The Art of Doing Mathematics

In Berys Gaut & Matthew Kieran (eds.), Creativity and Philosophy. Routledge. pp. 313-330 (2018)

Authors
Christian Wenzel
National Taiwan University
Abstract
Mathematicians often say that their theorems, proofs, and theories can be beautiful. They say mathematics can be like art. They know how to move creatively and freely in their domains. But ordinary people usually cannot do this and do not share this view. They often have unpleasant memories from school and do not have this experience of freedom and creativity in doing mathematics. I myself have been a mathematician, and I wish to highlight some of the creative aspects in doing mathematics. I always had the feeling that there is much freedom in mathematics and that one can do as one pleases as long as one avoids contradictions (and one can even live with contradictions for a while). In mathematics one only needs to define something and there it is! Just imagine it, and it immediately exists. Where else, besides fiction, does one have such power? --- This essay has three parts. In the first, I lay out some historical facts and views that I will need later. Second, I insert an interlude with Kant, pointing out some of his claims and insights in aesthetics, and some aspects in mathematics that I think he overlooked or underestimated. Third, I will bring out some aspects of higher mathematics that I will show are similar to art. These aspects are in the doing and creating of mathematics, not in the finished theories. They are usually not found in textbooks. I want to show that a researcher in mathematics is like a painter or composer, exploring and creating. To see this, one has to adopt a first-person perspective. In this way I will show that aesthetics plays a role and leaves its traces also in mathematics.
Keywords Aesthetics of Mathematics  Aesthetics in Kant  Creativity in Mathematics  Aesthetics  Philosophy of Mathematics
Categories (categorize this paper)
Buy the book Find it on Amazon.com
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,107
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Mathematics and Aesthetics in Kantian Perspectives.Wenzel Christian Helmut - 2016 - In Peter Cassaza, Steven G. Krantz & Randi R. Ruden (eds.), I, Mathematician II. Further Introspections on the Mathematical Life. The Consortium of Mathematics and its Applications. pp. 93-106.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Reflections on Mathematics and Aesthetics.John L. Bell - 2015 - Aisthesis: Pratiche, Linguaggi E Saperi Dell’Estetico 8 (1):159-179.
Reflections on Mathematics.Edward N. Zalta - 2007 - In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Beauty in Proofs: Kant on Aesthetics in Mathematics.Angela Breitenbach - 2015 - European Journal of Philosophy 23 (4):955-977.
The NCTM Standards and the Philosophy of Mathematics.Charalampos Toumasis - 1997 - Studies in Philosophy and Education 16 (3):317-330.
New Waves in Philosophy of Mathematics.Otávio Bueno & Øystein Linnebo (eds.) - 2009 - London, England: Palgrave-Macmillan.
Art and Imagination in Mathematics.Christian Helmut Wenzel - 2013 - In Michael L. Thompson (ed.), Imagination in Kant's Critical Philosophy. Walter de Gruyter. pp. 49-68.
Beauty Is Not All There Is to Aesthetics in Mathematics.R. S. D. Thomas - forthcoming - Philosophia Mathematica:nkw019.

Analytics

Added to PP index
2018-04-16

Total views
1 ( #1,508,138 of 2,454,612 )

Recent downloads (6 months)
1 ( #449,377 of 2,454,612 )

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes