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In undergraduate studies, I always had such respect for the professors and TA's that seemed so impossible to stump. The people who seemed to know everything, whether it be an intricacy in Galois theory or the Proof of the Implicit Function Theorem in Real Analysis. Many of the contributors on MSE seem very similar, that is, capable of answering a wide variety of complex questions. So, my question is how do I get better? How can I get to a place where it is near impossible to be stumped? Any advice is appreciated.

J. W. Tanner
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    Unfortunately, this question is off-topic on this site. The main advise is: just learn what you want to, and don't think you are not suited for that / insufficiently smart / whatever else stops you from this. Those people you admire got at this level of knowledge through years of hard work, and there is no other way to get there. – lisyarus Nov 11 '19 at 09:59
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    Experience makes a huge difference. But keep in mind people on math.stackexchange are only answering the questions they know how to answer. Also, a TA might have recently explained the same concept to some other student recently. Feynman makes some remarks about this in volume 1 of his lectures on physics, saying that professors might seem to be able to produce polished proofs on the spot but the truth is they might have spent three hours preparing their lecture the night before. – littleO Nov 11 '19 at 10:20
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    Is this a good question for Meta? – Mnifldz Nov 11 '19 at 14:11

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The only way to get better is to stop thinking about getting better and stop comparing yourself with other people. If your goal is to show off by throwing bunch of high lvel answers then it is not worth to start in the first place.

However, if your like math and want to study for the fun, symmetry and logic and beauty of it then i would suggest you to get some good books on Real Analysis. I would recommend Understanding Analysis by Stephen Abbot. And if you have fundamentals lacking then i would suggest you to study "How to prove it" by D. Velleman".

At last oi would strongly recommend you to stop comparing yourself. There are no levels. These undergraduate, graduate are just man made names. Main point is that you must enjoy your study and do it with sincerity asking many questions as you go along. Also better if you do group study with 3-4 students so that you can discuss ideas of proofs and other things.

My question to you : What will you do if you reach to a place where you will be impossible to be stumped by other people ? You will enjoy some respect or points (as on MSE), but after certain period what will you do ? What is your motive to achieve this in other words ?