What I Learned Writing the Little 2021 Mathematics A-to-Z


I try, at the end of each of these A-to-Z sessions, to think about what I’ve learned from the experience. The challenge is reliably interesting, thanks to the kind readers who suggest topics. While I reserve the right to choose my own subject for any letter, I usually go for what of the suggestions sounds most interesting. That nudges me out of my comfortable, familiar thoughts and into topics I know less well. I would never have written about cohomologies if I waited to think I had something to say about them.

I didn’t have any deep experiences like that this time, although I did get a better handle on tangent spaces and why we like them. Most of what I did learn was about process, and about how to approach writing here.

For example, I started appealing for topics more letters ahead than I had previous projects. The goal was to let myself build a reserve, so that I would have a week or more to let an essay sit while I re-thought what I’d said. Early on, this worked well and I liked the results. It also made it easier to tie essays together; multiplication and addition could complement one another. This is something I could expand on.

And varying from the strict alphabetical order seems to have worked too. The advantage of doing every letter in order is that I’m pushed into some unpromising letters, like ‘Q’ or ‘Y’. It’s fantastic when I get a good essay out of that. But that’s harder work. This time around I did three topics starting with A, and three with T, and there’s so many more I could write.

The biggest and hardest thing I learned was related to how my plans went awry. How I lost the several-weeks lead time I started with, and how I had to put the project on hold for nearly three months.

2021 was a hard year, after another hard year, after a succession of hard years. Mostly, these were hard years because the world had been hard. Wearying, which is why I started out doing a mere 15 essays instead of the full 26. But not things that too directly hit my personal comfort. During the Little 2021 A-to-Z, though, the hard got intimate. Personal disasters hit starting in mid-August, and kept progressing — or dragging out — through to the new year. Just in time for the world-hardness of the first Omicron wave of the pandemic.

I have always thought of myself as a Sabbath-is-made-for-Man person. That is, schedules are ways to help you get done what you want or need; they’re not of value in themselves. Yet I do value them. I like their hold, and I thrive within them. Part of my surviving the pandemic, when all normal activities stopped, was the schedule of things I write here and on my humor blog. They offered a reason to do something particular. If I were not living up to this commitment, then what was I doing?

The answer is I would be not stressing myself past what I can do. I like these A-to-Z essays, and all the writing I do, or I wouldn’t do it. It’s nourishing and often exciting. But it is labor, and it is stress. Exercising a bit longer or a bit harder than one feels able to helps one build endurance and strength. But there are times one’s muscles are exhausted, or one’s joints are worked too much, and you must rest. Not just stick to the routine exercise, but take a break so that you can recover. I had not taken a serious break since starting this blog, and hadn’t realized I would need to. Over the course of this A-to-Z I learned I sometimes need to, and I should.

I need also to think of what I will do next. I’m not sure when I will feel confident that I can do a full A-to-Z, or even a truncated version. My hunch is I need to do more mathematical projects here that are fun and playful. This implies thinking of fun and playful projects, and thinking is the hard part again. But I understand, in a way I had not before, that I can let go.


The whole of the Little 2021 Mathematics A-to-Z sequence should be at this link. And then at this link should be all of the A-to-Z essays from all past years. Thank you.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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