  Structures of chemical compounds can be synthesized and categorized through
mathematical means. Organic compounds are suitable targets because of their
simple valences. Acyclic organic compounds made of hydrogen and second-row
elements C, N, O, and F are presented as an example. In five categories of
organic compounds, chemical structures can be generated exclusively and
exhaustively using ab initio methods. It is shown that mathematical variables
can serve as chemical symbols and mathematical equations are chemical structure
generators.
