A remark on mathematical research

Ira Glass, of This American Life (http://www.thisamericanlife.org/), did an excellent four-part interview where he talked at length about writing news stories. They are here:

Ira Glass on Storytelling:
part 1 of 4 http://www.youtube.com/watch?v=loxJ3FtCJJA&feature=relmfu
part 2 of 4 http://www.youtube.com/watch?v=KW6x7lOIsPE&feature=fvwrel
part 3 of 4 http://www.youtube.com/watch?v=BI23U7U2aUY&feature=fvwrel
part 4 of 4 http://www.youtube.com/watch?v=baCJFAGEuJM&feature=relmfu

I thought a lot of what he said was based on general principles which applied to mathematical research as well. Here is perhaps what he would have said if he was talking about mathematics, sometimes with direct quotes from his interview:

There are two building blocks to a idea for a paper

  1. The problem or question. This is sometimes an issue in the intersection of two fields or a question of why some object of interest behaves the way you think it does, based on an example you know.
  2. The revelation. This might be a key example or technique that will hopefully reveal the answer to your question.

You can have a great question, but if they don’t turn out to have any useful techniques or examples to work with, your idea is uninteresting. Conversely you can have a significant revelation with a fantastically powerful method, but if the problem or examples themselves are uninteresting, again you’ve got a weak idea.

You have to set aside just as much time looking for good ideas as you do producing them. In other words, the work of thinking up a good idea to write about is as much work and time as writing it up.

Not enough gets said about the importance of abandoning crap. Most of your story ideas are going to be crap. That’s okay because the only way you can surface great ideas is by going through a lot of crappy ones. The only reason you want to be doing this is to make something memorable and special.

“The thing I’d like to say to you with all my heart is that most everybody I know who does interesting creative work went through a phase of years where with their good taste, they could tell what they were doing wasn’t as good as they wanted it to be … it didn’t have that special thing they wanted it to have … Everybody goes through that phase … and the most important thing you can do is do a lot of work.”

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s