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Some users on this site are insanely good at topology. For example: Eric Wofsey and Brian M. Scott. There are a few others as well.

How did they get so good? What's the secret? What tips can they give?

I'm asking because I'm working through Munkres right now and even though I think I'm doing well, there's some questions which I get utterly stuck on, and I look them up on this site. The answers to some of these questions are very slick, almost ingenious, which makes me wonder how one would come up with them.

This might not be the best question for this site. Nevertheless, I think getting some insight into how the minds of the best mathematicians work is relevant to a lot of people.

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MathematicsStudent1122
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    Do lots of problems, think of lots of examples and counterexamples of definitions you see, think of applications of theorems and propositions and understand via counterexamples (or other means) why (and if) they fail if you remove some hypothesis. Ask people who do understand the material about their intuitions for concepts you can't quite grok. Work until you get stuck, then work some more, and when all else fails, ask for help (getting someone to show you a solution is of course less beneficial than getting a nudge in the right direction so you can complete the problem on your own). – Stahl Dec 02 '16 at 18:16
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    And don't be afraid to consult sources other than the one you have. A different perspective or even just a different wording can be incredibly valuable. – Stahl Dec 02 '16 at 18:17
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    The same way you get better at anything. You practice, practice and practice some more. – Asaf Karagila Dec 02 '16 at 19:33
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    I fell in love with it very early and had a superb introduction to it as well, from John Greever. I took my first topology course second semester of my freshman year from a man who taught it using a modified Moore method, so I ended up proving most of the theorems and finding most of the counterexamples myself. It was great fun, so I never thought of it as work, but in retrospect I can see that I did in fact put a lot of time and energy into the subject even then. Jim Cannon taught the first graduate topology course at Madison the same way, ... – Brian M. Scott Dec 02 '16 at 20:09
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    ... so I had a lot more practice. That said, I agree with those who emphasize the value of counterexamples: they are frequently what show exactly what makes a theorem tick. – Brian M. Scott Dec 02 '16 at 20:13

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I bet their secret spell is hard work!

You might consider to look up some of the books suggested in the post "Best book for topology?" and work through as many problems as possible.

Also, whenever reading mathematics, it is a good thing to try to understand the theorems, and, if possible, find your own proof before reading the particular proof given.

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I am not an expert in topology, but studying counter examples helped me a lot. For example, when a theorem says:

If a closed and a compact subset of $\mathbb R^n$ are disjoint, then there is a positive distance between them.

Although studying the proof of the above theorem is important, I think you need to ask yourself:

"what if both sets are only closed but neither is compact?"

I think this way you can get rid of wrong assumptions about topology. For example, you can start with:

What is true in Hausdorff spaces but not necessarily true otherwise?

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