February 13, 2014
MRI Study Shows How The Brain Finds Beauty In Mathematics
Peter Suciu for redOrbit.com - Your Universe Online
To many people math is work, often times hard work. Yet for those who appreciate the beauty of mathematics it can activate the same part of the brain that can appreciate great art or music. To those math lovers an aesthetically pleasing formula is art, and this now suggests that there could be a neurobiological basis to beauty.
Thus beauty is truly in the eyes of the beholder, and researchers from University College London, Imperial College London and the University of Edinburgh have found that this could include a beautiful face, a picturesque landscape or a great symphony, but it could also be a mathematical formula as well.
The findings of this study were published in the open-access journal Frontiers in Human Neuroscience.
“Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art,” the researchers wrote. “This makes it interesting to learn whether the experience of beauty derived from such a 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.”
For the study, the research team used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae. The mathematicians had individually rated each formula as beautiful, indifferent or ugly.
Each subject was given 60 mathematical formulae to review and was told to rate each on a scale of -5 (ugly) to +5 (beautiful), two weeks later they were asked to re-rate the same formulas while in the fMRI scanner.
The results suggested that the experience of mathematical beauty could correlate parametrically with activity in the same part of the emotional brain, the field A1 of the medial orbitofrontal cortex (mOFC), as that of experiences of beauty derived from other sources including music and art.
“To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintescence of beauty,” Professor Semir Zeki, lead author of the paper from the Wellcome Laboratory of Neurobiology at UCL, said in a statement. “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 that were most consistently rated as beautiful – both before and during the scans – were Leonhard Euler’s identity, the Pythagorean identity and the Cauchy-Riemann equations; while the mathematicians found the Srinivasa Ramanujan’s infinite series and Riemann’s functional equation as the ugliest.
Of course beauty is still in the eye of the beholder so those who understand these formulae might appreciate them more than the untrained eye.
Professor David Percy of the Institute of Mathematics and its Applications is one who certainly can see beauty in the numbers and symbols of a formula.
“It is a real classic and you can do no better than that,” Percy told the BBC on how he views Euler’s identity formula. “It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants - zero (additive identity), one (multiplicative identity), e and pi (the two most common transcendental numbers) and i (fundamental imaginary number).”
For the researchers, they may see beauty in this study as well.
“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,” Zeki added. “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.”