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At 12.04 +0200 2001-05-22, Hans Aberg wrote:
>At 23:20 +0200 2001/05/21, Lars Hellström wrote:
>>>Could you define the _problem_ you are trying to solve?
>>
>>...On one side, the problem is that in LaTeX today, I'm not
>>expected to write what I mean in math, I'm expected to specify the visual
>>expression for what I mean. This goes very much against the general trend
>>in the development of LaTeX, which is that you should say what you mean and
>>leave to the style (documentclass, packages used, preamble declarations,
>>etc.) to sort out what is the visual expression for this.
>
>There is nothing wrong with this objective in itself, but the complication
>is the diverse use of mathematics and how mathematicians write it.

The conceivable limitations this would impose (and you still haven't
produced a single example of a published paper in which there would have
been any limitation at all!) are negligible in comparison to the
limitations posed by the blackboard as the primary medium for new
mathematical notation and the fine motor skills of the average
mathematician. If you don't believe this, you can try the following
experiment:

1. On a blackboard, using a piece of chalk, write down the calculations
showing Jacobi's identity
$$[[\phi,\emptyset],\varnothing] + [[\emptyset,\varnothing],\phi] + [[\varnothing,\phi],\emptyset] = 0$$
where $[a,b]:=ab-ba$ is the commutator, the underlying ring is associative
but not commutative, and using precisely those glyphs from Computer Modern
to denote your variables (you've claimed yourself that they can be used to
denote different quantities).

2. Convince another mathematician that it is possible to see which symbol
is which without relying on the structure of the calculations.

I doubt you'll make it. I know I wouldn't.

Lars Hellström