One of the biggest challenges for many young mathematicians is creating work they feel worthy of sharing with the world. This feeling transcends well beyond the mathematical community and is quite prevalent in many fields. How does one deal with this, and what are the true challenges that one faces?
One of my favorite pieces on this subject is by the well-known host of NPR’s “This American Life”, Ira Glass. You can find his thoughts here:
But I want to paraphrase and focus on some key points that he mentions:
You have good taste, but feel like you create work that doesn’t taste so good: So many of us at the early stages of our careers feel like our contributions are relatively minor. However, we are missing the bigger picture. This is our time to learn how to contribute novel mathematics to the community. Our impressions of our results are myopic, and we need to reflect upon the fact that our contributions are meaningful despite the fact that we are new to crafting our technique. Moreover, through continually sharing our mathematical discoveries, we become much more skilled at developing our own mathematical strengths, and consequently strengthen our contributions.
Just do it! Writing can only be done by writing. It is commonplace for young mathematicians to discover interesting mathematics they want to share with the world, but feeling “stuck” when looking at a .tex file that has a title, a list of authors, and a few definitions. Like a famous company we all know promotes, “Just Do It!”. A quote of Jodi Picoult (fiction writer) that one of my collaborators shared with me is perfect for this:
“You might not write well every day, but you can always edit a bad page. You can’t edit a blank page.”
Writing is a daily habit. It is surprising how much a little bit of regular writing can add up. In my first semester as an Assistant Professor, I wrote .pdf files for each lecture of a Discrete Mathematics class I taught. Each lecture only amounted to 1-2 pages of notes. What I was shocked to see was the culmination of this work at the end of the semester. What seemed to be relatively minimal regular writing ended up amassing 50-60 pages of notes. It felt like I had a draft of a small book without really thinking about it! Regular writing has surprising consequences.
Remember why we write! I close with what I feel is the most important point of all. Why do we write? It is our way of sharing our thoughts with a community, that is imprinted for all time. We have strong voices with interesting things to say. It is extremely important for the mathematical community to hear our voices, read our thoughts, and view our perspectives. It is through our writing that we share our world with everyone else.