> 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?
Yes
I skipped past the long list of properties and went straight for his long list of ways to write the inner product of two vectors and his illustrations of why you want to use different notation in different cases.
Here's a question for you, do you think Tao's primary mission is to be a "professional mathematician" or is he just enjoying the math, enjoying teaching, enjoying notation...?
> Here's a question for you, do you think Tao's primary mission is to be a "professional mathematician" or is he just enjoying the math, enjoying teaching, enjoying notation...?
I definitely think that he's earned the right to contribute to the mathematical community in whatever way he sees fit, and, especially if it benefits other people, which it clearly does, then my opinion of it shouldn't and doesn't matter a hill of beans. I just usually feel that he combines those missions—not that he has to, but that he does—and felt that he didn't here; but, again, that is, if at all, very much my problem and not at all his.
Yes
I skipped past the long list of properties and went straight for his long list of ways to write the inner product of two vectors and his illustrations of why you want to use different notation in different cases.
Here's a question for you, do you think Tao's primary mission is to be a "professional mathematician" or is he just enjoying the math, enjoying teaching, enjoying notation...?