Bahls: The more formally recognized genres would be like research articles or expository articles or reviews of one another's work. Sometimes you'll see technical reports, depending on what area you're working in. Statisticians will frequently write technical reports for folks for whom they're doing consulting or for government work.

But I think the day-to-day writing, to me, is much richer and often goes overlooked when you think about the finished product of a five- or six-page research article, I'll look back over the notes that I would have written to generate the work to end up with that article. And even if you only see five or six pages of polished writing, I look back over my notes and see 100 or 200 pages of just scribbles here and scribbles there, notes one day that I jotted down and thankfully put a date on so that I could keep track of what the order in which the ideas came to me.

And in just all of this mishmash of ideas is this very informal, low-stakes writing that's going on on a day-to-day basis might be the stereotypical description is the coffee shop napkin, you know, the computations you do on the back of the napkin to try to understand what's going on with your data or to understand what's going on with your proof. That often gets overlooked. But there's an enormous amount of writing of that kind.

And when I'm talking to students who are pursuing a math major, just kind of getting into math beyond, say, the level of calculus, I'm always, always exhorting them to write, to write, to write. Because as long as they're writing, the ideas are going to come out in their writing. And they can't just sit there and stare at the paper and expect that the solution is going to present itself.

They really have to try things out. And the best way to do that is just to write it out, to get it out on paper. And so that can't be-- the importance of that kind of writing can't be overstated.