It was the third semester of grad complex analysis. I dread analysis to this day... but it was worse then. I didn't know my stuff. I hadn't done well the previous semesters; my homework scores were continuing to droop... no way that I could pass this final. I didn't have a clear idea of what I wanted out of my next action: to cry in my professor's office. He had some questions for me. Asked me how I'd gotten into grad school. Not in a mean way, just, we all have our own things that work. He gave some nice words of encouragement, and a kleenex, but he was right to send me back to my own toolshed.
My first real math class was undergraduate differential equations. The teacher was legendary; gave a speech on the first day saying it's normal to repeat the class and you can drop without penalty, even after the final. I bricked his first exam; didn't even smudge the back page with a sweaty fingerprint -- he tells me with a tsk, my handwriting is too sloppy: I should be deliberate in my thoughts, not rushed. So I did speed drills before subsequent exams. Later in life, I'd write sloppier answer keys for my own students.
But you can't speed drill for a graduate course in complex analysis -- proving an unfamiliar theorem is quite a bit different than applying a standard method for a familiar diff.eq problem with carefully-chosen coefficients.
The problem wasn't just believing in myself -- my prof boosted me over that fence. It was believing in abstractions hidden even from mathematical lore. Back to undergrad: I wrote a note sheet that night. I summarized every important theorem from the class into the most compact statement possible, along with a cliffnote about the proof. And then came the drills, copying the notesheet again and again, with as few peeks as possible.
The actual hard problem that I grappled with on the exam is memorable only for its beauty. The 24h transition from paralyzed fear, to justified confidence, was where the real work happened.