Those who see beauty in mathematics activate the same part of their brain when they look at pleasing formulae as others do when appreciating art or music, according to a new study.
The sources of beauty are limitless: a face, a landscape, a sunrise, a great piece of music, a vibrant art work.
A lot of beauty comes from a sensory experience but there are intellectual sources.
Mathematicians often describe formulae in emotive terms and the experience has often been compared by them to the emotion derived from great art.
Now researchers have used magnetic resonance imaging (MRI) to see the brain activity of 15 mathematicians when they view formula that they had previously rated as beautiful, neutral or ugly.
The results show 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.
Professor Semir Zeki of the Wellcome Laboratory of Neurobiology at the University College London says mathematical formula appear dry and inaccessible to many.
“But to a mathematician an equation can embody the quintessence of beauty,” he said.
“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.”
The formulae most consistently rated as beautiful 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.
Professor Zeki said:
“We have found that 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.”
The results of the study,’The experience of mathematical beauty and its neural correlates’, are reported in a paper published in the open-access journal Frontiers in Human Neuroscience.
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