I remember when I was working on my Master's Thesis 7 years ago, I had to find a closed form for a pretty ugly integral. It involved integration by parts, but there was also a parameter (n) whose value varied from 2 to infinity. I worked on the specific cases, but only got so far (the case for n = 4 took a couple pages). I didn't think I was ever going to figure it out.
Then, after some research, and the right tricks, I got it. I remember vividly standing in the grad office in front of a portable blackboard, staring at this god-awful statement involving factorials, exponentials, summations and even a gamma function. I also remember skipping down the hallway to show my advisor, who confirmed that it was right.
A secondary success came later when I applied the math to C++ programs (we were creating various statistical distributions from Uniform). I remember sitting in the computer lab (just down the hall from the grad office) with my advisor as he checked the accuracy of my programs. When the statistics program plotted 1000 data values and the pretty little black dots fell within the parameters, my normally stoic advisor looked at me and smiled.
Now I'm in a PhD program after taking many years off. The WoW moments come few and far between lately, and with less fanfare when they do, but it's always nice when 5 PhD students are working for hours on one problem (or even one step of one problem) and I'm the one who finally cracks it. Makes me feel like my choice to go back to school wasn't a bad one.
Hopefully I feel the same way after my comps in January and August.