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Foundations of Science

, Volume 20, Issue 4, pp 339–355 | Cite as

Mathematical Beauty, Understanding, and Discovery

  • Carlo CellucciEmail author
Article

Abstract

In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research.

Keywords

Mathematics Beauty Enlightenment Understanding 

Notes

Acknowledgments

I wish to thank Arthur Bierman, Angela Breitenbach, Arlette Dupuis, Donald Gillies, Reuben Hersh, Hansmichael Hohenegger, Nathalie Sinclair, Semir Zeki and four anonymous reviewers for their comments and suggestions.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophySapienza University of RomeRomeItaly

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