Then my dissertation advisor locked me in a classroom. He was not happy. The proof was suppose to be simple, it was just a jump from one dimension to two. We needed it for an obvious, intuitive claim I was making. In mathy circles, however, obvious and intuitive doesn’t count for squat so we needed the proof. And it should have been easy.
A few weeks before, my advisor told me to make sure all my ducks were crossed and all our ‘i’s lined up by proving a simple thing that both of us agreed should be easy enough because, well, it was just an extension of a well known result, so I skipped home singing with the telephone line blue birds, paired and swaying, while a happyfaced sun bobbed along with me humming among fluffypuffy clouds in a unicorn-magic blue sky. But the proof would not come. I tried for a week. I worked on little else, twisting my brain this way and that, trying to lug veiled knowledge from the Platonic world of forms. It defeated me.
Broken and humble, I walked into my adviser’s office, eyes cast down, mumbling that I could not seem pull it together. He scowled and told me to keep trying, reminding me of his great confidence, and patting me on the back heartily and with ‘chin up ol’ boy’ expressions of encouragement, sent me back down the hall to my grad student cubicle (crucible?). I redoubled my efforts, filled my mind with positive energies, sang songs of courage and determination, worked late into the night filling up pages and pages of equations, took cloudy walks on the green-way trying to see if I could bend my mind in new ways. I reexamined the proofs used in the one-dimensional case, and tried to articulate where I was going astray. It was to no avail. I was a failure.
The next week, I returned to my adviser’s office shamefaced and embarrassed. This was a character flaw. A failure of personhood. He listened to me try to explain my shipwreck. He looked disappointed, which turned to impatience, which turned to frustration, which was expressed in a cold, “This is NOT a hard problem!” Whereupon, he took me by the arm and marched me, like an miscreant child to an empty classroom and threw me in and said, “Don’t come out until you’ve finished the proof.” My first thought was, “What if I have to go to the bathroom?” then I sighed and sat down at one of the enrowwed desks. Forsaken of hope. I said an empty faithless prayer and turned to the task. But my mind was locked into modes I had tried over and over the last two weeks. I kept hoping that some Rumpelstiltskinish figure would poof into the room to spin my straw scribblings into some hard math currency. The little mythical creature did not appear.
And so I sat for three hours (with one secret, and dangerous, guilt-ridden, trip to the bathroom) but the last hour was really spent picturing what my wife would say when I didn’t come home that night. Finally, my advisor peeked in. He was genuinely surprised. And vexed. But, like a kindly father figure disappointed in his errant child, he sat down and said, “Let’s see what you are doing.” I showed him my approaches, and he nodded genially, “Yes, very promising.” Then he said, “Look all you have to do is . . .” He tried something, “um . . . let’s see, if we just . . .um . . .” Then he was off to the races. I watched him go through the same motions I’d been trying. And ending up in the same places I did. “Um . . . I’m sure if we just . .” more writing. Pages of equations were now falling on the floor, expressions of frustration, “ . . . um . . . this is harder than I thought . . .” The minute hand crawled past the place marking an hour we’d sat together.
Self-satisfaction now is running through me like a narcotic as I watch him try to come at it from the bottom. Like I had. It doesn’t work, it always brakes down right there, right when you try to bring it together from the forward or backward direction. However, my advisor is no slouch and he once studied under a great Princeton biomathematician and is of similar genius. Suddenly he rockets into the starry realms of math that I had only dim hints existed. He abandons the entire the framework in which I am seeped (like someone raised in the ‘angle ABC’ methods of Euclidean geometry, suddenly watching someone switch to algebra to solve a problem). It was stunning. I watch breathlessly as he pulls off some wondrous, cleaver, brilliant moves; his hands are flying, his mechanical pencil dancing esoteric alchemy across the page, his eyes glazed like a zen mystic staring simultaneously at both the page and an ethereal world where truths are manifest only to the initiated; he is improvising like a Jazz musician. Yes, only the mixed metaphor of dance, zen masterizing, and Jazz can capture what he did. Banach spaces are pressed and twisted and wrung out in way that can only be called occult. He commands the Gods of Lebesgue integration to perform deeds that would have made a Riemann integral blush. Topological battles are fought on turf that can only be described as manifesting the quality Unteraliceimwunderlandheit–a place of such strangeness that Alice’s Wonderland would seem a tame and provincial country. Then like some kind of cosmological surgeon he stitches it all together. The proof is done.
He finishes with a satisfied harrumph. He looks over at me, his arms folded and says, “That was harder than I thought.” We both stared at what he had done. “I not only would not have thought of that, I could not have thought of that. Not in ten years.” I said in awe. He chuckled. “Oh, I think in three or four years you could have pulled it off.” He patted me on the back and walked out smiling. I had had enough stochastic process theory to follow, mostly, what he’d done, but it was a creative act I could never have duplicated.
Easy? He could not, as it were, write with my mechanical pencil until he had set down and wrestled with the problem himself. From the position of his office, this was something so easy that any graduate student should have been able to do it. I believed I could do it. Until I tried. But it was a non-trivial problem. Only, in the experience of his trying to do what he asked me to do, did the difficulty of the proof appear. A proof I could have never done. Not in a million years.