number Theory and I want that to be part of my career. What do I do?. Where do I start with?. I know this is weird because people go the other way!. I am planning for a PhD after two years or so. How do I go about choosing a topic for research related to the fields I like?.