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I graduated from college with a physics degree faster than my peers (because of various reasons: financial constraint and ambitions as well as near-burn-out state). My undergrad is a decent research university, not the best of the best, but many well-known researchers. I did well in most classes but I sometimes think it's because my classes are not rigorous enough. Just saying my thought is not out of thin air because I attempted to take a graduate course at the time and I had to work really really hard for it. I don't think I really understood many things from undergraduate classes, even though I'm really good at solving problems from examples. Now I think many of the basic things I didn't understand before start to haunt me in my graduate program. Just to emphasize, the gaps I'm talking about is not just some details but in some occasions the whole subject. I still have many gaps from my peers at graduate school. Even though I'm finally filling in the gaps starting grad school, I still feel like there are a lot I need to revisit.

Perhaps my state is a result of me graduating early and pushing my schedule to a limit where I can barely sit down with a class and understand it. Perhaps I fooled everyone in grad admission into thinking I'm some sort of smart student. Perhaps it's because my undergrad didn't really have the best structure preparing me for what I'm doing now. Or perhaps I didn't really know how to learn effectively before graduate school. I don't know.

I feel worrisome sometimes about my abilities, but relieved other time when I revisit what I didn't know and finally understand it. I want to ask if other people experience similar things about not understanding many things and eventually filling in the gaps later (I mean a lot of gaps :)? Or is it a debt of a student who didn't properly go through their education?

As a final word, I know about imposter syndrome. I think I have evidence in my lack of qualifications as said rather than only disregarding my achievements. And thank you in advance for reading my long concerns.

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    It's totally normal to study something and then find out later that you don't understand it as well as you thought at the time. This happens to everyone and is part of the way learning works. As such, having to re-learn topics from your undergrad coursework is a normal and expected part of graduate study; you just have to budget the time and energy to do it.
    – Nate Eldredge
    Commented Aug 16, 2020 at 16:42
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    Indeed, I would say that studying something more advanced is precisely how you force yourself to fill in the inevitable gaps in your previous learning.
    – Nate Eldredge
    Commented Aug 16, 2020 at 16:43
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    I don't think that's unusual either. But I also don't know that there's a lot to be gained by agonizing over whether it's better or worse than it should be (which sounds like classic impostor syndrome); focus on what you can do to get it to be good enough.
    – Nate Eldredge
    Commented Aug 16, 2020 at 16:57
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    Being "good enough" is not an innate characteristic, and your success at research will depend far more on what you do in the next two years than on what you have done before now. There is no point in trying to make that decision now.
    – Nate Eldredge
    Commented Aug 16, 2020 at 17:10
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    Your experience reminded me very strongly of how I learned fusion arguments (in set-theoretic forcing). I studied them once and didn't catch on. I studied them again and still didn't catch on. I studied them a third time and felt "Oh, is that simple idea all that's going on?!" It's possible that the book I used the third time was a lot clearer than the first two, but I don't think that's the case. More likely, the first two attempts and my unsuccessful struggles with them prepared me (subconsciously?) to catch on the third time. May you have (and enjoy) similar revelations.
    – Andreas Blass
    Commented Aug 17, 2020 at 1:14

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I think this question is, in fact, about imposter syndrome. But I will answer it anyway.

Many rigorous studies have shown that it is common for students who have completed physics courses to maintain the same misunderstandings of basic physics that they had when they started those courses. So yes, it is normal to not understand things.

It is unlikely that you fooled anyone.

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    (+1) I think this is normal in most subjects. There simply is a lot to learn, and working through material once isn't enough to gain a deep understanding and maintain it. I find that the topics I know really well are those that I studied, restudied, and revisited many times (undergrad and grad level), where I re-asked (and sometimes answered) even very fundamental questions in every iteration. "In semester X we learned about ... " mostly means I remember having heard some of the terminology before.
    – cheersmate
    Commented Aug 17, 2020 at 7:26
  • @AnonymousPhysicist Thanks for your answer and the link to the other question. An answer from the other post describes it well: I only see what I don't know and as a result maybe exaggerating my own failures. I will keep working to the best of my abilities.
    – MoreConfi
    Commented Aug 18, 2020 at 0:41
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    Do you have links to those studies?
    – user111388
    Commented Aug 18, 2020 at 7:12
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    @user111388 I don't look up links for people. In this case, there are many examples, often published in the American Journal of Physics over the past 30 years.
    – Anonymous Physicist
    Commented Aug 18, 2020 at 7:16
  • I'm adding the link @MoreConfi mentioned here: academia.stackexchange.com/questions/11765/…
    – user2768
    Commented Aug 18, 2020 at 11:28
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I want to ask if other people experience similar things about not understanding many things and eventually filling in the gaps later (I mean a lot of gaps :)? Or is it a debt of a student who didn't properly go through their education?

I do very often feel the same way and asked my advisors their opinion. Here is a batch of answers fused with my commentary on the subject.

  • There is a big gap between getting an A and actually understanding the subject.

  • It is normal to not understand something in your first try. It takes few tries for some people.

  • Those gaps will be filled over time as you work on those subjects further.

  • You can't really fully understand something before teaching a course on it (verbatim from my advisors).

I personally feel like I really understand 2-3 subjects and have a passing understanding of other 4-5. Unlike your case, I did not graduate early. I personally approach this with solving textbook problems without rereading the text. It really help, at least to me, to figure out what I do or do not understand. Another method is taking more advanced courses which inevitably require, at some point, some of those gaps you are missing. That is a good time to go back and repeat, learn in context.

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  • Thanks for the answers. These sound good. I just had a (possibly impossible) idea of a good research who understands most things they learn. Typical story of someone like Landau. But realizing that's not realistic for everyone is pretty important.
    – MoreConfi
    Commented Aug 21, 2020 at 2:19

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