Mathematical Notation: Past and Future
[Mathematical Notation: Past and Future By Stephen Wolfram. At http://www.stephenwolfram.com/publications/mathematical-notation-past-future/ , accessed on 2015-09-30 ]
A great article on math notation, This article should teach those coding sophomorons and idiotic authors in the computer language design community, who harbor the notion that syntax is not really important, picked up by all the elite i-reddit and twittering and “Hacker News” am-hip dunces.
Personally, particular interesting info i've learned is that, for all my trouble in the past decade expressing problems of traditional math notation, i learned from his article this single-phrase summary: “traditional math notation lacks a grammar”.
The article is somewhat disappointing though. I was expecting he'd go into some details about the science of math notations, or, as he put it aptly: “linguistics of math notations”. However, he didn't touch the subject, except saying that it haven't been studied.
There are some errors in his article. In this article:
[[The Reform of Mathematical Notation] Computation, Mathematical Notation, and Linguistics By Stephen Wolfram. At http://blog.wolfram.com/data/uploads/2015/02/MathematicalNotation-SW.pdf , accessed on 2015-09-30 ]
He mentioned the Plimpton 322 tablet. It is widely taught in math history books, that this table is pythagorean triples. However, in recent academic publications (2002), it is suggested that this is not pythagorean triples, but rather: “a list of regular reciprocal pairs” as teacher's solutions to exercises for students. See [ Plimpton 322 ] [ https://en.wikipedia.org/wiki/Plimpton_322 ]. (Later on i realized, that the news about Plimpton 322 is discovered in 2002, which is 2 years after Stephen's talk. So, it's not really a error on Stephen's part.)