Proof Technology in Mathematics Research and Teaching

  • Gila Hanna
  • David A.  Reid
  • Michael de Villiers

Part of the Mathematics Education in the Digital Era book series (MEDE, volume 14)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Gila Hanna, David A. Reid, Michael de Villiers
      Pages 3-9
  3. Automatic Theorem Provers

    1. Front Matter
      Pages 11-11
    2. M. Ganesalingam, W. T. Gowers
      Pages 13-57
    3. Rob Arthan, Paulo Oliva
      Pages 91-111
  4. Theoretical Perspectives on Computer-Assisted Proving

    1. Front Matter
      Pages 113-113
    2. Viviane Durand-Guerrier, Antoine Meyer, Simon Modeste
      Pages 115-138
    3. Philippe R. Richard, Fabienne Venant, Michel Gagnon
      Pages 139-172
    4. Lorenzo Lane, Ursula Martin, Dave Murray-Rust, Alison Pease, Fenner Tanswell
      Pages 197-212
  5. Suggestions for the Use of Proof Software in the Classroom

    1. Front Matter
      Pages 213-213
    2. Markus Hohenwarter, Zoltán Kovács, Tomás Recio
      Pages 215-236
    3. Pedro Quaresma, Vanda Santos
      Pages 237-253
  6. Classroom Experience with Proof Software

  7. Afterword

    1. Front Matter
      Pages 347-347
    2. Nicolas Balacheff, Thierry Boy de la Tour
      Pages 349-365
  8. Back Matter
    Pages 367-379

About this book


This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning.

Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs.   

Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field. 


Computer-assisted mathematical proof Interactive proof assistants Polymath collaborative proofs Teaching proving with technology Conjecture generation or refutation by computer Proof in social media

Editors and affiliations

  • Gila Hanna
    • 1
  • David A.  Reid
    • 2
  • Michael de Villiers
    • 3
  1. 1.Ontario Institute for Studies in EducationUniversity of TorontoTorontoCanada
  2. 2.AG Didaktik, Fachbereich 3Universität BremenBremenGermany
  3. 3.Faculty of EducationStellenbosch UniversityStellenboschSouth Africa

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Education Education (R0)
  • Print ISBN 978-3-030-28482-4
  • Online ISBN 978-3-030-28483-1
  • Series Print ISSN 2211-8136
  • Series Online ISSN 2211-8144
  • Buy this book on publisher's site