I’ve decided to take a (permanent?) hiatus from writing this blog, and wanted to conclude with some reflections and analysis on the posts to date.
A look at the Table of Contents shows that there are 25 flavors and 7 seasons, and a few posts on background and analysis. I think that these posts capture the main recurring mathematical experiences that I’ve had as a graduate student and now a postdoc. In a strange way, the blog feels complete, not to say done. When I reflect on my day-to-day and month-to-month experience doing research math, I mostly find that I’m revisiting experiences, not undertaking new ones. Am I approaching a comprehensive list? I’m sure it can’t be so, and look forward to the unknown.
The process of writing the blog has, I think, accomplished the goals I set out with. Writing posts has forced me to be more self-reflective about how I do math. This self-reflection has helped me to tweak my process, to be more efficient, productive, and enjoyable. It has also brought meaning and depth to my academic research life. Writing posts has also helped me articulate the recurring aspects of my experience, and confirmed for me the stability and intersubjectivity of these experiences. Although no one else’s voice appears on this blog, in conversations and other mathematicians’ writings I’ve seen parallel experiences described. I think that other mathematicians would find a lot (of course not 100%!) to agree with in my posts.
If I were to do it all again, I would probably use the same procedure and the same questions for flavors and seasons. Except I’d change flavor question #6 to “what experience does it resolve to, after how much time?”, and maybe rephrase the questions as actual grammatical sentences.
Where to go from here?
This blog aimed to articulate recurring math research experiences. I left out quite a few singular experiences, and a careful description of these might also be interesting. For example, the night I submitted my first paper to a journal, then spent hours walking the streets in an intense rain and wind storm. Or when I found out my first paper got published. But maybe this becomes too subjective and less relevant.
This blog avoided discussing the experience of specific mathematical ideas (what does it feel like to think about a Bousfield lattice? what do you see in your mind? how?). Doing so could be interesting.
My next step, however, will be learning more about first-person methods for understanding experience. I’m obviously not the first one to try to carefully describe his or her lived experience, and lately I’ve been finding out about a body of research that establishes specific techniques for doing so, uses these techniques to examine certain experiences and draw conclusions, and analyzes the limitations and pitfalls of these techniques. I wrote about these first-person methods in a paper I wrote for the Journal of Humanistic Mathematics about contemplation in mathematics. So I’ve been reading, and will continue reading, these books and related material: On Becoming Aware, The View From Within, and Ten Years of Viewing From Within. With more theory under my belt, I’m excited to think about how I could integrate this sort of intentioned self-reflection into a classroom setting (as a kind of metacognition), to get students thinking about (and consequently improving) their learning process.