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I am really in a fix in my career.

I completed my Masters in 2014. I qualified in a PhD Scholarships Test in 2015 and in the same year joined in a University for research work.

My interest lies in Linear Algebra, Topology, Abstract Algebra. My guide offered me to work in Spectral Graph Theory. As I was not quite acquainted with the topic I took up this topic for research.

As I am reading on my own, I am getting stuck on many theorems and some problems.

My guide has said recently that he does not have much expertise on this topic besides the preliminaries and hence he can't answer each and every problem of mine. He has said that the topic is new to him also. I have found now that also does not have any research papers to his name on Spectral Graph Theory as well. I was not aware of this before

My question is how important is the choice of a guide/adviser for pursuing PhD in a topic and what needs to be checked before joining him.

Is it wise continuing to work with him or should I look for some alternatives. Does getting a PhD depend a lot on your guide or I am expecting a lot from my guide? Does pursuing a PhD mean you have to do all along yourself?

I know there are many in this site who have got a PhD or have served as guides/advisors for many students. Please help. Any suggestions will be helpful. I would be happy to give more inputs if required.

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  • There's still hope. If your advisor doesn't have domain expertise, search for a mentor who does.
    – Ébe Isaac
    Apr 16, 2016 at 10:14

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Working on a PhD in an area where your advisor appears to have little to no expertise in is fraught with danger. A PhD degree is in some sense an apprenticeship - while you need to do the heavy lifting, you also get/need to learn the tricks of the trade from an accomplished master. Every craft has subtler/finer aspects that are not acquired easily. Would you want to rely on someone who himself doesn't appear to know much, even at a high level? I wouldn't do a PhD with such an advisor for the same reasons I wouldn't learn painting from someone who doesn't know it himself/herself.

On a more important side note, it might not be very wise to jump into a doctorate in an area you have such little knowledge/interest in. You do appear to have the right background, but even with that, doctoral level research in Spectral Graph Theory (and applications, if you are interested in them) is not going to be easy to pick up, even with an expert advisor.

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  • I disagree. Many very successful PhD students have worked in areas that are not precisely in the expertise of their supervisor. Certainly nowadays, when you have the web, and easily connection to other resources this is quite common. It also indicates independence and shows initiative.
    – Dilworth
    Apr 16, 2016 at 15:52
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    @Dilworth;is it possible to pursue a phd only relying on the web ?
    – Learnmore
    Apr 16, 2016 at 17:21
  • @learnmore, the web as a starting point, yes. Then you should meet with people, and especially let them know your work. Also, you can almost never rely on your adviser to teach you things. You should be able to develop your own self-studying routine. This is essential in phd. PhD is a lonely road (in math, and other theoretical areas).
    – Dilworth
    Apr 16, 2016 at 17:41
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    @Dilworth: PhD studies require 'independence' and 'initiative' regardless. The question is, why make your life harder still, esp when you have the option of making it easier? How is this extra machismo going to be of use, given that the enormous risks of picking a dilettante advisor are only too well known? The OP would be competing against peers (for awards, publications, jobs, etc.) who have better equipped advisors. It makes much more sense to keep it simple and play it safe. This business of working with amateur advisors ends badly all too often (exceptions of course are always there).
    – andy
    Apr 16, 2016 at 18:12
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    @Dilworth, Yes that's what I meant. I didn't mean, amateur per se, but an amateur in that particular research area. And yes, like I said, exceptions are always going to be there. But for a vast majority of the cases, this approach is simply just inviting trouble. Ounce of prevention is worth a pound of cure.
    – andy
    Apr 16, 2016 at 18:50
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A chief hazard in working on a topic (in mathematics, for example) in which your advisor is not expert (and for which you have no other immediate expert co-advisors) is analogous to the idea of trying to make money on the stock market only with knowledge available to everyone else. Yes, there is the internet, but it is available to everyone else, too. The way to make big money on the stock market is with "insider information", but in the U.S. this is illegal (unless you are in Congress!) Analogously, unless one imagines that one is "special", it is not so easy to get started in some line of research without expert advice. Luckily, it is legal, and certainly desirable, to have expert advice! Otherwise, one may fail to understand relevant keywords, for example, and thereby be unaware of work already done. Or be unaware that dozens of other people are already working on whatever problem one sets as project goal, setting up a situation in which one's thesis inadvertently turns out to be old news? Or that one's project-idea is known (to experts) to be infeasible? How to avoid such issues?

Despite frequent claims on this site and others about a Ph.D. simply being "learning how to do research", I would also claim that there is such a thing as "expert knowledge base(s)", and these are not easily replicated simply in software (with or without the internet).

(By the way, the usual style in mathematics is that advisors are not co-authors on PhDs, in any case.)

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  • ... that is, yes, there are considerable risks in the situation you describe, and they are not standard and certainly not required. Unless you consciously choose to accept them, you should change your situation.
    – paul garrett
    Apr 21, 2016 at 18:43
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It's crucial. You can get technical help elsewhere, but your advisor is ultimately the gatekeeper to your future career. And it is a career; just being good at math is not sufficient without the set of contacts and public presence that your advisor controls access to. You're in theoretical mathematics, and it's extremely difficult to get an academic position in that area, and it's extremely difficult to do any significant research outside of such a position. (It isn't difficult to find a random high-paying job with a degree in pure math; but if you only wanted that, getting a PhD is not an efficient method of going about it.)

The point of grad school is to prepare you from an academic career, and that involves (and, honestly, is mostly about) getting the appropriate CV that will allow you to enter that career. Your goal at this point is to churn out publications. Ask your advisor if, given the difference in your research interests, he can help you with that. This involves knowing enough about the subfield to direct you toward the better journals and conferences, identifying the cool problems that will attract notice, and avoiding the problems that are intractible or just not interesting. He may be able to do this; if so, there's really no reason for you to switch advsiors. If he can't, find someone who will.

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