The beauty of mathematics

What do you consider beautiful? Perhaps you find beauty in a sunset? Maybe a Mozart flute concerto or a Mahler symphony are quintessentially beautiful to you? Or maybe beauty to you is a Shakespearean soliloquy? It could be that you find a John Olsen painting, or perhaps a Raphael, achingly beautiful? Most of us could accept that all of these things could be considered beautiful, even if we might not appreciate it as much as the next person. Could you though, accept that a mathematical equation could also be beautiful? This question was answered recently by researchers who wanted to see whether mathematics could excite the brain in the same way as a piece of art.

For the study 15 mathematicians were given 60 mathematical formulae to take away and consider, then rate for how beautiful they considered the formula to be. A score of +5 was “beautiful” and -5 was “ugly”. Then two weeks later the mathematicians came into the laboratory to rate the formulae again but this time they did it while MRI scan were taken of activity in their brains.

The formulae that the participants consistently rated as beautiful were Leonhard Euler’s identity, the Pythagorean identity, and the Cauchy-Riemann equations. Euler’s identity is also known as Euler’s Equation and using only three operations links the mathematical constants e, I, ∏, 1, and 0. According to some in mathematical circles the beauty of this equation matches that of Hamlet’s “to be or not to be” soliloquy. In case you are wondering, the formulae rated as ugly were Srinivasa Ramanujan’s infinite series and Bernhard Riemann’s functional equation.

What really was at interest here though, was not which formulae were beautiful but how they affected the brain.

The MRI scans showed that when the mathematicians were considering the formulae that they considered beautiful, there was a lot of activity in a part of the brain called the medial orbito-frontal cortex. This is the same part of the brain that gets activated when someone experiences beauty from music or art.

Beauty, as far as your brain is concerned, is beauty whether it is something abstract like a mathematical formula or more concrete like a work of art. Mind you, that doesn’t mean you should take down your Manet and replace it with a Fibonacci sequence.