Maths, Beauty, and Brain Scans
A recent post of +John Baez
about patterns in Pascal's triangle was followed by the following discussion:
Commenter 1: That proof is so simple, an A-Level student could understand it. It's so inspiring that this beautiful result is so lightly hidden!
Commenter 2: Beautiful? It's maths ! What are you on?
Commenter 1: truly, you don't feel delight at this discovery, nor see beauty in that proof?
Commenter 2: Uh..no. Sorry, history and English are more my areas of expertise. However, I realise that everyone has their own loves so,.yeah.
While commenter 2 may have been trolling just a tiny
bit, I've no doubt that their sentiments are genuine. We maths-fans are constantly banging on about "beauty" and "elegance" among our formulae, to the utter bemusement of everyone else. Is it just possible that we're a load of smart-arse poseurs?
Happily, we can now point to solid scientific evidence that the answer is no! In a recent paper The experience of mathematical beauty and its neural correlates
by the neuroscientists Semir Zeki and John Romaya, the physicist +Dionigi Benincasa
and the Fields medal-winning mathematician Michael Atiyah, fourteen mathematicians were asked to rate sixty equations on a scale of -5 (hideous) to +5 (sublime).
They then had their brains scanned while viewing the equations. The researcher's finding after all this was that "that the experience of mathematical beauty correlates with activity in the same brain area(s)... that are active during the experience of visual, musical and moral beauty... the activity there is parametrically related to the declared intensity of the experience of beauty, whatever its source"
That's good news for mathematical aesthetes!
On a side note, it's perhaps unsurprising that Euler's identity was voted as the most beautiful formula: http://en.wikipedia.org/wiki/Euler%27s_identity
And the ugliest? Ramanujan's astonishing series expression for 1/pi: http://math.stackexchange.com/questions/14115/motivation-for-ramanujans-mysterious-pi-formula
I'd have a little bet, though, that people would rate it as more beautiful if they understood it. (I don't.)