Intellectual Junkyards

Summary

Despite some preliminary support for structured representation of high-level mathematical idioms via , MathML is not intended to be an authoring language: it is a target language for other tools. Moreover, the content dictionaries (collections of basic elements) of Content MathML are chosen to pertain to the needs of grade-school and secondary-school mathematics and not at all to the needs of professional mathematics: The base set of content elements is chosen to be adequate for simple coding of most of the formulas used from kindergarten to the end of high school in the United States, and probably beyond through the first two years of college, that is up to A-Level or Baccalaureate level in Europe. Nonetheless, it seems that the goal was for the content dictionaries of Content MathML to be extended by the individual “communities of practice” to meet their specific needs: Hence, it is not in general possible for a user agent to automatically determine the proper interpretation for values without further information about the context and community of practice in which the MathML instance occurs. However, in contexts where highly precise semantics are required (e.g. communication between computer algebra systems, within formal systems such as theorem provers, etc.) it is the responsibility of the relevant community of practice to verify, extend or replace definitions provided by OpenMath CDs as appropriate. It seems that there is a possibility to define your own semantic notational macros, and this certainly bears further investigation. Due to the mutually reinforcing combination of historically poor vendor support and near-absolute isolation from actual communities of practice, i.e. working mathematicians, sophisticated direct use of MathML has never caught on. On the other hand, there is a great deal of MathML on the web today in the form of and output — tools which are not only currently necessary for obtaining consistent (and professional-quality) rendering of mat...