Date Published: 13 February 2014

Mathematical beauty activates same brain region as art and music

How music affects the human brain

Above: Research about how music is perceived

According to new research recently published in the journal 'Frontiers in Human Neuroscience', when people appreciate the beauty of mathematics by observing aesthetically pleasing formula, the same part of their brain is activated as that which is activated when people appreciate art or music. This observation has been interpreted as suggesting that there may be a neurobiological basis to beauty.

What is beauty ?
There are many different sources of beauty - a beautiful face, a picturesque landscape, a great symphony are all examples of beauty derived from sensory experiences. There are also some other, highly intellectual, forms of beauty. They might not be appreciated by everyone!

What research method was used in the recent study ?
Researchers based at University College London (UCL) worked with 15 'subjects', all mathematicians, who took part in the study. Each subject was given 60 mathematical formulae to review at leisure and rate on a scale of -5 (ugly) to +5 (beautiful) according to how beautiful they experienced them to be. Non-mathematicians and scientists might be interested by the idea that mathematical formulae have a level of 'beauty' associated with them. According to the report of this study, not only do mathematicians often describe mathematical formulae in such emotive terms, but the experience of "mathematical beauty" has previously been compared by them to the experience of beauty derived from the greatest art.

Two weeks later the same mathematicians were asked to re-rate the same mathematical formulae while in a functional magnetic resonance imaging (fMRI) scanner. The scanner imaged the brain activity of the mathematicians at the precise time when they viewed mathematical formulae that they had previously rated as beautiful, neutral or ugly.

For those interested in which formulae were rates as the most beautiful: Those most consistently rated as beautiful (both before and during the scans) were Leonhard Euler's identity, the Pythagorean identity and the Cauchy-Riemann equations. Leonhard Euler's identity links five fundamental mathematical constants with three basic arithmetic operations each occurring once and the beauty of this equation 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.

Overall, the results of the study indicated 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.

Expert comment:

Professor Semir Zeki, of UCL and lead author of the paper, said:

" To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintescence of beauty. The beauty of a formula may result from simplicity, symmetry, elegance or the expression of an immutable truth. For Plato, the abstract quality of mathematics expressed the ultimate pinnacle of beauty.
_ This makes it interesting to learn whether the experience of beauty derived from such as highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources
."

He added that ...

" We have found that, as with the experience of visual or musical beauty, the 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, one which has been debated since classical times, namely whether aesthetic experiences can be quantified."

Source: University College London (UCL),
part of London University, England.

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