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February 11, 2014

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Beauty in math may touch same brain area as art, music

Feb. 12, 2014
Courtesy of UCL
and World Science staff

Peo­ple who enjoy the beau­ty of math­e­mat­ics ac­ti­vate the same part of their brain when they look at an aes­thet­ic­ally pleas­ing for­mu­la as many do when en­joy­ing art or mu­sic, a study finds.

The for­mu­la that math­e­mati­cians in the study rat­ed most beau­ti­ful? Le­on­hard Eu­ler’s ident­ity (e = –1.) (See here for more in­forma­t­ion on it).

There are many dif­fer­ent sources of beau­ty—a beau­ti­ful face, a pic­tur­esque land­scape, a great sym­pho­ny. But there are oth­er, highly in­tel­lec­tu­al sources of beau­ty. Math­e­mati­cians of­ten de­scribe math­e­mat­i­cal for­mu­lae in emo­tive terms and com­pare it go great art.

In a new pa­per pub­lished in the re­search jour­nal Fron­tiers in Hu­man Neu­ro­sci­ence, re­search­ers used the brain scan­ning tech­nique func­tion­al mag­net­ic res­o­nance im­ag­ing to im­age the brain ac­ti­vity of 15 math­e­mati­cians when they looked at for­mu­lae that they had pre­vi­ously rat­ed as beau­ti­ful, neu­tral or ug­ly. 

The re­sults showed that the ex­pe­ri­ence of math­e­mat­i­cal beau­ty cor­re­lates with ac­ti­vity in the same part of the emo­tion­al brain – namely the me­di­al orbito-frontal cor­tex – as the ex­pe­ri­ence of beau­ty from art or mu­sic.

“For Pla­to, the ab­stract qual­ity of math­e­mat­ics ex­pressed the ul­ti­mate pin­na­cle of beau­ty,” said Semir Zeki, lead au­thor of the pa­per from the Well­come Lab­o­r­a­to­ry of Neuro­bi­ol­o­gy at Uni­vers­ity Col­lege Lon­don.

“To many of us math­e­mat­i­cal for­mu­lae ap­pear dry and in­ac­ces­si­ble but to a math­e­ma­ti­cian an equa­t­ion can em­body the quin­tes­sence of beau­ty. The beau­ty of a for­mu­la may re­sult from sim­pli­city, sym­me­try, el­e­gance or the ex­pres­sion of an im­mu­ta­ble truth.”

The for­mu­lae most con­sist­ently rat­ed as beau­ti­ful both be­fore and dur­ing the scans were Eu­ler’s ident­ity, the Py­thag­o­rean ident­ity and the Cauchy-Riemann equa­t­ions. Eu­ler’s ident­ity links five fun­da­men­tal math­e­mat­i­cal con­stants with three bas­ic arith­me­tic opera­t­ions each oc­cur­ring once. The equa­t­ion’s beau­ty has been likened to that of the so­lil­o­quy in Ham­let.

Math­e­mati­cians judged Sri­ni­va­sa Ra­manu­jan’s in­fi­nite se­ries and Rie­man­n’s func­tion­al equa­t­ion as the ugli­est.

“Ac­ti­vity in the brain is strongly re­lat­ed to how in­tense peo­ple de­clare their ex­pe­ri­ence of beau­ty to be – even in this ex­am­ple where the source of beau­ty is ex­tremely ab­stract. This an­swers a crit­i­cal ques­tion in the study of aes­thet­ics, namely wheth­er aes­thet­ic ex­pe­ri­ences can be quanti­fied,” Zeki said.


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People who appreciate the beauty of mathematics activate the same part of their brain when they look at aesthetically pleasing formula as others do when appreciating art or music, a study finds. The formula that mathematicians in the study rated most beautiful? Leonhard Euler’s identity (eiπ =-1.) (See here for more information on it). There are many different sources of beauty—a beautiful face, a picturesque landscape, a great symphony. But there are other, highly intellectual sources of beauty. Mathematicians often describe mathematical formulae in emotive terms and compare it go great art. In a new paper published in the open-access journal Frontiers in Human Neuroscience, researchers used the brain scanning technique functional magnetic resonance imaging to image the brain activity of 15 mathematicians when they looked at formulae that they had previously rated as beautiful, neutral or ugly. The results showed that the experience of mathematical beauty correlates with activity in the same part of the emotional brain – namely the medial orbito-frontal cortex – as the experience of beauty derived from art or music. “For Plato, the abstract quality of mathematics expressed the ultimate pinnacle of beauty,” said Semir Zeki, lead author of the paper from the Wellcome Laboratory of Neurobiology at University College London. “To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintessence of beauty. The beauty of a formula may result from simplicity, symmetry, elegance or the expression of an immutable truth. “ The formulae most consistently rated as beautiful both before and during the scans were Euler’s identity, the Pythagorean identity and the Cauchy-Riemann equations. Euler’s identity links five fundamental mathematical constants with three basic arithmetic operations each occurring once. The equation’s beauty has been likened to that of the soliloquy in Hamlet. Mathematicians judged Srinivasa Ramanujan’s infinite series and Riemann’s functional equation as the ugliest. “Activity in the brain is strongly related to how intense people declare their experience of beauty to – even in this example where the source of beauty is extremely abstract. This answers a critical question in the study of aesthetics, namely whether aesthetic experiences can be quantified,” Zeki said.