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Re: How to write a "proper" math document
*To*: mathgroup at smc.vnet.net
*Subject*: [mg120123] Re: How to write a "proper" math document
*From*: AES <siegman at stanford.edu>
*Date*: Sat, 9 Jul 2011 07:31:00 -0400 (EDT)
*References*: <201107041044.GAA02461@smc.vnet.net> <iuukk8$epi$1@smc.vnet.net> <15944200.6757.1309943765495.JavaMail.root@m06> <iv45b8$es8$1@smc.vnet.net> <iv6gqo$s5p$1@smc.vnet.net>
In article <iv6gqo$s5p$1 at smc.vnet.net>,
Richard Fateman <fateman at cs.berkeley.edu> wrote:
> I find it far preferable to take stuff out of a computer algebra system
> as TeX and paste it into a static document. This also provides an
> opportunity to fix the broken displays. E.g. we really don't expect a
> display of f=ma to come out f=am. Or E=mc^2 to come out e=c^2m
> (note also that E=2.718... not energy). Mathematica thinks it knows
> better than Einstein and Newton.
This is an absolutely valid and substantial observation in my opinion as
well.
The structuring of mathematical expressions -- that is, the choice of
symbols or notation, and the organizing and grouping and ordering of
terms within an expression -- is a vitally important feature in reading,
grasping, recognizing, understanding, and internalizing what they are
saying, and what are their connections to other expressions and
concepts.
There is no set of rules for doing this -- only a large body of
informally accepted conventions that have evolved over time, but that
are very widely used. (Anyone who wrote a treatise on e-m theory and
used E for the magnetic field and H for the E field would be a fool;
even writing the Poynting vector as H cross E with the normal meanings
of those symbols would be unnecessarily stupid.)
I appreciate why Mathematica does -- even has to do -- what it does in
structuring mathematical expressions in its internal operations. But
it's very hard work to convert between that and readable mathematical
expressions.
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