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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Mathematical beauty | 3/3 | https://en.wikipedia.org/wiki/Mathematical_beauty | reference | science, encyclopedia | 2026-05-05T07:24:17.882469+00:00 | kb-cron |
=== Information-theory model === In the 1970s, Abraham Moles and Frieder Nake analyzed links between beauty, information processing, and information theory. In the 1990s, Jürgen Schmidhuber formulated a mathematical theory of observer-dependent subjective beauty based on algorithmic information theory: the most beautiful objects among subjectively comparable objects have short algorithmic descriptions (i.e., Kolmogorov complexity) relative to what the observer already knows. Schmidhuber explicitly distinguishes between beautiful and interesting. The latter corresponds to the first derivative of subjectively perceived beauty: the observer continually tries to improve the predictability and compressibility of the observations by discovering regularities such as repetitions and symmetries and fractal self-similarity. Whenever the observer's learning process (possibly a predictive artificial neural network) leads to improved data compression such that the observation sequence can be described by fewer bits than before, the temporary interesting-ness of the data corresponds to the compression progress, and is proportional to the observer's internal curiosity reward.
=== Neural correlates === Brain imaging experiments conducted by Semir Zeki, Michael Atiyah and collaborators show that the experience of mathematical beauty has, as a neural correlate, activity in field A1 of the medial orbito-frontal cortex (mOFC) of the brain and that this activity is parametrically related to the declared intensity of beauty. The location of the activity is similar to the location of the activity that correlates with the experience of beauty from other sources, such as visual art or music. Moreover, mathematicians seem resistant to revising their judgment of the beauty of a mathematical formula in light of contradictory opinion given by their peers.
== Mathematical beauty and the arts ==
=== Music === Examples of the use of mathematics in music include the stochastic music of Iannis Xenakis, the Fibonacci sequence in Tool's Lateralus, and the Metric modulation of Elliott Carter. Other instances include the counterpoint of Johann Sebastian Bach, polyrhythmic structures (as in Igor Stravinsky's The Rite of Spring), permutation theory in serialism beginning with Arnold Schoenberg, the application of Shepard tones in Karlheinz Stockhausen's Hymnen and the application of Group theory to transformations in music in the theoretical writings of David Lewin.
=== Visual arts ===
Examples of the use of mathematics in the visual arts include applications of chaos theory and fractal geometry to computer-generated art, symmetry studies of Leonardo da Vinci, projective geometries in development of the perspective theory of Renaissance art, grids in Op art, optical geometry in the camera obscura of Giambattista della Porta, and multiple perspective in analytic cubism and futurism. Sacred geometry is a field of its own, giving rise to countless art forms including some of the best known mystic symbols and religious motifs, and has a particularly rich history in Islamic architecture. It also provides a means of meditation and comtemplation, for example the study of the Kaballah Sefirot (Tree Of Life) and Metatron's Cube; and also the act of drawing itself. The Dutch graphic designer M. C. Escher created mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, visual paradoxes and tessellations. Some painters and sculptors create work distorted with the mathematical principles of anamorphosis, including South African sculptor Jonty Hurwitz. Origami, the art of paper folding, has aesthetic qualities and many mathematical connections. One can study the mathematics of paper folding by observing the crease pattern on unfolded origami pieces. British constructionist artist John Ernest created reliefs and paintings inspired by group theory. A number of other British artists of the constructionist and systems schools of thought also draw on mathematics models and structures as a source of inspiration, including Anthony Hill and Peter Lowe. Computer-generated art is based on mathematical algorithms.
== See also ==
== Notes ==
== References ==
== Further reading == Aigner, Martin; Ziegler, Günter M. (2018). Proofs from THE BOOK (6th ed.). Springer. ISBN 978-3-662-57264-1. Cain, Alan J. (2024). Form & Number: A History of Mathematical Beauty. Lisbon: Ebook. Hadamard, Jacques (1949). An Essay on the Psychology of Invention in the Mathematical Field (2nd enlarged ed.). Princeton University Press. ISBN 0-486-20107-4. {{cite book}}: ISBN / Date incompatibility (help) Hardy, G.H. (1967) [1st published 1940]. A Mathematician's Apology. Cambridge University Press. ISBN 978-1-107-60463-6. Huntley, H.E. (1970). The Divine Proportion: A Study in Mathematical Beauty. New York: Dover Publications. ISBN 978-0-486-22254-7. Stewart, Ian (2007). Why beauty is truth : a history of symmetry. New York: Basic Books, a member of the Perseus Books Group. ISBN 978-0-465-08236-0. OCLC 76481488.
== External links == Mathematics, Poetry and Beauty Is Mathematics Beautiful? cut-the-knot.org Justin Mullins.com Edna St. Vincent Millay (poet): Euclid alone has looked on beauty bare Terence Tao, What is good mathematics? Mathbeauty Blog The Aesthetic Appeal collection at the Internet Archive A Mathematical Romance Jim Holt December 5, 2013 issue of The New York Review of Books review of Love and Math: The Heart of Hidden Reality by Edward Frenkel