After giving a quick overview of MathML, we discuss the issues arising in conversion between TeX and MathML. We consider the problem of how conversion between these formats can conserve any mathematical semantics implied by the markup of the original document.

Rather than expanding all macros to low-level formatting instructions, we hypothesize that in many interesting cases it shall be possible to map macros in one setting to corresponding macros in another, thus conserving implied semantics. We have adopted the assumption that certain TeX style or class files will naturally have counterpart XSLT style-sheets for use with MathML. Particular TeX macros then correspond to specific XSLT template definitions.

We shall present the overall architecture of a pair of programs -- one converting TeX to MathML and one converting MathML to TeX. Both permit macros to be translated at a high semantic level.