Compartmentalizing mathematics and natural language as disparate studies may be counterproductive.  Maybe we should admit fruitful interrelationships between the two.  

Mathematics is a collection of very different, but all formal languages.  One of these, Game Theory, may model (describe) some of our behavior quite accurately.  Another, Catastrophy Theory, may model other parts of our behavior, such as violence.  Another, Logic, models some kinds of thinking.  There is a lot of behavior involved in communication, and the use of natural language is just one of them.  Some mathematicians work to expand the Logic of Set Logic, Predicate Logic, and Propositional Logic, etc., into Modal Logic or Fuzzy Logic, etc., just so as to have a better model of how we think.  More power to the mathematicians who develop new studies to model natural language!  So far generative grammar has been quite useful for describing certain problems in natural language computer programming. Often the syntax of computer languages is described using phrase structure rules.  GT-grammar seems to have caught on in Computer Science.  We ought to be aware of the areas where some of these theories may shed some light, and Syntax, even of a natural language, is certainly one of them.  

Bruce Despain

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