For some reason, I feel very sluggish and like having brain fog.
I feel stuck in my PhD, because for the past couple of years, all of my proposed proofs for theorems in my math papers have been either very elementary, or were just not precise enough i.e. I unintentionally oversimplified or overlooked something.
It's sad that either a proof idea sounds very creative but is somehow wrong, or sounds correct but is just not creative (and thus elementary at best and can't prove any more other difficult things).
I kind of feel like as if yesterday I was just a fresh undergraduate student and now I am in my 4th year of my PhD.
I don't know what kind of brain exercises could help me in this situation. I am not looking for "Ways to increase my IQ", but just for ways on how to get rid of this brain fog I have been feeling, not being able to find the mix between analytical thinking and creative problem solving.
It sounds weird but even just thinking about engaging with my brain in something makes my head hurt (I do have stress-induced migraines, confirmed by a neurologist), as if it was something so stressful and uncomfortable that I would avoid it and rather try to be the "smart lazy guy" - only thing is that it's not working out at all. Like even thinking about printing out a math paper and studying it for the whole day is enough to make me have a headache again.
In the end, I escape into watching Facebook Reels for the whole day and do the bare minimum required just to keep my advisor somewhat happy. When meeting other mathematicians my age at a conference, seminar, etc. I can't talk with them at all about mathematics, it's literally like watching the Big Bang Theory and seeing those guys talk in their own scientific language.
So my two more specific questions would be:
What activities engage the brain the most? Especially with regards to my main goals of improving analytical, precise thinking and creative problem solving?
How can I overcome this uncomfortable, stressful feeling - making me give a headache and escape into watching Facebook Reels all day long - accompanied by having to put in some effort in them?