I found this part interesting:

"I asked him why he'd worked on it. He said he'd seen it as a nice puzzle. That at first he was pretty sure the Turing machine's behavior was simple enough that he could prove that it wasn't universal. But then, as he studied it, he realized that there were little bits of behavior that were more complicated. And it was with these that he managed to show universality."

Just another data point in favor of tinkering, I guess.