After a while, my set of pictures started to look like a particular set of graphs that were listed in a book about Coxeter groups that was in my office, and I began to hope that it was this exact set of graphs. If it was, then that would fill in the hole in my proof, and my theorem would be finished. But I couldn’t check for sure until I got back into the university after Christmas — this was before you could just Google everything. I think the anticipation of having to wait to confirm my hunch made it even better when I got to the book and compared my handwritten set of diagrams with the ones in the book, and they were indeed a match.
What do you think about the question of whether math is created or discovered? Almost nobody would argue that any of the novelists you write about in your book “discovered” their novels. Is this a fundamental difference between math and literature or not?
It probably is, though there are still some resonances.
Doing mathematics feels like discovery. If we were inventing the mathematics, it surely wouldn’t be so hard to prove things! Sometimes we desperately want something to be true, and it isn’t. We can’t avoid the consequences of logic, I suppose.
It all feels like discovery when you are doing it. Some choices mirror what we experience in the real world, like the axioms of geometry we work with, which are chosen because that seems to be roughly what reality is like — though even there, there’s no such thing as a “point” or a “line” (because we can’t draw something that takes up no space, and a line in geometry has no breadth and extends infinitely far).
To some extent, there are parallels to this continuum in literature. Once you define the rules of a sonnet, you will be hard-pressed to write one whose first line ends with “orange” or “chimney.”
But I can’t resist sharing something J.R.R. Tolkien said about writing The Hobbit: “It all began when I was reading exam papers to earn a bit of extra money. … Well, one day I came to a blank page in an exam book and I scribbled on it. ‘In a hole in the ground there lived a hobbit.’ I knew no more about the creatures than that, and it was years before his story grew. I don’t know where the word came from.”
Hobbits — did he create them or discover them?
