The aesthetic lives of mathematicians

February 17, 2014

Zeki et al., The experience of mathematical beauty and its neural correlates, in Frontiers of Human Neuroscience reports on the following study (paragraph break added):

Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art. 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.

To determine this, we used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources….

The formula most consistently rated as beautiful (average rating of 0.8667), both before and during the scans, was Leonhard Euler’s identity,


which links 5 fundamental mathematical constants with three basic arithmetic operations, each occurring once; the one most consistently rated as ugly (average rating of −0.7333) was Srinivasa Ramanujan’s infinite series for 1/π,

Other highly rated equations included the Pythagorean identity, the identity between exponential and trigonometric functions derivable from Euler’s formula for complex analysis, and the Cauchy-Riemann equations (Data Sheet 1: EquationsForm.pdf—Equations 2, 5, and 54). Formulae commonly rated as neutral included Euler’s formula for polyhedral triangulation, the Gauss Bonnet theorem and a formulation of the Spectral theorem (Data Sheet 1: EquationsForm.pdf—Equations 3, 4, and 52). Low rated equations included Riemann’s functional equation, the smallest number expressible as the sum of two cubes in two different ways, and an example of an exact sequence where the image of one morphism equals the kernel of the next (Data Sheet 1: EquationsForm.pdf—Equations 15, 45, and 59).

These were expressed ratings by the subject, but the study claims that they were correlated with actual results visible in the fMRI.

Thanks to Robert Dittmer for the pointer, and to Wikipedia for the copied code for Ramanujan’s series.

Eugene Volokh teaches free speech law, religious freedom law, church-state relations law, a First Amendment Amicus Brief Clinic, and tort law, at UCLA School of Law, where he has also often taught copyright law, criminal law, and a seminar on firearms regulation policy.
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