The Most Beautiful Equation?

There was an objective way to find the answer:

[R]esearchers led by Semir Zeki of University College London asked 16 mathematicians to rate 60 equations on a scale ranging from “ugly” to “beautiful.” Two weeks later, the mathematicians viewed the same equations and rated them again while lying inside a functional magnetic resonance imaging (fMRI) scanner.

The scientists found that the more beautiful an equation was to the mathematician, the more activity his or her brain showed in an area called the A1 field of the medial orbitofrontal cortex. The orbitofrontal cortex is associated with emotion, and this particular region of it has shown in previous tests to be correlated with emotional responses to visual and musical beauty. …

The study found … that the beauty of equations is not entirely subjective. Most of the mathematicians agreed on which equations were beautiful and which were ugly, with Euler’s identity, 1+eiπ=0, consistently rated the most attractive equation in the lot. “Here are these three fundamental numbers, e, pi and i,” [mathematician Colin] Adams says, “all defined independently and all critically important in their own way, and suddenly you have this relationship between them encompassed in this equation that has a grand total of seven symbols in it? It is dumbfounding.”

(Image of Euler’s Identity scarification via Flickr user gruntzooki)