Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

  • Ulianov Montano

Part of the Synthese Library book series (SYLI, volume 370)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Antecedents

    1. Front Matter
      Pages 1-1
    2. Ulianov Montano
      Pages 3-19
    3. Ulianov Montano
      Pages 21-31
    4. Ulianov Montano
      Pages 33-43
    5. Ulianov Montano
      Pages 45-56
    6. Ulianov Montano
      Pages 57-69
  3. An Aesthetics of Mathematics

    1. Front Matter
      Pages 71-71
    2. Ulianov Montano
      Pages 85-116
    3. Ulianov Montano
      Pages 117-130
    4. Ulianov Montano
      Pages 131-148
    5. Ulianov Montano
      Pages 149-159
    6. Ulianov Montano
      Pages 161-163
  4. Applications

    1. Front Matter
      Pages 165-165
    2. Ulianov Montano
      Pages 167-177
    3. Ulianov Montano
      Pages 179-195
    4. Ulianov Montano
      Pages 197-203
  5. Closing Remarks

    1. Front Matter
      Pages 205-205
    2. Ulianov Montano
      Pages 207-209

About this book

Introduction

This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics.

The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory.

The theory comprises explications of three central topics: aesthetic experience (in mathematics), aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities.

Keywords

Application of Aesthetic Judgment Beauty, Elegance and Ugliness in Mathematics Concept of Aesthetic Judgment Function of Aesthetic Judgment Introduction to a Naturalistic Aesthetic Theory Issues of Mathematical Beauty Mathematical Aesthetic Judgments Philosophy of Mathematics Problems of the Aesthetic Induction aesthetic judgments in mathematics

Authors and affiliations

  • Ulianov Montano
    • 1
  1. 1.Mexico CityMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-03452-2
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-3-319-03451-5
  • Online ISBN 978-3-319-03452-2
  • About this book