What's beautiful to you? A sunset? The face of a loved one? A favorite poem or song?

Mathematicians sometimes say they find beauty in mathematical formulas, and a new brain scan study confirms that equations can activate the brain in much the same way that great art does.

"To many of us, mathematical formulae appear dry and inaccessible, but to a mathematician an equation can embody the quintessence of beauty," study author Dr. Semir Zeki, professor of neuroesthetics at University College London, said in a written statement. "The beauty of a formula may result from simplicity, symmetry, elegance or the expression of an immutable truth."

For the study, which was published in the journal Frontiers in Human Neuroscience, Zeki and his colleagues recruited from local colleges 16 male and female mathematicians between the ages of 22 and 32. The mathematicians were asked to review 60 mathematical formulas and to rate them on a scale ranging from minus five (ugly) to plus five (beautiful). Two weeks later they re-rated the equations while in a functional MRI (fMRI) scanner.

fMRI scanners show neurological activity by measuring changes in the flow of blood inside the brain. The scans in the study showed that appreciating beautiful formulas is correlated with activity in the medial orbito-frontal cortex, a region at the front of the brain. Appreciating art or music is correlated with activity in that same region.

Srinivasa Ramanujan's infinite series (below) and Riemann's functional equation didn't fare well in the study. They were rated ugliest.



Srinivasa Ramanujan’s infinite series of 1/pi, which was rated as the ugliest mathematical formula.

Which of the 60 math formulas were rated as especially beautiful? There were three: the Pythagorean identity, the Cauchy-Riemann equations, and Leonhard Euler's identity (see above, top).

"It's a real classic, and you can do no better than that," Dr. David Percy, a professor affiliated with the Institute of Mathematics and Its Applications in the U.K., told the BBC about Euler's identity. "It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants... It also comprises the three most basic arithmetic operations--addition, multiplication, and exponentiation."