Josefina Alvarez in Plus Magazine:
[H]ow is this mathematical beauty similar to, or different from, the beauty we ascribe to a work of art? There are frequent references to mathematics as an art. In an article published in The Mathematical Intelligencer with the title Mathematics: art and science, the mathematician Armand Borel has this to say: "… mathematics is an extremely complex creation which displays so many essential traits in common with art and experimental and theoretical sciences that it has to be regarded as all three at the same time, and thus must be differentiated from all three as well."
So, as to how and why mathematics is connected to art or to other endeavours, the answer is typically ambiguous. It seems that questions of this nature are destined to remain a part of the mathematical folklore. Still, perhaps unknown to most mathematicians, something has been happening somewhere else.
A brain revolution
As early as 1909, an anatomist, Korbinian Brodmann, divided the cortex of the human brain into 47 areas, now called Brodmann areas, according to the structure and organisation of the cells. Later, as researchers began to understand the functions of different cells in the cortex, they were astounded by the fairly close relation emerging between certain Brodmann areas and the location of specific cell functions. Today, much is known about a wide range of these functions, showing the prodigious complexity of our brain. For instance, there seem to be about three thousand interconnected neurons, controlling most of our breathing and involving about 65 types of neurons!
Besides what we might call the physical functions, researchers are understanding the locations of what we might call intellectual functions. For example, an articlepublished in 2011 in the journal NeuroImage, discussed the findings of a study locating the brain areas needed for numbers and calculations. Coincidentally, a study published the same year in the journal PLoS ONE, presented evidence towards a brain-based theory of beauty. Several studies had already shown how beauty, as related to visual, auditory and moral experience, was connected to activity observed in a specific region of what researchers call the emotional brain.
Based on all these findings, a team of two neurobiologists, Semir Zeki and John Paul Romaya, a physicist, Dionigi M. T. Benincasa, and the mathematician Michael F. Atiyah conjectured that the perception of mathematical beauty should excite the same parts of the emotional brain, roughly described by a collection of Brodmann areas. Their study, published in the journal Frontiers of human neuroscience in 2014, seems to confirm their conjecture, indeed placing mathematical beauty, as perceived by trained mathematicians, in the same areas previously identified with other manifestations of beauty.