© 2005

Visualization, Explanation and Reasoning Styles in Mathematics

  • Paolo Mancosu
  • Klaus Frovin Jørgensen
  • Stig Andur Pedersen


  • Unique focus on the relationship between philosophy of mathematics and mathematical practice

  • Contains groundbreaking contributions on visualization, explanation and reasoning styles in mathematics


Part of the Synthese Library book series (SYLI, volume 327)

Table of contents

  1. Front Matter
    Pages i-x
  2. P. Mancosu, K.F. Jørgensen, S.A. Pedersen
    Pages 1-9
  3. Mathematical Reasoning and Visualization

    1. Paolo Mancosu
      Pages 13-30
    2. James Robert Brown
      Pages 57-73
    3. M. Giaquinto
      Pages 75-87
  4. Mathematical Explanation and Proof Styles

  5. Back Matter
    Pages 295-314

About this book


This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.


Algebra calculus geometry mathematics philosophy of mathematics proof

Editors and affiliations

  • Paolo Mancosu
    • 1
  • Klaus Frovin Jørgensen
    • 2
  • Stig Andur Pedersen
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Roskilde UniversityDenmark

Bibliographic information

Industry Sectors
Finance, Business & Banking


From the reviews:

"As its title suggests, the book deals with themes that are of great interest to mathematics educators. … this book is a collection of excellent papers by distinguished authors. It also shows a high standard of book production, in its layout, paper quality, draftsmanship and binding. … this book deserves the attention of all those with an interest in mathematics education." (G. Hanna, Educational Studies in Mathematics, Vol. 64, 2007)

"This fascinating collection of essays is a must-have for those who are interested in the history and philosophy of mathematics … . this is a book that libraries will want to have, particularly if they strive to have good collections on the history and philosophy of mathematics." (Fernando Q. Gouvêa, MathDL, August, 2005)