There’s something magical in that when you go to your advisor to tell you can’t do X except with Y; and he says “well, I think this is not an obvious disaster; run with X-plus-Y and see what happens.”
There are a lot of other advisor moments, too: all the moments when it becomes apparent that you have a penlight and he has a giant-ass halogen disco ball. All the moments when it is obvious that you are still a learner, and he is the master. (And maybe, one day, you will be the doctor? And in your case, it could be a “she” just as well as a “he”.) Your advisor is kind of like a third parent; it’s not trivial that one instance of tracking these relationships is called the Mathematics Genealogy Project.
There’s the dreadful moment when he offhandedly, and possibly jocularly, drops a word that after the year of head-walling you’ve done, you probably know and understand more about that particular theorem than anyone else alive. There’s the moment when you see you’re really at the edge of knowledge, and he’s about to throw you out so you can see what lies beyond.
There’s the moment he pulls a trick out of thin air, and fixes the one detail you had no idea how to deal with. Probably it’s a trick you should have known; but “trivial” is not a constant but highly time-dependant.
There’s the moment you see he hasn’t understood something, and it feels so good to step in to explain. (Because maybe you’re the bigger expert now, as regards this tiny subject, and this moment in time? Or maybe your handwriting just is really awful?)
There’s the moment you say “And next we—” and then you see the mistake, the horrible gap you totally forgot, and there’s that terrible three-second delay before he sees it. It’s not that he would be upset or angry, but that you want to be bright at him. You’re the penlight and he the halogen, but you want to show him you’ve changed out some of your dimbulbs. He’s radiant, and in his company you want to be the same, as good and a thousand times more.
There’s the moment you spend a double lungful explaining your approach, and he breathes out the two-word name for it — and if you’re lucky it’s “basically Hölder’s?” and not “Weird nonsense!” And then there is the thing when you’re explaining what you have done and in the middle of it you see what you’ve done is wrong and you have to offhandedly admit it and dance madly backwards trying to fix it as you talk and walk and write, chalkdust flying and the arrows becoming twistier, the letters sketchier, because you have all the details still in your head and you’ll show him how it goes… because for that moment you’re still the circus director, he the audience, and the proof may still be there, if you just reach and twist a bit.
There’s the feeling of being much smarter than you are, when he explains things to you, suggests and goads and outlines; and there’s the feeling of staring at an empty computer screen later and thinking, “It seemed so easy when he was talking about it. If only I’d taken more notes. Now was I supposed to see if this thing was bounded, or what?” When he is there, all is anchored by his understanding; when you are alone, it’s not only dark; the solid ground melts away, too. And then you run back and whine; back to the light, and then away carrying a little bit of it with you.
And though every single day you feel as dumb as the previous day, you’re pretty sure you’re feeling equally dumb about ever smarter things.
I guess what I’m trying to say is I don’t need no drugs: I meet my advisor at least once a week, and that’s a good enough altered state all by itself.