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Re:Boiling lead and black art: a history of mathematical typ... by svat on Sunday October 15, 2017 @11:36AM (#15477562)
Wouldn't that be backwards? The purpose of notation is to aid human thought and communication. Technology should adapt to whatever notation would be most useful to mathematicians, rather than mathematicians adapting their notation for the sake of technology (like “more easily typesettable”).

The blackboard-bold fonts are an interesting example of this, with computer typefaces being created for what mathematicians use in the real world. (Though Knuth and Serre and some other mathematicians don't approve of them in typesetting.) Besides, typesetting is a small part of the usage of notation; most of it is written in private by mathematicians for themselves or collaborators, in the classroom for students, in talks for each other, etc. (Typeset papers are a low-bandwidth communication medium, though good for broadcast and archival.) While it may make sense to optimize the ease of creation of typeset mathematics (and that is what Knuth etc. have done to some extent), changing the notation (for this reason) is not a sensible place to do that.

(Some related links: https://micromath.wordpress.com/2010/09/24/psychophysiology-... http://sites.math.rutgers.edu/~zeilberg/Opinion60.html http://okasaki.blogspot.com/2008/01/why-i-dont-use-powerpoin... http://sites.math.rutgers.edu/~zeilberg/Opinion78.html Section 3 of https://arxiv.org/abs/math/9404236)

Re:Boiling lead and black art: a history of mathematical typ... by canjobear on Sunday October 15, 2017 @11:48AM (#15477619)
The cryptic nature of math notation is a major hindrance for people learning and using it: for detailed arguments along these lines see [1].

Maybe if math notation were forced to be easily typesettable, it would be simpler or more programming-language-like.

[1] https://mitpress.mit.edu/sites/default/files/titles/content/...

Re:Boiling lead and black art: a history of mathematical typ... by svat on Sunday October 15, 2017 @01:30PM (#15478076)
My point was that the notation should be optimized for the people using it, not for the technology used to typeset it. If the notation is suboptimal for the people then it can definitely be changed, but that's a different reason.

Note that some of these notational improvements may actually make it harder to typeset. For example, the second part of Knuth's paper "Two Notes on Notation" (https://arxiv.org/abs/math/9205211) introduced improved notation for the Stirling numbers "of the first kind" and "second kind", replacing easier-to-typeset but less informative notation like S(n,k). This notation has gained a good degree of acceptance, the paper won a writing award (https://www.maa.org/programs/maa-awards/writing-awards/paul-...), and another paper citing it calls this “The best thing that has happened to the Stirling numbers during their 400 years of chequered history” (https://www.jstor.org/stable/2974533?seq=1). (See also a talk of his on Notation https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4... for which someone has taken notes: https://crypto.stanford.edu/pbc/notes/misc/notation.html)

I think there are valid questions to be raised on which people to optimize for: whether the students encountering the notation for the first time, or the people who use it every day for years. In either case (to make my point again) it's a question about people, and not about the technology — a programming-like notation isn't better unless that's how the people who use it think (or want to think).

Re:Boiling lead and black art: a history of mathematical typ... by safisher on Sunday October 15, 2017 @12:37PM (#15477864)