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I am currently writing my master’s thesis. It is like a survey and contains lots of theorems with or without proofs. Everything that I am writing, I studied and proved before. However, I see that I forgot some proofs or even definitions and cannot do it without looking at the books. So, I am studying those again, try to prove them my own, and then write them after I understand them – but I feel lost.
What should I do and what have you done when you face a problem like this?
This is not a genuine problem. Everyone forgets things. A true scholar may nor may not be blessed with an exceptional memory, but the operational issue is about having personal resources that accommodate one's limitations, and sufficiently point to the relevant resources. So: self-management.
It is true that having a good memory, or an exceptionally-good memory, is generally an advantage in knowledge-based enterprises, obviously, but things are more complicated than memory-per-se.
And, in any case, being able to reproduce fluently all the basic things on a moment's notice is irrelevant. True, a certain fraction of more-senior people happen to have the sort of memory that allows them to reproduce certain things on-the-spot, but this is really not relevant to professional practice.
Yes, the most conflict-laden point is that faculty teaching graduate-level courses, and who've had the misfortune to have either a deterioration of memory, or have always had some memory problems, have difficulties with teaching. Not that they don't "know math", but that the details are not easily present in their minds. The other point is that this does not mean that their critical/critique-ing faculties have deteriorated. An awkward state...
But/and, after all that "too much information", the point is that no one (no professional mathematician) is required to be able to reproduce everything upon command at every possible moment.
(The whole "final exam" or "contest" concept of mathematics greatly and sadly corrupts our collective concept of that the thing is.)
Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it.
-- quote by Samuel Johnson.
So don't worry about it. I know (roughly) the statement of the Fundamental Theorem of Calculus, but being able to prove it from scratch is another matter. But I know where to look.
