18
Mar
my kingdom for a screwdriver
I don’t like hearing mathematicians talk about how inelegant or uninteresting a particular problem is. If a problem has an inelegant solution, that says nothing about the solution, but everything about the code that’s used to solve it. Our symbolic mathematical code (and by extension, all our codes) crumbles around the edges. It is out on the edges of a code’s utility to make sense of a problem that the solution becomes inelegant.
I can solve driving a screw with a hammer. The method is inelegant, but the problem isn’t. Using a screwdriver would be an elegant way to solve the problem. When a mathematician talks about inelegant solutions, he’s not talking about the problem (even if he thinks he is); he’s talking about the way he went about solving it. It’s not true that the problem is uninteresting, it’s just distasteful to tackle a problem that your tool (symbolic mathematics) can’t handle adequately. So there are problems out there waiting for elegant solutions, waiting for elegant tools; waiting for their screwdrivers to be invented.
A lot of solutions were inelegant until the appropriate tool was invented. For example, problems needing calculus to adequately describe or solve them were inelegantly solved (or not solved at all) until calculus was invented.
We as people are not done creating codes that solve intractable problems elegantly. I hope I’m here to see it the next time it happens.
