ABSTRACT
Mathematics is organised through vast sets of relations between symbols. These relations arise through the complexing of symbols into expressions and of expressions into statements. This strong ability for complexing is highly significant for the power of mathematics in physics and in science more broadly. This chapter focuses on the lower levels of mathematics concerned with the internal organisation of symbols to show that these maintain their own structures derived from their own systems. The rank scale proposed by Halliday for English involves multivariate structures associated with the experiential component of the ideational meta-function. The predominant structural organisation of the grammar is a univariate structure. Statements are built from an indefinitely iterative complex of expressions and expressions are built from an indefinitely iterative complex of symbols. This is reflected in the paradigmatic organisation of the statement where all choices are potentially recursive.
