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I just finished my masters and am currently working as a research assistant before starting a PhD in applied mathematics. I was doing some preliminary work for a possible project and derived some minor results which I find interesting, but in the end, we decided not to go ahead with the project.

I still find the minor results interesting and thought of digging a little bit deeper by myself. However, since the group is no longer interested in this, I would have to do this by myself, unsupervised. Is this a very bad thing? Or a good learning experience?

I had a bad experience doing unsupervised research (wasted a lot of time for no results). However, I know that as a PhD student, I must eventually publish first-authored papers. How do I know when to make the switch?

  • 8
    You can work with your advisor and get a first-authored paper. – Piotr Migdal May 20 '13 at 18:11
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It is a common thread - see "Go rogue too soon/too late" in 10 easy ways to fail a Ph.D. and Going Rogue at The Chronicle of Higher Education. An excerpt from the first:

The advisor-advisee dynamic needs to shift over the course of a degree.

Early on, the advisor should be hands on, doling out specific topics and helping to craft early papers.

Toward the end, the student should know more than the advisor about her topic. Once the inversion happens, she needs to "go rogue" and start choosing the topics to investigate and initiating the paper write-ups. She needs to do so even if her advisor is insisting she do something else.

The trick is getting the timing right.

Going rogue before the student knows how to choose good topics and write well will end in wasted paper submissions and a grumpy advisor.

On the other hand, continuing to act only when ordered to act past a certain point will strain an advisor that expects to start seeing a "return" on an investment of time and hard-won grant money.

Advisors expect near-terminal Ph.D. students to be proto-professors with intimate knowledge of the challenges in their field. They should be capable of selecting and attacking research problems of appropriate size and scope.

Personally, I have a lot of experience with unsupervised research (yes, usually wasted a lot of time for no results), starting from high school.

Sure, doing advisor's project is much safer (as, in some sense, (s)he is responsible for the big picture, references, judging which result is good enough) and allows to forget about doubts (for good or bad) and concentrate on work.

However, what I've discovered after 1.5 of my PhD (mostly "going rogue") is that there are two important things:

  • asking experts (or peers), and
  • day-to-day collaboration.

Sure, you can have an expert and a collaborator in the same person of your advisor, but as long as you are not afraid of talking to other people and have some knowledge in the topic, it shouldn't be hard to ask experts appropriate questions. When it comes to collaboration - it may be trickier (but not if you locally have people with an interest overlap).

On contrary, working alone for months on a theoretical problem, with little feedback, may be very hard (both technically and psychologically). I've learnt it the hard way. It is not a problem for one research line, but it is when all research is done alone (may be inefficient and depressive, perhaps unless you are in a deep love with it).

11

My former Ph.D. advisor's philosophy is that a student should become a teacher of their supervisor. He seems to give the green light when the student

  1. explains their own research problem clearly,
  2. shows a clear sign of familiarity with all relevant work,
  3. puts their work in context,
  4. gives a convincing argument about why it's important and interesting,
  5. looks they can make it, and, somewhat more importantly,
  6. chose a topic that isn't too unfashionable to the extent that devoting their time during their Ph.D. student phase to that kind of topic is a career suicide.

I wrote my first paper when I was a second year grad student, and my first joint paper with my former Ph.D. supervisor is after I got my degree. My friend who got his Ph.D. from the same advisor at the same time as me was also like this, and he's doing pretty well in academia. So probably all that matters when it comes to starting your own math research is if you're ready for it. And if you're ready, I don't think your advisor can talk you out of it anyway. At least, randome guys on the internet like us surely can't.

So, I'd say if you're being honest to yourself and still confident that you know about your research topic better than your advisor, and if you can get him interested in your research, it should be fine.

6

It is not necessarily a bad thing to forge ahead on your own and it will certainly be a learning experience. It is definitely a good thing to try this, because it will demonstrate and help reinforce that you are an independent researcher, something which you need to be at the end of your PhD studies.

But this is not without some risk.

Part of the role of the supervision that would otherwise be provided is to improve your skills as a researcher and writer of scientific texts. Without this guidance, your skills at the end of your PhD may not be as good as they could be. You may have gaps in your knowledge that would need to be filled. The presentation of scientific material in your writing may end up being suboptimal, because you won't have someone to proposed better ways of writing. And worse still, your ideas may not end up being the best they could be, because you won't have someone questioning them and your assumptions, ultimately forcing you to produce better versions of your ideas.

I've seen it before. Some highly independent students I've seen in action fail to follow recognised mathematical conventions, produce new notations for existing concepts, miss key references and lack understanding of key concepts that would help improve their work, and so on.

Independence is a good trait, but try to take advantage of opportunities to receive guidance from your supervisor(s) while you can.

  • 5
    The risk Dave describes comes more from not working with your advisor than from working on something without your advisor. See the difference? You can (perhaps even should) work independently on X while working with your advisor on Y. – JeffE May 20 '13 at 19:36
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    I don't think your description of highly independent students is extremely accurate. What you wrote seems to me describes myopic students who don't learn others' work by reading papers and attending conferences/seminars. Being independent doesn't mean you don't listen to others or ask for advice. In my obnoxiously arrogant opinion, it simply means you decide. You should take into account every piece of information you can get, including what your advisor says. – Yuichiro Fujiwara May 20 '13 at 19:38
  • @YuichiroFujiwara: You are right. It is a description of some highly independent students, not all of them. I reworded a little. – Dave Clarke May 20 '13 at 19:50
3

Basically, the only restrictions are issues related to funding. If your funding is intended for you to work on a specific topic, then your primary efforts should be given to the designated topic. However, you can, if so motivated, pursue the research topic independently. In mathematics, this might not be such a huge issue, as the infrastructural demands are not so large (except for some applied math projects). However, in other disciplines, where this "unsupervised research" may require experimental supplies and other resources, this is a much bigger issue. In the latter case, you must obtain approval from the PI whose equipment, material, and other resources you will be using!

If your time is "unrestricted," in the sense that it is not tied to any particular project or program, then you should talk with your supervisor to see if you can use some of your "normal" time to devote to the "side" project. If you can, great; if you can't, then again, this needs to be "on the side"—beyond your main project.

As for the question of doing "first-authored" research, well, that transition process, in many respects, is the goal of the PhD! If you are to be a successful researcher, then during your doctoral studies you will learn how to do research independently, and eventually unsupervised. (Moreover, you will hopefully also have the chance to learn how to supervise others!)

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Performing unsupervised research is also a great way to develop the self-discipline needed for a PhD and developing your own research strategies. This time could be considered a valuable time for personal and academic growth.

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Think of research as a learning paradigm, whenever you learn something new spend time asking yourself how you would develop it if what you just learned was the state of the art, and what interesting directions would be. As you learn more about the topic you can see whether you were right. This makes learning to do research a constant part of your life rather than something you are learning to do when you start your thesis or dissertation.

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