Re: A recent Wolfram discussion on mathematical syntax

I'm not sure if you knew this or not, but I worked for Wolfram Research in
the previous century (that makes me feel old!). In particular, I was a big
part of the changes to the notebook frontend that Stephen Wolfram mentioned
as "introduced in version 3". The StandardForm/TraditionalForm ideas were
largely mine. We even had (probably still there) a WYSIWYG way where you
could type in a notation and associate it with any Mathematica function so
that you could enter an expression using that notation and if the answer
came back that used that Mathematica function, it would display with the
notation you picked. I thought it was really neat, but I don't think it was
used much.

Also, the idea of a mostly universal precedence ordering (such as '<'
always binding tighter than '+') was something I presented to Stephen. He
was very skeptical, but after looking through a lot of books, he ended up
agreeing it was true. There are of course some exceptions ('|' being one of
them and obscure symbols that are rarely used being others since they don't
have well-established usages). However, having a notation where a
relational operator binds more tightly than an arithmetic one is just
begging for confusion and will almost always get rejected by others when
discussing the same topic, and hence die away.

Finally, I'd be a little cautious about the 7k number. I don't think
Stephen Wolfram was referring specifically to notation. I think he was more
likely referring to the number of functions in Mathematica, many of which
do have notations associated with them, but some of which (e.g, programming
constructs) don't (but of course could).

    Neil


On Sun, Nov 7, 2021 at 7:56 AM Deyan Ginev <deyan.ginev@gmail.com> wrote:

> Hi everyone,
>
> Stephen Wolfram has released a public Q&A a couple of days ago
> (November 3, 2021).
> A part of it is dedicated to elaborating the Wolfram Language approach
> to the presentation and content aspects of mathematical syntax.
> For those with 90 free minutes, the full video covers various aspects
> of the history of mathematics, standardization, typesetting, as well
> as publication culture. As filtered through Wolfram's own
> experience/perspective/vision.
>
> I will share timed links to excerpts I found relevant to our current
> group work here.
>
> 1. His brief position statement on MathML and participating in the W3C
> Math group:
> https://youtu.be/-dxcmvl8294?t=1801
>
> 2. Mini discussion on presentation vs content in math syntax:
> https://youtu.be/-dxcmvl8294?t=2977
>
> The examples he gives (differential-d and sin^-1) are ones our group
> has discussed on multiple occasions. The Wolfram Language appears to
> have a large set of these primitives which Stephen refers to as
> "standard form" input.  There is a second, freer, "traditional form"
> of input, which they can not guarantee parsing into computable
> Mathematica expressions, but can still typeset well.
>
> He hits on some valid distinctions between math grammar and math
> meaning, where grammatical consistency (e.g. operator precedence and
> operator fixity - prefix, infix, postfix, fenced...) is the main
> aspect one requires to successfully typeset an expression, without
> ever knowing the specific mathematical concept intended by an author.
> In a way, we have a kind of a technical consensus with the way we've
> approached our "intent" attribute discussions.
>
> 3. Some helpful ballpack numbers were provided, on the distinct
> mathematical primitives already supported by Wolfram Language:
> https://youtu.be/-dxcmvl8294?t=4825
>
> 7,000 primitive constructs, with an estimated 1,500 still needed to
> fully "cover all of standard current pure mathematics". This may be a
> helpful number to approximate a lower bound for content symbols used
> in CAS practice today. Some of these are likely to also require our
> "intent" values, when they have relevance for AT.
>
> ---
>
> An obvious sentiment is: "it would have been great to have a Wolfram
> Alpha representative participating in our group", but clearly the
> history here makes that difficult.
>
> Nevertheless, I am encouraged to have a very recent statement on the
> Wolfram perspective on mathematical expressions, as their products are
> clearly major potential adopters of any new MathML revisions.
>
> Greetings,
> Deyan
>
>