For centuries beauty has been ascribed to the mathematical description of reality, from Newton’s law of universal gravitation to Einstein’s theory of relativity.1 In a 1939 lecture the theoretical physicist Paul Dirac (1902–1982) argued that any fundamental law of physics possesses mathematical beauty, so, conversely, any beautiful mathematical theory has the potential to form the basis of new laws of physics—an assertion that might be seen as the mathematical equivalent of Keats’s “Beauty is truth, truth beauty.”2 Seventy-five years later, mathematical beauty was still a topic of inquiry: In 2014 neuroscientist Semir Zeki found that, among mathematicians, certain equations activate the same area of the brain that responds to beauty in art or music.3 But though mathematical (often geometrical) principles have been frequently employed in the creation of art, architecture and music, the presentation of formulae in art is a rarity.
- Beauty in mathematics was the subject of the BBC documentary Beautiful Equations, hosted by artist and writer Matt Collings, last aired on BBC Four, 2 January 2012, accessed 1 May 2016, http://topdocumentaryfilms.com/beautiful-equations/. For Dirac’s 1939 lecture, see Paul Adrien Maurice Dirac, “The Relation between Mathematics and Physics,” University of Cambridge, Department of Applied Mathematics and Theoretical Physics, accessed 7 May 2016, http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html. Originally published in The Proceedings of the Royal Society (Edinburgh) 59:2 (1938–39): 122–129. For more on Dirac’s Principle of Mathematical Beauty, see Alexey Stakhov, “Dirac’s Principle of Mathematical Beauty, Mathematics of Harmony and ‘Golden’ Scientific Revolution,” Mathematical Institute of the Serbian Academy of Sciences and Arts, 2009, accessed 7 May 2016, http://www.mi.sanu.ac.rs/vismath/stakhov2009/mathharm.pdf. See also Graham Farmelo, “Paul Dirac and the Religion of Mathematical Beauty,” lecture presented at The Royal Society, London on 4 March 2011, accessed on YouTube 7 May 2016, https://www.youtube.com/watch?v=jPwo1XsKKXg.
- Dirac said that beauty in mathematics “is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.” See Paul Adrien Maurice Dirac, “The Relation between Mathematics and Physics,” University of Cambridge, Department of Applied Mathematics and Theoretical Physics, accessed 7 May 2016, http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html.
- See Seth Newman, “Beauty in Math and Art Activate Same Brain Area,” Scientific American Online, 1 September 2014, http://www.scientificamerican.com/article/beauty-in-math-and-art-activate-same-brain-area/.