The Pigeonhole Principle

By Melanie Laffin

We have all heard the analogy of how we, as humans, are a fraction of a speck of dust with regard to the vastness of the universe. If we ceased to exist, the universe would really not change. Even if our solar system ceased to exist, it would be no loss to the universe. I often feel this way when working in mathematics — the problems I work on are a tiny speck of dust in the galaxy of mathematics, and even if my subfield ceased to exist, the universe of mathematics would continue to go on existing. At the beginning of my graduate career (or as I like to call it, my apprenticeship) I had the realization that mathematics does not need Melanie Laffin to continue functioning.

Despite how demotivational the above thoughts are, I have absolutely no desire to be anything other than a mathematician. In particular, I love working on my tiny subfield of a subfield of mathematics (namely, design/graph theory in combinatorics).  This was reinforced by going to my first international conference (as in, a conference in a far away country). I had the opportunity to meet many of the superstars in design/graph theory, who fed my enthusiasm and motivated me to continue my summer research projects. It was *awesome*.

While I enjoy living on my tiny area of my planet that is a speck of dust in the universe, it does not mean I do not have a telescope to view other parts of the galaxy. Much like humans have been rather unsuccessful in many of their outer space endeavors, I feel that I am often incompatible in one or more ways with other areas of mathematics (mainly, my understanding is not as immediate or fluid and I am lazy). However, I grow as a mathematician, I gain anxiety that I am pigeonholing myself into a tiny subset of the problems of mathematics. I do not pretend to be a savant, but I am slowly trying to make more of an effort to reach out to other areas of mathematics. In other words, I am trying to fund my inner mathematical NASA.

Does anyone else feel that they are being affected by the “pigeonhole principle?” How do you avoid having this problem (if it is a problem at all)? Any advice in trying to reach out to other fields?

Looking forward to reading the comments.

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