A recent study published in the journal of Frontiers in Human Neuroscience found that mathematicians perceive the same degree of beauty in elegant equations as an artist does admiring beautiful architecture, or a musician listening to Bach.
“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 most elegant and beautiful equation was Euler’s identity.
We physicists spend so much time with mathematics, we also have this same sense of beauty. Paul Dirac once said, “What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.”
I spend so much time with mathematics these days, I now viscerally “feel” and “perceive” the beauty in equations. It’s the same feeling I have when I look at the blue sky and think that the clouded dome above us is a realm of the gods. Who could define exactly what it is that makes a group of big poofy white clouds so beautiful? The same thing happens with mathematical expressions.