I like the idea of math and art -- symmetry, fractals, perspective, frieze patterns -- but today after a month of absence I would rather touch on math as art. I said something wrong in my NSF proposal, I realized today on a walk, and it's stupid wrong rather than profound wrong. This is incredibly depressing to me. It's not depressing that I made a mistake -- I make lots of mistakes and don't worry too much. It's depressing that it's a stupid mistake that I would hope I would not make. I worry that I can't hold in my head the things that I know. Yes, I can't even remember what I know. I haven't made my knowledge a coherent web, and so I forget that this is also that and then I say that that is a wave and can't be a particle even though if I remembered it was also this I'd remember that in 1992 McGoucher proved a subtle theorem showing that this is a particle, because I myself wrote a paper about the particle nature just three years ago.
(Fine, I'll stop.)
Anyhow. I am afraid that I am not very good at my art, the art of mathematics, because I have some idea what is good and I know that I am not producing at that level.
What do cellists do when they listen to Yo-Yo Ma and find themselves wanting?
On good days I remember that I do this for fun, for joy, because I love playing with ideas and discovering new things (new to me, at least). On bad days I think I should find something I'm actually good at.
I call this post the artist's struggle because the only other people I hear this from are painters, poets, and musicians, people who struggle against poverty to keep doing what they love, even if they doubt that they are any good at it. In art it seems respectable to doubt your ability or talent. It's part of the path. In mathematics, I'm not sure. Plenty of well-respected people mention that they still don't think they're very smart, but we know the truth!! They are brilliant people unlike us. Evidence: stupid mistakes. The best part about math: they're provably stupid. In cello, the wrong note just floats away.
Whether or not I'm actually any good at this, I have a job lined up for the rest of the year. Guess I'll keep pretending for now.