The experience of mathematical beauty and its neural correlates

Abstract

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.

Origins of the brain networks for advanced mathematics in expert mathematicians

“…One fMRI study scanned 15 professional mathematicians, focusing entirely on their subjective sense of beauty for math expressions (49). The results revealed a medial orbito-frontal correlate for this subjective feeling but could not determine which brain areas are responsible for the mathematical computations that precede it.…”

Beauty as a factor of economic and social development

“…For some scholars, mirror neurons may even be the building blocks upon which the culture of a human being is founded, because the dissemination of knowledge would occur principally by imitation (Ramachandran, 2000). In any case, these studies show a substantial equivalence, when aesthetic appreciation or creative impulse are concerned, in both the scientific and the artistic world (Andreasen, 2012;Zeki et al, 2014).…”

The Importance of Surprise in Mathematical Beauty

“…One may think of mathematical beauty as falling under the umbrella of an aesthetic phenomenon, of experiencing an emotional response to something. When mathematicians experience mathematical beauty, this correlates with activity in the same part of the brain associated with enjoying art [26]. There exist various definitions for what constitutes aesthetics, across disciplines.…”

“…As another example of beauty dependent on surprise, let us consider Euler's identity e iπ + 1 = 0 which is often cited as one of the most beautiful pieces of mathematics [21,25,26]. One given reason for its beauty is that it relates five important mathematical constants -e, i, π, 1, and 0 -together in one equation.…”