  Formal logic has often been seen as uniquely placed to analyze mathematical
argumentation. While formal logic is certainly necessary for a complete
understanding of mathematical practice, it is not sufficient. Important aspects
of mathematical reasoning closely resemble patterns of reasoning in
nonmathematical domains. Hence the tools developed to understand informal
reasoning, collectively known as argumentation theory, are also applicable to
much mathematical argumentation. This chapter investigates some of the details
of that application. Consideration is given to the many contrasting meanings of
the word ``argument''; to some of the specific argumentation-theoretic tools
that have been applied to mathematics, notably Toulmin layouts and
argumentation schemes; to some of the different ways that argumentation is
implicated in mathematical practices; and to the social aspects of mathematical
argumentation.
