A study finds that mathematical brains respond to formulae as they do to paintings and music

GREAT works of art such as Turner’s paintings, Mozart’s concertos or Rodin’s sculptures delight many. Others get their kicks elsewhere. According to the philosopher Betrand Russell, for example, “mathematics, rightly viewed, possesses not only truth, but supreme beauty”. Plato thought along similar lines—nothing without understanding could be more beautiful than with understanding—making maths matchless in his eyes. A new study published in Frontiers of Human Neuroscience, authored by three academics from the University of London—Semir Zeki and John Paul Romaya from University College and Dionigi Benincasa from Imperial College—alongside Michael Atiyah from the University of Edinburgh, has found that the brain activity of mathematicians looking at equations correlates with the same area of the emotional brain which many previous studies (including those of the authors) have reported as active during the experience of beauty in other domains. In other words, formulae can thrill in the way that visual art and music do.

Functional magnetic resonance imaging (fMRI) showed that maths and art excite the same cerebral area: field A1 of the medial orbito-frontal cortex. This in spite of the fact that mathematical beauty derives from intellectual sources whereas, for example, the tears induced by Manon Lescaut’s misery stem from experiencing the opera itself.

Thirteen male and three female mathematicians studying at postgraduate or postdoctoral level participated in the study, as did 12 other volunteers not so mired in maths. The more numerate were asked to rate 60 formulae on a scale from -5 (ugly) to +5 (beautiful) in a survey, allowing the creation of four groups of equations with equal numbers of low, medium and high-rated formulae. The mathematicians then viewed the groupings while having their brains scanned, and were asked to judge whether a formula appeared “ugly”, “neutral” or “beautiful” to them.

A few days after the scanning, participants reported their level of understanding for each formula on a scale from 0 (none) to 3 (profound). The whole process was then repeated for the participants not studying maths.

The first formula below, Leonhard Euler’s identity (which links five fundamental mathematical constants with three basic arithmetic operations, each occurring once) was most consistently rated as beautiful with an average score of 0.8667.

The second, Srinivasa Ramanujan’s infinite series for 1/π, was the least popular with an average score of -0.7333. One of the most difficult problems involved deciphering beauty from understanding in the study. This was possible for the group of mathematicians, but tricky with the other participants as to separate comprehension from beauty altogether, a group entirely illiterate in maths would have needed to be assembled, actually “a very difficult task” according to Professor Zeki. Of the 720 equations distributed across the 12 non-mathematicians, 89.6% rang no intellectual bells whatsoever. Nevertheless, less-well understood formulae led to more intense cerebral activity in visual areas. Hubub in field A1 of mathematical brains suggests then that, neurobiologically, there is an abstract quality to beauty independent of culture and learning. But as other instances of cerebral activity could not be accounted for by understanding, another question arises from the study: could beauty, even in maths, point to what is true in nature?

Perhaps the mathematical formulations of Hermann Weyl, which tried to reconcile electromagnetism with relativity, are a case in point. Pooh-poohed by Einstein because they were thought to conflict with experimental evidence, the formulations were accepted only after re-interpretation in the light of quantum mechanics.

Weyl may prove a model for others wanting to explore the relationship between brains, beauty and the beyond. As he is reported to have said: “My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.”

Which turned out to be true, anyway.