I have been having a mild depression in the past few days. Mostly because I felt a bit lost: I was not sure what exactly that I should be doing or whether I have been working hard enough. And Math has begun to feel more like work and less like fun.

Somehow it all got better today.

First I got a burst of energy in me to work on the Yang-Mills problems again. And then later in the day I decided to volunteer to talk about Moser iteration for Alice's class on elliptic PDEs (it is about time I learned it better). But the real life-shot came at tea time.

Aaron and I went to grab some tea. We turned and saw Sucharit, Arik, and Margaret there. We walked nearer and I saw Sucharit had in his hands a copy of a table of knots. Apparently Margaret is preparing to talk about the Jones polynomial etc. in an upcoming seminar. Knot theory stuff. So she was learning to draw knots "quickly and cleanly". I said that it would be most impressive to draw the unknot in a complicated fashion quickly and cleanly, and Sucharit said that while he doesn't remember any good complicated unknots, he does know a few good unlinks. So he draw one. Starting with the Turk's three braid five head knot and making a symmetric cut, one gets this complicated looking mess, that is, according to Sucharit, "obviously an unlink". (It is dangerous when Mathematicians start using the word obviously.) And he says it is easy to prove it too. So I asked whether the definition of "easy" was "drawing it out using Reidemeister moves", and his response was "yes and no".

Sucharit turned around and went toward a hatbox. Apparently he had gotten permission from John Conway to use Conway's personal collection of rubber ropes. (Conway also studies a bit of knot theory, and his approach to algebra and such are often, let's say, hands-on.) He handed the ropes to Margaret, and she started reconstructing the link diagram in neon green and pink.

It was like magic. Or Childhood.

For the next half hour or so we were just there playing with physical and mathematical knots. And that was fun. It reminded me why I like Fine Hall so much.

I think I am back.