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Dear Math Stack Exchange advisers,

I recently started to develop an OCD-like symptom about reading books in mathematics. Whenever I read previous pages and proceed to next, I always feel under a huge suspicion and fear that I did not understand and memorize the materials presented on those previous pages, which leads me to re-read those pages, doubt again, and re-read those pages words-to-words, and waste my time eventually. I am sure this is not a normal behavior, and I would like to seek your advices and opinions about this anxiety coming from learning.

Somehow, I always under huge fear that I did not perfectly understand previous pages of book, even if I do understand for most parts, and under involuntary response of re-reading those pages. I am quite frustrated about this action.

I need to stop that behavior as it demands a lot of time, but I simply cannot stop due to anxiety.

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closed as off-topic by Stefan Mesken, user223391, Em., user91500, Claude Leibovici Jul 14 '16 at 7:27

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – Community, Em., user91500, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ OCD is a medical diagnosis. It is not a synonym for "persnickety" or anything like that. If you really believe you might have OCD you should see a psychiatrist. If you just mean you are persnickety then well that's fairly common among mathematicians. $\endgroup$ – user223391 Jul 14 '16 at 4:13
  • $\begingroup$ I think it is ridiculous to say you are anxious about reading maths when in the same time it seems you like to come on MSE. $\endgroup$ – reuns Jul 14 '16 at 4:14
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    $\begingroup$ These are classic signs of learning. But on a serious note, this is not the place to discuss whether or not you have a serious mental health issue. $\endgroup$ – Em. Jul 14 '16 at 4:37
  • $\begingroup$ This is obsessive, unhealthy, and unproductive. Deal with it as you would deal with any issue of obsessive thinking. $\endgroup$ – Elchanan Solomon Jul 14 '16 at 4:52
  • $\begingroup$ @user1952009 Why do you think so? I visit MSE to resolve my confusion. $\endgroup$ – MathWanderer Jul 14 '16 at 5:29
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I think this is a perfectly valid question. By no means I am a good mathematician/math learner, but here is what I think based on my own experience. Usually, if you doubt whether you have understood something or not, it is quite likely that you did not. For example, will you ever doubt that the solutions of $ax^2 + bx + c=0$ is given by $\frac{-b\pm \sqrt{b^2 - 4ac}}{2a}$? Probably not. Because you have solves quadratic equations for so many times. Even if somehow, you start doubting whether this is true or not, you can always verify that this indeed is true easily.

Things get a little bit trickier when you study more advanced math, for example, real analysis. My suggestion would be that, if you have enough time, it does not really hurt trying to redo/relearn the proofs that you did before but confuses you now. Notice that however if you have limited time then probably this is not the best idea.

To give you a concrete example, yesterday I was playing around with the following problem:

Consider the function $f(x)=\sin(\frac{1}{x})$ when $x\ne 0 $ and $f(x)=k$ when $x=0$. For what $k$ is the graph of the function not connected?

This is a topology question. However,somehow I was reminded of the continuity of the function. I remember that this function is not continuous at $x=0$ because I did the exact same question when I was taking analysis. However, when I tried to redo the proof, I started confusing myself, which resulted in the following question:

Negation of definition of continuity

Was it normal that I confused myself? It is hard to say. However, one thing is for sure. That is, I relearned something that I probably overlooked and now I have a better understanding of the subject, which is good. Going back to your question, what you are experiencing is normal. What should you do? Think it over and over until you are totally convinced. As long as you are learning, you are never wasting your time.

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  • $\begingroup$ Thank you very much for your advice! I agree with you that it is probably the case that i did not understand the concept if I doubt about my understanding. Although I seem to focus little more on trivial stuffs, so I needed to get those out of my mind and focus on important concepts $\endgroup$ – MathWanderer Jul 14 '16 at 5:28
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    $\begingroup$ @MathWanderer "Trivial" could be a dangerous word in a sense that it really depends on the person. For example, $\mathbb{Z}/p$ is a field might seem trivial to a professor but certainly not to someone just started learning algebra! If something does not seem trivial to you, then it is in fact not trivial to you and you need to figure it out. $\endgroup$ – 3x89g2 Jul 14 '16 at 5:30

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