To summarize, this math fonts discussion seems to follow several lines:

1. Discussions about glyphs, old and new, and how to classify them, and
bring them to proper use.

2. Creating a new math fonts encoding for the LaTeX3 project, and
otherwise, for the purpose of enabling new mathfonts packages to be
developed.

3. Discussions about math fonts packages, and which of them should be a
part of the LaTeX3 distribution, and which should be independent packages.

  These topics clearly interact in an intricate manner.

  Frank Mittelbach says something to the effect that 1 does not really fit
into the objectives of the LaTeX3 project, and if 2 should be changed, it
is rather to pick something out, rather than adding, because of the
requirements of 100% upwards compatibility, and some other technical
concerns.

  So it seems me that 1, which is very laudable that people take up the
effort to work with, could continue the discussion, as suggested by J%org
Knappen, Mainz <[log in to unmask], on the group
[log in to unmask], and they can report back their findings
to the LaTeX3 group.
  One remark I have here, is that I think it is going to be hard to get
prescriptive standardizations of symbols to be accepted in the math
community, but the symbols created thus might get a good use anyhow. Also,
using a symbol, over a name has the advantage of producing very compact
formulas, but has the disadvantage that the meaning of the symbol has to be
remembered.

  Concerning 3, I personally feel that the combined LaTeX2e and AMS-fonts
are a little too restricted for conveniently writing math manuscripts,
especially when these are interdisciplinary. It would be good to settle for
some reasonable, well structured, extension of the current packages. Other,
more special packages, could then be developed as independent packages.

  I will indicate two such possible extensions:

  Frank Mittlebach writes:

>we should get of the next hill and that is:
>
>  take the euler math fonts and implement them as well

  The discussions revealed that both the AMS-fonts Euler script and TeX
calligraphic are a little too restricted for actual math use, as they do
not have lower case letters, and do not come in bold/leaning/bold-leaning
shapes, and in addition, these are not sufficiently "scripty" for many
purposes. (I use "leaning" as a gerneric for slanted or italic shapes).

  So I am inclined to believe that the best way to handle this, is leaving
the Euler script and the TeX calligraphic, for upwards compatibility,
whereas designing two completely new, complete series, one less scripty,
and one more scripty, having both upper-case letters, and lower-case
letters, also coming in the bold/leaning/bold-leaning shapes.

  I have also noted that it would be good if the typewriter style would
come (officially) in the bold/leaning/bold-leaning shapes.

  The "black-board bold", or outline, should probaly also be extended to
include lower case letters.

  Another such package is indeed an arrows packages, which would implement
extendible arrows, so that one can independently choose head, tail and body
of the arrows; perhaps the ideas of Matthias Clasen
<[log in to unmask]> could come into play here.

  In addition, for the purpose of the LaTeX3 project, I think one should
consider some limited symbols extension, in as much as it fits into the
classification patterns of the new math fonts selection scheme.

  Hans Aberg