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When I study into algebraic topology, I found some theorem proved quite algebraically and hard to understand in geometry. Should I work hard to find the geometric intuition for all this theorem? And generally speaking, should I set up geometric intuition for all concepts in algebra or other mathematical fields? Or there is something called algebraic intuition which I should foster?

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    $\begingroup$ Some people have highly visual imaginations. Others have very weak visualization capabilities. So you should find what works for you. This may even determine which branches of mathematics are easier and which are harder for you. $\endgroup$ – GEdgar Jul 12 at 13:55

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