Wednesday, May 2, 2012
Juggling 2: How do you learn new math?
How do you start on problems that require learning the basics of another mathematical field? All I know how to do is read. I read the papers I'd like to understand, I follow back through the bibliographies, I try to get back to the basics in the field. Sometimes that is not so easy, as there is no basic introduction. Talking to people seems to be a very effective way to learn the basics of another area of mathematics, but this requires finding a person who knows what you want to know and who is willing and able to explain these things. I have had particular difficulty with this when I've seen some words that make me think that the ideas from another area might help me out but I'm unable to formulate a good question. "Tell me about how combinatorics might help me with my PDE problem" is awfully vague.
Collaborators are also phenomenally useful in this regard: they are usually people who like you and respect you at least a little bit, so you can ask questions without feeling terribly stupid. I have collaborators with complementary expertise and really enjoy learning from them.
Looking forward to summer -- I have an immense pile of reading I'd like to get to.............