Doing high level thing great but forgetting simple things I'm a mathematics PhD student and I have a question.
I am writing my thesis, and I'm looking for a postdoc too. I would like to do research long-term, but I am not sure that I will be successful as a researcher because of the following problem.

I am very good in the research that I am doing. Everyone confirms that I am very good in what I am working on. But, I have a big problem that I can not solve simple questions. Let me explain in further details, some month ago, I wanted to use the fact that supremum attains for every upper semicontinuous function on compact space. My supervisor asked me to prove it in front of him, but I couldn't do it. These happens a lot to me. My supervisor said he did not know how to possible someone do high-level research, but he couldn't prove simple things either. I am suffering because I think everyone can prove simple things, but they can not do high-level research. Does someone have any ideas or advice for me? I want to improve this issue, because I have a final exam for my PhD. I am so scared that they maybe ask some basic questions that I do not know.
Sounds completely normal for PhD level work. 

Many people doing PhD:s are like this. Some people who are envious or feel threatened of your high level abilities may try to shame you or make you unconfident with your lack of low level skills. There really is only one advice to give for this...

Trust in yourself and don't let it discourage you.