I am a PhD student mid stage, working on computational aspects of mathematics. I am working on a research problem with my supervisor. I am at a stage where I can’t take much help from the supervisor because I am in the fourth year. I can’t do something like going to supervisors office to verify my answers. I did these things in the initial years of my PhD, but now I can’t poke my supervisor that often.
I am facing a difficulty that how to come with something non-trivial on myself. The problem with me is that I go into wrong directions many times, and in the past I have spent many days, weeks, or longer on these wrong directions. I want to minimise the number of these trials and failures. Does it come with age?
Question: Is there any way to pick a right direction (which yields a paper) in research while solving a problem? I can take the help of my research supervisor once in two weeks. However, many times a day or week, I also need to discard some of the possible directions of research.