It probably is, though there are still some resonances.<\/p>\n

Doing mathematics feels like discovery. If we were inventing the mathematics, it surely wouldn\u2019t be so hard to prove things! Sometimes we desperately want something to be true, and it isn\u2019t. We can\u2019t avoid the consequences of logic, I suppose.<\/p>\n

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 \u2014 though even there, there\u2019s no such thing as a \u201cpoint\u201d or a \u201cline\u201d (because we can\u2019t draw something that takes up no space, and a line in geometry has no breadth and extends infinitely far).<\/p>\n

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 \u201corange\u201d or \u201cchimney.\u201d<\/p>\n

But I can\u2019t resist sharing something J.R.R. Tolkien said about writing The Hobbit<\/em>: \u201cIt all began when I was reading exam papers to earn a bit of extra money. \u2026 Well, one day I came to a blank page in an exam book and I scribbled on it. \u2018In a hole in the ground there lived a hobbit.\u2019 I knew no more about the creatures than that, and it was years before his story grew. I don\u2019t know where the word came from.\u201d<\/p>\n

Hobbits \u2014 did he create them or discover them?<\/p>\n<\/div>\n

<\/br><\/br><\/br><\/p>\n