Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics - Ulianov Montano

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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.


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ISBN :  9783319034522

Language : English

Formats : epub ,
mobi , PDF

 

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Math eBooks

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