Nice presentation. I would probably have written it as an additive group (and then shown that the two strand braid was isomorphic with ℤ) as a further bidirectional intuition anchor (both "look, this new thing relates to something you are familiar with" and "this thing you are familiar with generalizes in unexpected ways").

Definitely liked the exploration of how theorems arise from speculation, and don't spring fully formed straight from Zeus's forehead.

this is pretty interesting but i don't think i can justify dropping everything to study it. but it did remind me of an adjacent "field", that guy who explores all the ways to lace shoes

(i think this is the one, but whereas old search engines would find it right away, now the results are full of "i made this" or me-too spam)

https://www.fieggen.com/shoelace/lacingmethods.htm

Very nicely explained. I find the mathematics of weaving, knitting, braiding very dopamine squirt inducing.

It seems this interest is shared by many here on HN because there have been many threads on them. @dang had once compiled a list.

Let me repost one of mine where Richeson explores Maypole dancing through the lens of Braids.

https://news.ycombinator.com/item?id=44225324

Im bad at mathematics, but this looks great. Gonna use it in my app to make 'braidy' connections :) thank you very much!