I enjoy doing research in recreational mathematics. The biggest problem is that the probability that something I’ve done has already been done before is very high. This is partially because of the nature of this area of research. Trying to find new questions that are not buried deep in the abstract means someone else could have stumbled upon the same question. In addition, I like going in different directions: geometry, number theory, probability, combinatorics, and so on. That means I am not an expert in any of the areas. This too increases my probability of doing something that has already been done before.
This is quite unpleasant: to discover that I reinvented the wheel. And I keep reinvented different wheels on a regular basis. When I complain, my mathematician friends give me the same advice over and over:
Find your own niche!
I’ve been trying to understand what they mean, and finally I got it:
Do something no one else is interested in using methods no one else can understand.
Finding a topic that is not interesting almost guarantees that other people didn’t do it before. Developing new complicated methods helps limit the number of followers and prevents the niche from becoming crowded.
Now I know why I see so many boring math papers I can’t understand.
To hell with my own niche!Share: