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I am a PhD student in the area of CS/math. My dream (for a long time) is to develop an academic career, and I work really hard (like any of us) to achieve that.

This semester I am taking a class which is semi relevant to my area. This class made me feel like a complete idiot. I have been spending hours on HW questions which other students solved quickly, it takes me a while to even understand parts of the solutions/concepts presented. This is very different from a struggle in research, where sometimes nothing works but at least you know that you are trying to solve something yet unsolved.

I know that the academic career path has so many struggles to come. However, this class kinda made me think that maybe I am not good enough for this type of theoretical research. How come other students invested so much less effort on that?

I guess I am looking for advice on this. Should I take that as a hint for actually not being able to do that type of research? Should I just forget about it? Have you been in such a situation?

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    I would try not to compare yourself to others, it’s only a recipe for self loathing. You should try to reflect on what you find hard about the problems - really - try to write down what you find hard about it, and then ask yourself why you think that you’re struggling. Self reflection is an indispensable tool. Furthermore, ask your peers how they are thinking about the problems, maybe you just need to retool how you think about a particular component of the problem. – GrayLiterature May 12 at 14:26
  • Is the area connected to your specialization fields? – user111388 May 12 at 14:36
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    Your description of your difficulties leads me to guess that your teacher may be assuming some background knowledge that you don't have. Such assumptions should be listed in the prerequisites for the course, but sometimes they aren't. If you can pin down what exactly you don't understand (in homework, lecture, etc.), you could ask the teacher for suggested reading to fill in what you need to know. – Andreas Blass May 12 at 20:23
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    This class made me feel like a complete idiot.I'll just leave this here. It's not just about research. – JeffE May 12 at 20:29
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What you may be experiencing is the fact that insight into some areas of mathematics don't translate into insight into others. I had a lot of insight into Analysis (my field) and General Topology, but little in Abstract Algebra. I once took a course (grad level) in discrete math and did terribly, experiencing much of what you describe.

To be successful you need a fairly general understanding of much (but not all) of mathematics and a deep understanding of one or two narrow areas. If you can achieve that then you can be a success.

It hasn't been possible for an individual to understand (at any deep level) all of mathematics for about 100 years. There are likely only a few living computer science professionals that understand all of CS, if that is even possible at all anymore, given what has gone on in the last 10 years or so.

If you are early in your studies then work on breadth. If you are mid to late, then it is time for a deep dive.

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    Implicit in any advice request like this question is a career advice request. Hence the question isn't only whether the OP can do good research, but whether the OP can do good enough research to get a job. Maybe I'm being unduly pessimistic, but would you have been able to get a job if the job market in the first few years after your PhD was like today's job market? I'm skeptical I could, and it hasn't been that long for me (2005 PhD). – Alexander Woo May 12 at 18:17
  • Do you have a different answer based on this criteria? Will be happy to hear – Ronald d May 12 at 20:34
  • I graduated into a terrible job market, actually. There were PhDs pumping gas. We had landed on the moon and funding for science and math suddenly disappeared. There are no guarantees in life. Sometimes you have to just "make do" until the economy improves. It took me years to find a really good position. – Buffy May 12 at 20:48
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    @Buffy - in your case, the job market eventually improved. But what if the job market in mathematics ends up looking like the job market in classics, permanently? It would not surprise me if, from now on, the only mathematicians getting positions with less than 2/2 teaching were candidates to be future ICM speakers. Realistically, I believe my department will never hire into a PhD-required position (though undoubtedly some of the people we hire into teaching positions will have PhDs) again. – Alexander Woo May 12 at 21:13
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I don't know the answer to this question, but I do have some idea for questions you might ask yourself.

I would guess that you are doing better in this class than you think you are, and overall you are probably stronger than this particular class indicates.

However, the job market is competitive, and I have every expectation that the current crisis will make the job market worse, permanently. How much worse I don't know. While you're not directly competing against your classmates, they are probably similar to some of the people you will be competing against.

I don't know where you are going to graduate school, so I don't know how good (on average) the other students are. If you are in a situation where only 5% of the students in your program get the kind of job you want, then you're probably in trouble; those 5% are likely to be at least above average at everything. If you are in a situation where 50% of the students in your program get the kind of job you want, then you could very well be part of that 50%.

Of course, it could very well be that, historically, 50% of the students in your program got the kind of job you want, but, because of the new job market, only 5% will going forward.

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  • Thanks. Why would the covid situation change things permanently? Why would it affect hiring? – Ronald d May 12 at 22:53
  • State funding to universities dropped significantly in the dot com crash in 2000-2002, and never recovered to former levels. There was another drop in 2008. State budgets are under severe strain right now, and many public universities could be seeing 20% or more budget cuts over the next two years, with only partial recovery afterwards. Furthermore, overproduction of math PhDs has finally hit the point where almost any math department can find part-timers willing to teach for $3000 a course (just like English departments started doing this 20-30 years ago). – Alexander Woo May 13 at 0:16
  • I see. Thanks for the answer. By the way - is there a strong correlation between high grades and good research? I mean, your analysis assumes that the top 5% high graders are also the top in research. From your experience - is that so? – Ronald d May 13 at 5:33
  • There is correlation, but I wouldn't call it strong. My analysis did NOT assume that the top 5% in classes are top in research. My analysis assumed that the top 5% in research are among the top 50% in their classes. – Alexander Woo May 13 at 15:37
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You're developing a cognitive distortion in regard to your ability. Comparing yourself to another only will increase you anxiety in this respect. I've seen it destroy teachers. One day they're told that they're consumate professionals. Then one observation later they're deemed inadequate and then put under review until they leave because the stress becomes too much.

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However, this class kinda made me think that maybe I am not good enough for this type of theoretical research.

Well, maybe you aren't for this type. Isn't that natural? What it does not mean is that you are not good enough for your main field. You are going through something very normal, so a pragmatic approach might be the best one.

If you are doing this out of personal interest, just enjoy the experience and don't measure with other people. If you are aiming for specific skills, focus on getting the useful, applicable parts you can apply and don't measure with other people - you are not there for that. The field is semi-relevant, so I consider it as either a potential extension or something helpful but not essential. There is also a chance that you are used to learning in a way that is inappropriate to that particular field, and that may hinder you. E.g. some people work very well when a topic is presented to them as a problem to be solved rather than an abstract theoretical construct, and some people are exactly the opposite.

An analogy with learning languages at an older age is very tempting - many people have felt that struggle.

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