First year Math PhD student; My problem solving skill has been completely atrophied and continues to decline
I think it’s not a coincidence that the timing of this decline matches up with the pandemic.  A lot of people are really struggling right now, I feel like I can’t do math as well as I could a year ago.  In this post it sounds like you’re being really hard on yourself.  Counterintuitively I think a big part of what might help is being more compassionate with yourself.  It’s ok that you’re struggling, and it’s ok to just not solve some of the problems.  Research math mostly involves failing to solve problems most of the time, so it’s really ok to just not answer some of the questions and get used to that feeling and be kind to yourself because they’re hard problems.  You can always come back to those problems next year.  I guess what I’m saying is that you also want to develop the skill of giving up on a problems as well as the skill of solving them.  The former is perhaps more valuable in research than the latter.