This volume examines mathematics as a product of the human mind and
analyzes the language of "pure mathematics" from various advanced-level
sources. Through analysis of the foundational texts of mathematics, it
is demonstrated that math is a complex literary creation, containing
objects, actors, actions, projection, prediction, planning, explanation,
evaluation, roles, image schemas, metonymy, conceptual blending, and, of
course, (natural) language. The book follows the narrative of
mathematics in a typical order of presentation for a standard
university-level algebra course, beginning with analysis of set theory
and mappings and continuing along a path of increasing complexity. At
each stage, primary concepts, axioms, definitions, and proofs will be
examined in an effort to unfold the tell-tale traces of the basic human
cognitive patterns of story and conceptual blending.
This book will be of interest to mathematicians, teachers of
mathematics, cognitive scientists, cognitive linguists, and anyone
interested in the engaging question of how mathematics works and why it
works so well.