Logo - springer
Slogan - springer

Philosophy - Logic & Philosophy of Language | Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Series: Synthese Library, Vol. 370

Montano, Ulianov

2014, XVIII, 220 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$99.00

(net) price for USA

ISBN 978-3-319-03452-2

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$129.00

(net) price for USA

ISBN 978-3-319-03451-5

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • Most comprehensive, systematic and scientifically informed study of aesthetic judgments in mathematics
  • Develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics
  • Draws upon a broad spectrum of insights, from experimental psychology to the history of science and linguistics, to advance a rigorous and comprehensive theory of beauty and the aesthetic in mathematics

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.

Content Level » Research

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

Related subjects » Logic & Philosophy of Language - Mathematics - Philosophy

Table of contents 

Introduction.- Part 1. Antecedents.- Chapter 1. On Non-literal Approaches.- Chapter 2. Beautiful, Literally.- Chapter 3. Ugly, Literally.- Chapter 4. Problems of the Aesthetic Induction.- Chapter 5. Naturalizing the Aesthetic Induction.- Part 2. An Aesthetics of Mathematics.- Chapter 6. Introduction to a Naturalistic Aesthetic Theory.- Chapter 7. Aesthetic Experience.- Chapter 8. Aesthetic Value.- Chapter 9. Aesthetic Judgement I: Concept.- Chapter 10. Aesthetic Judgement II: Functions.- Chapter 11. Mathematical Aesthetic Judgements.- Part 3. Applications.- Chapter 12. Case Analysis I: Beauty.- Chapter 13. Case Analysis II: Elegance.- Chapter 14. Case Analysis III: Ugliness, Revisited.- Chapter 15. Issues of Mathematical Beauty, Revisited. ​

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Logic.