Terry Tao on some desirable properties of mathematical notation
I found this post a shame.  (The post itself, not putting it here; I love seeing math posts on HN, and automatically upvote.  Bringing hackers and mathematicians together is highly worthwhile for both.)Usually Tao's posts are so insightful, and crystallise some idea so perfectly that it feels like I was just on the cusp of discovering it myself—a rare talent, and hard to cultivate since it goes against the ego.  In this case, though: I'm a professional mathematician, and as prone as anyone in my discipline to use mathematical language to describe not strictly mathematical things, but the pseudo-mathematisation here ("Notation^{-1}(C)", for example) seems more like wit than clarity.  Not that there's anything wrong with wit, but in this case it seems to me that it's at the expense of, rather than a pleasant addition to, the central point.I'd like to hear especially from anyone who isn't a professional mathematician:  did you feel that this post improved your understanding of the purpose and function of good notation?(EDIT:  I was scared about making this post, since there's rightfully a lot of respect and appreciation for Tao—and I hope it's clear that I concur on both counts—and I wasn't sure how my reticence on his post would go over; but I'm super glad I asked.  Thanks so much to everyone downthread; these are wonderful responses and I feel that it benefited me a lot to read them.)