Beauty of mathematics excites emotional brain

A new study suggests beauty may have a neurological basis. Using brain scans, researchers in the UK found appreciation of abstract beauty - such as in finding aspects of mathematics beautiful - excites the same emotion centers in the brain as appreciation of beauty that comes from more sensory experience - like listening to music or looking at great art.

They report their findings in the open access journal Frontiers in Human Neuroscience.

Having read reports about how some people compare experiencing the beauty of mathematics to appreciating a fine work of art, the researchers decided to see if the brain's emotion centers are active in the same way for these different experiences of beauty.

Lead author Semir Zeki, a professor at the Wellcome Laboratory of Neurobiology at University College London (UCL), says the amount of activity in a person's brain correlates with how intensely they report their experience of beauty to be - even when the object of their attention is an abstract concept.

He adds:

"To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintessence of beauty."

The quality that the mathematician finds beautiful may lie in the expression of an immutable truth, or just in the simplicity, symmetry or elegance of a concept.

"For Plato," Prof. Zeki notes, "the abstract quality of mathematics expressed the ultimate pinnacle of beauty."

Beautiful equations activated same part of brain as beautiful music

For their study, the team asked 15 mathematicians to take away and consider 60 mathematical formulae, rate how beautiful they experienced each one to be and to note this as a score between -5 (for ugly) and +5 (for beautiful).

Leonhard Euler's identity equation
Participants found Leonhard Euler's identity formula "beautiful." (Image credit: UCL)

Then 2 weeks later, the researchers invited the participants to rate the formulae again as they took functional magnetic resonance imaging (fMRI) scans of their brains.

The scans showed that when the participants looked at mathematical formulae they consistently rated as beautiful, this activated an area of the emotional brain - the medial orbito-frontal cortex - that is also active when people's experience of beauty comes from a piece of music or great art.

The formulae that the participants most consistently rated as beautiful, both before and during the scans, were Leonhard Euler's identity, the Pythagorean identity and the Cauchy-Riemann equations.

Euler's identity (also known as Euler's equation), links five important mathematical constants (e, i, π, 1 and 0) with three basic arithmetic operations, each occurring only once. Some say the beauty of this equation is equal to that of Hamlet's soliloquy, "To be, or not to be, that is the question..."

The participants rated Srinivasa Ramanujan's infinite series and Bernhard Riemann's functional equation as the ugliest.

Prof. Zeki says as with visual experience of art and listening to music, they found the activity in the brain strongly correlated with how intensely the participants declared their experience of beauty to be, "even in this example where the source of beauty is extremely abstract." He concludes:

"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."

In 2010, Medical News Today reported a study by scientists at Florida Atlantic University that supported the idea that the brain has a mechanism through which experienced music listeners feel the emotions of the performers, making musical communication a form of empathy.

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