© 2018

How We Understand Mathematics

Conceptual Integration in the Language of Mathematical Description

  • Analyzes the language of pure mathematics in various advanced-level sources

  • Systemically covers the whole course of advanced, academic-level algebra

  • Presents topics in the order usually taught to students, allowing for a close scrutiny of the development of the multilayered and intricate structure of mathematical concepts


Part of the Mathematics in Mind book series (MATHMIN)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Jacek Woźny
    Pages 1-5
  3. Jacek Woźny
    Pages 31-49
  4. Jacek Woźny
    Pages 51-59
  5. Jacek Woźny
    Pages 61-81
  6. Jacek Woźny
    Pages 83-108
  7. Jacek Woźny
    Pages 109-114
  8. Back Matter
    Pages 115-117

About this book


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. 


linear transformations fields set theory vector spaces ring theory blending theory mappings Abelian groups finite groups Cayley's theorem

Authors and affiliations

  1. 1.Institute of English StudiesUniversity of WrocławOtmuchówPoland

Bibliographic information

  • Book Title How We Understand Mathematics
  • Book Subtitle Conceptual Integration in the Language of Mathematical Description
  • Authors Jacek Woźny
  • Series Title Mathematics in Mind
  • Series Abbreviated Title Mathematics in Mind
  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-77687-3
  • Softcover ISBN 978-3-030-08513-1
  • eBook ISBN 978-3-319-77688-0
  • Series ISSN 2522-5405
  • Series E-ISSN 2522-5413
  • Edition Number 1
  • Number of Pages X, 118
  • Number of Illustrations 6 b/w illustrations, 10 illustrations in colour
  • Topics Combinatorics
    Cognitive Linguistics
    Group Theory and Generalizations
  • Buy this book on publisher's site