This conversation form has been seared into my brain:
"Hi A.J.! What have you been doing this break?"
"Reading! So much reading. It's been so fun."
"Ooh, what have you been reading?"
*silence*
"Ummmmm . . . well there's this book . . . that, um . . . talks about, uh. . . ."
Stumbling through tangled thoughts was frequent enough to convince me that I had to do something to not blank on subjects that had seemed so fulfilling and understandable when reading them. This happened especially when people asked about math: I had felt that I had understood something until my classmate's confusion or friend's interest prompted me to explain it—and begin a journey through um's and uh's.
During spring quarter, I delightfully discovered a temporary solution. One of my professors from the previous quarter agreed to mentor me in a reading course, and part of the contract was to present on the mathematics that I read each week. To keep myself accountable for readings—and help ease my nerves—I asked a few of my classmates if they would be interested in hearing a preliminary version the day before. Graciously they agreed. The mental pressure of preparing to present and answer their questions did not let me just memorize the theorems; it forced me to question whether I knew the material myself: not just the definition of a knot but why we consider only closed curves as knots; not just the definition of the continued fraction associated with a rational knot but the helpfulness of introducing this new representation for these knots. I had to understand the why for each of concepts. Heretofore my classmates' rationale for continuing to explain math concepts to me seemed just like an excuse to be kind, but now I also used it: it helped them understand it too.
However, now it is summer break, and presenting is neither as convenient nor as fun. But since my goal was to organize my thoughts, one day, John Adams' strategy unburied itself from my mind:
A video essay by Odysseas that I providentially came across during that quarter formed a plan. Here was a simple argument: Writing mini-essays helps one exposit ideas to others. Practice helps one do something better. Therefore, writing mini-essays frequently will help me exposit ideas to others.
So during this summer break, having more time than during the quarter, I shall be writing more. Some of my thoughts will be submitted here written for the world to see. What I post will be determined by first whether it might be helpful for others to read and second whether forcing myself to explain it might be helpful.