I used to tell people I was a “failed mathematician”. I went to school for mathematics, and I liked the mathematics part but not so much the school part. When I got out of school I wasn't sure what I wanted to do with myself, but I was sure what I didn't want to do, and graduate school was near the top of that list. So I didn't go to graduate school, I didn't get a doctorate, and I didn't become a professional mathematician. Which as I think I've said before, is probably for the best, since I don't think I would have been that good at it — at best I think I would have been respectably second-rate.
Still I really love mathematics. I was sad when I told people that I was a failed mathematician.
But that all changed one day. I had read or heard the following claim:
Some people disagree with this formulation. Trying to track down the source, I found a number of articles purporting to explain the difference between “a writer” and “someone who writes”. As a published, successful writer, I say fuck those articles. If you write, and you call yourself a writer, you are a writer. Maybe not a professional writer. Maybe not a published writer. Maybe not even a talented writer. But a writer nevertheless, and your writing is as fully legitimate as anyone's.
One day I decided that was true of mathematics also. Who is a mathematician? A mathematician is anyone who does mathematics, and who calls themselves a mathematician. I certainly did do mathematics, seriously, persistently, and almost every day. All that remained was for me to start calling myself a mathematician.
I started at once. I am a mathematician. Not a professional mathematician, not a published mathematician, and not even a particularly talented mathematician. But a mathematician nevertheless, and not a “failed” one.
It is a more accurate description of the real state of things, and it feels good to recognize that.