To introduce myself: I'm an undergraduate mathematics student in Germany. Currently I'm studying in the second semester and until now I'm doing well, but I still got the feeling that my ability to develop proofs (or just solving complex issues in general) needs to be improved.
Let me explain myself: Sometimes, (especially) when it comes to proof tasks I'm being given, I feel like I dont know how to find my way through the proof, it rarely happens that I not even know where to start. Somehow I'm missing the feeling that my thoughts guide me to the correct answer, which I always used to have in school. This makes me feel a lack of "creativity" or in other words the ability to find my own path to reaching the solution.
If there is any advice you could give me, I would appreciate that.
Best Answer
I remember having a similar feeling in my first undergraduate year. I could comprehend the proofs I was taught, and could mimic them afterwards on very similar problems, but I felt I lacked the creativity to actually think of proofs myself. Two realizations I had helped me get through this stage:
Practice actually helps. The more you prove, the more tools are added to your inventory, even if this is not immediately apparent. In two years from now, you'll look back and may not even understand what you found difficult.
Each of these proof "tools" was developed by someone very smart, generally over long periods of time thinking about the problems at hand. If you managed to come up with all the tricks and techniques by yourself, without first seeing some similar examples online or in books, you would indeed be a genius.
In short, you shouldn't be feeling too bad about not "getting" proofs immediately - this does not mean you aren't creative, just that you have more to learn and that things that are presented as trivial actually took quite a while to get to. One could almost say that this is what university is for - to save you the time it would take to reinvent everything yourself.