Mathematical beauty (English Wikipedia)

Hardy, G.H. "18". A Mathematician's Apology – via Internet Archive.
Russell, Bertrand (1919). "The Study of Mathematics". Mysticism and Logic: And Other Essays. Longman. p. 60. Retrieved 2008-08-22. Mathematics rightly viewed possesses not only truth but supreme beauty a beauty cold and austere like that of sculpture without appeal to any part of our weaker nature without the gorgeous trappings Russell.
Devlin, Keith (2000). "Do Mathematicians Have Different Brains?". The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip. Basic Books. p. 140. ISBN 978-0-465-01619-8. Retrieved 2008-08-22.

arxiv.org

J. Schmidhuber. Simple Algorithmic Principles of Discovery, Subjective Beauty, Selective Attention, Curiosity & Creativity. Proc. 10th Intl. Conf. on Discovery Science (DS 2007) pp. 26–38, LNAI 4755, Springer, 2007. Also in Proc. 18th Intl. Conf. on Algorithmic Learning Theory (ALT 2007) p. 32, LNAI 4754, Springer, 2007. Joint invited lecture for DS 2007 and ALT 2007, Sendai, Japan, 2007. arXiv:0709.0674.

atm.org.uk

"Paul Ernest: Mathematics and Beauty" (PDF). Mathematics Teaching. 2015-09-01. Retrieved 2024-09-15.

bbc.co.uk

Gallagher, James (13 February 2014). "Mathematics: Why the brain sees maths as beauty". BBC News online. Retrieved 13 February 2014.

books.google.com

Phillips, George (2005). "Preface". Mathematics Is Not a Spectator Sport. Springer Science+Business Media. ISBN 0-387-25528-1. Retrieved 2008-08-22. "...there is nothing in the world of mathematics that corresponds to an audience in a concert hall, where the passive listen to the active. Happily, mathematicians are all doers, not spectators.
Franco, Francesca (2017-10-05). "The Systems Group (Chapter 2)". Generative Systems Art: The Work of Ernest Edmonds. Routledge. ISBN 9781317137436.

br-online.de

Schmidhuber's theory of beauty and curiosity in a German TV show: http://www.br-online.de/bayerisches-fernsehen/faszination-wissen/schoenheit--aesthetik-wahrnehmung-ID1212005092828.xml Archived June 3, 2008, at the Wayback Machine

caltech.edu

feynmanlectures.caltech.edu

Feynman, Richard P. (1977). The Feynman Lectures on Physics. Vol. I. Addison-Wesley. ISBN 0-201-02010-6.

ceasefiremagazine.co.uk

"Alain Badiou: Ontology and Structuralism". Ceasefire Magazine. 2014-04-02. Retrieved 2019-10-31.

doi.org

Rota (1997), p. 173. Rota, Gian-Carlo (1997). "The phenomenology of mathematical beauty". Synthese. 111 (2): 171–182. doi:10.1023/A:1004930722234. JSTOR 20117626. S2CID 44064821.
Rota (1997), p. 172. Rota, Gian-Carlo (1997). "The phenomenology of mathematical beauty". Synthese. 111 (2): 171–182. doi:10.1023/A:1004930722234. JSTOR 20117626. S2CID 44064821.
Sowell, E (1989). "Effects of Manipulative Materials in Mathematics Instruction". Journal for Research in Mathematics Education. 20 (5): 498–505. doi:10.2307/749423. JSTOR 749423.
Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F. (2014). "The experience of mathematical beauty and its neural correlates". Frontiers in Human Neuroscience. 8: 68. doi:10.3389/fnhum.2014.00068. ISSN 1662-5161. PMC 3923150. PMID 24592230.
Zhang, Haoxuan; Zeki, Semir (May 2022). "Judgments of mathematical beauty are resistant to revision through external opinion". PsyCh Journal. 11 (5): 741–747. doi:10.1002/pchj.556. ISSN 2046-0252. PMC 9790661. PMID 35491015.
"Rentuya Sa, Lara Alcock, Matthew Inglis and Fenner Stanley Tanswell: Do Mathematicians Agree about Mathematical Beauty?". Review of Philosophy and Psychology. 2024-02-21. doi:10.1007/s13164-022-00669-3.
J. Schmidhuber. Low-complexity art. Leonardo, Journal of the International Society for the Arts, Sciences, and Technology (Leonardo/ISAST), 30(2):97–103, 1997. doi:10.2307/1576418. JSTOR 1576418.
Schmidhuber, J. (1991). Curious model-building control systems. International Joint Conference on Neural Networks. Vol. 2. Singapore: IEEE press. pp. 1458–1463. doi:10.1109/IJCNN.1991.170605.

exeter.ac.uk

John Ernest's use of mathematics and especially group theory in his art works is analysed in John Ernest, A Mathematical Artist by Paul Ernest in Philosophy of Mathematics Education Journal, No. 24 Dec. 2009 (Special Issue on Mathematics and Art): https://www.exeter.ac.uk/research/groups/education/pmej/pome24/index.htm

idsia.ch

J. Schmidhuber. Papers on the theory of beauty and low-complexity art since 1994: http://www.idsia.ch/~juergen/beauty.html

jstor.org

Rota (1997), p. 173. Rota, Gian-Carlo (1997). "The phenomenology of mathematical beauty". Synthese. 111 (2): 171–182. doi:10.1023/A:1004930722234. JSTOR 20117626. S2CID 44064821.
Rota (1997), p. 172. Rota, Gian-Carlo (1997). "The phenomenology of mathematical beauty". Synthese. 111 (2): 171–182. doi:10.1023/A:1004930722234. JSTOR 20117626. S2CID 44064821.
Sowell, E (1989). "Effects of Manipulative Materials in Mathematics Instruction". Journal for Research in Mathematics Education. 20 (5): 498–505. doi:10.2307/749423. JSTOR 749423.
J. Schmidhuber. Low-complexity art. Leonardo, Journal of the International Society for the Arts, Sciences, and Technology (Leonardo/ISAST), 30(2):97–103, 1997. doi:10.2307/1576418. JSTOR 1576418.

mathcomm.org

"Proof elegance - MAA Mathematical Communication MAA Mathematical Communication". 2011-04-01. Retrieved 2024-04-28.

nih.gov

ncbi.nlm.nih.gov

Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F. (2014). "The experience of mathematical beauty and its neural correlates". Frontiers in Human Neuroscience. 8: 68. doi:10.3389/fnhum.2014.00068. ISSN 1662-5161. PMC 3923150. PMID 24592230.
Zhang, Haoxuan; Zeki, Semir (May 2022). "Judgments of mathematical beauty are resistant to revision through external opinion". PsyCh Journal. 11 (5): 741–747. doi:10.1002/pchj.556. ISSN 2046-0252. PMC 9790661. PMID 35491015.

pubmed.ncbi.nlm.nih.gov

Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F. (2014). "The experience of mathematical beauty and its neural correlates". Frontiers in Human Neuroscience. 8: 68. doi:10.3389/fnhum.2014.00068. ISSN 1662-5161. PMC 3923150. PMID 24592230.
Zhang, Haoxuan; Zeki, Semir (May 2022). "Judgments of mathematical beauty are resistant to revision through external opinion". PsyCh Journal. 11 (5): 741–747. doi:10.1002/pchj.556. ISSN 2046-0252. PMC 9790661. PMID 35491015.

semanticscholar.org

api.semanticscholar.org

Rota (1997), p. 173. Rota, Gian-Carlo (1997). "The phenomenology of mathematical beauty". Synthese. 111 (2): 171–182. doi:10.1023/A:1004930722234. JSTOR 20117626. S2CID 44064821.
Rota (1997), p. 172. Rota, Gian-Carlo (1997). "The phenomenology of mathematical beauty". Synthese. 111 (2): 171–182. doi:10.1023/A:1004930722234. JSTOR 20117626. S2CID 44064821.

st-andrews.ac.uk

www-history.mcs.st-andrews.ac.uk

"Quotations by Hardy". www-history.mcs.st-andrews.ac.uk. Retrieved 2019-10-31.

stanford.edu

plato.stanford.edu

Linnebo, Øystein (2018), "Platonism in the Philosophy of Mathematics", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2018 ed.), Metaphysics Research Lab, Stanford University, retrieved 2019-10-31

web.archive.org

Schmidhuber's theory of beauty and curiosity in a German TV show: http://www.br-online.de/bayerisches-fernsehen/faszination-wissen/schoenheit--aesthetik-wahrnehmung-ID1212005092828.xml Archived June 3, 2008, at the Wayback Machine

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Quadratic Reciprocity Theorem". mathworld.wolfram.com. Retrieved 2019-10-31.
Weisstein, Eric W. "Fundamental Theorems of Calculus". mathworld.wolfram.com. Retrieved 2019-10-31.

worldcat.org

search.worldcat.org

Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F. (2014). "The experience of mathematical beauty and its neural correlates". Frontiers in Human Neuroscience. 8: 68. doi:10.3389/fnhum.2014.00068. ISSN 1662-5161. PMC 3923150. PMID 24592230.
Zhang, Haoxuan; Zeki, Semir (May 2022). "Judgments of mathematical beauty are resistant to revision through external opinion". PsyCh Journal. 11 (5): 741–747. doi:10.1002/pchj.556. ISSN 2046-0252. PMC 9790661. PMID 35491015.