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I'm a 3rd year PhD student in pure Math in a Canadian university. I feel like in last one year I haven't made much progress. I definitely tried some problems, had regular discussions with my supervisors, but, either I couldn't get any new result or what I did turned out to be wrong. Surely, I read some other topics, gave some talks and attended some conferences/seminars, but that hasn't helped in getting some new result.

I'm starting to get worried that I'm not making enough progress towards completion of my PhD.

The reason I'm worried is because my PhD is only 4 years and I'm already in my 3rd year now, so in above a year I'll have to start applying and if I don't have results then getting a postdoc would be difficult. Let alone the fact how competitive the job market is.

I would like to know the opinions of more expert and experienced people here. Thanks!!

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    Shouldn't you also be worried about graduation? If you don't have results, how do you graduate?
    – k99731
    Sep 22, 2022 at 4:39

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I don't have the numbers, but I would be very surprised if half of Canadian pure math PhDs (just counting those who graduate) get another academic job, not counting those who return to an academic job in a developing country with a serious shortage of PhDs. I guess UofT and UBC and maybe McGill might manage to place more than half their PhDs into postdocs, but, even then, statistically speaking, your concern is valid.

However, there really is nothing you can do about it other than continuing to do research and hoping you get results. If it helps with the worrying, you might want to get yourself some idea of what you might want to do if you don't get an academic job, but there isn't really anything else you can do.

You should know that a substantial portion of pure math dissertations are basically figured out in a week, though it takes a good deal of more time to get all the details completely straight and of course time to get yourself to the place where you can have that week. Progress is not even. Enlightenment can be sudden. In fact, the dissertations that are figured out in a week are usually the best dissertation; the ones where the student methodically works through things and makes gradual progress over a longer period tend to be the boring dissertations.

However, many students never get that week, and failure to get that week can be just some kind of bad luck with the problems you pursue. It does happen that some people just keep running into unexpectedly intractable problems (and the problems don't get solved by anyone else either, or get solved 20 years later when new methods become available). When the job market was friendlier to applicants, an advisor could explain and give evidence that you are obviously capable but couldn't get substantial results due to bad luck, but that's unlikely to get you a job nowadays considering there are more very capable applicants than jobs.

It sounds to me that you don't need to worry about graduating, since you could write up your attempts at problems and results for some special cases (even if they are almost trivial) for an acceptable dissertation, but that's unlikely to get you a postdoc.

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