: Well, what follows in your posting
: seems to me precisely an attempt to define a formal language for
: (ie to parse) mathematics.

No.  It is an attempt to enable authors, if they wish, to include
enough information so that a sgml or xml processor can set the math
environments into MathML.

: I don't know what "vertex" means,

Under a formal typing system of this kind, it need only have meaning
relative to the article context.

: but there are many meanings that A B could have,
: eg A(B) [the value of the function A at B]
: or (A)B [the value of the function B at A]
: or the composition of two functions B and A
: or the composition of A and B,
: etc etc

: Are you going to require mathematicians to write f(x) [ie with brackets]?
: Can they write (x)f if they prefer?

Perhaps you neglected to the follow the reference to
http://www.albany.edu/~hammond/gellmu/notation .

: It seems to me much easier to design a browser that understands LaTeX,
: or DVI, or PDF, than to persuade mathematicians to write in MathML.
: Surely the computer should be the slave, not the master.

One of my objectives here is to make it possible for a two-tiered
system of publication to emerge in which one tier -- beautifully
typeset documents -- is sold (as now by journal publishers) and the
other tier is available free on the web.

If the documents in the second tier are well constructed it should
be easily possible to do notation based searches in a sound way and
to enable, consistent with the plans of the MathML folk, computer
algebra systems to digest clipped segments.

                                   -- Bill