Category: Euler

Beauty and Form

“But there are other, highly intellectual sources of beauty. Mathematicians often describe mathematical formulae in emotive terms and the experience of mathematical beauty has often been compared by them to the experience of beauty derived from the greatest art.” For this, my thanks to the only female statistician I know – you know who you are.

MRI studies have recently concluded that mathematicians experience similar cerebral stimulation when viewing ‘equations of great beauty’ as others do when exposed to great works of art.
So. Let’s do a not-very-well-thought-through gedankenexperiment. I show you an equation thought by some to be ‘beautiful’ together with a piece of art which I think matches its beauty in some way. You get to look at them both then make up your mind. OK?




First, Euler and Botticelli. Leonhard Euler’s identity has been likened to Hamlet’s soliloquy in terms of its beauty – I have paired it with Sandro Botticelli’s Venus which took my breath away several years ago when I saw it in Florence. Euler’s identity is ubiquitous in science and mathematics; Richard Feynman once described it as “a jewel”. It links five fundamental mathematical constants with three basic arithmetic operations each occurring once.
I think it’s glorious, like a matryoshka doll. Unwrapping it reveals more wonders. The Botticelli’s purity of form, perfect curves and spectacular precision touches a different place.



Next, the Pythagorean identity, beginning with the-square-of-the-hypoteneuse-is-equal-to-the-sum-of-the-squares-on-the-other-two-sides paired with Piet Mondrian. You’ll notice that the diagram shows it better. Both of these resonate for me – but which is “numerically” superior?
The authors of this study are suggesting that it seems to provide a partial answer to a critical question in aesthetics, one which has been debated since classical times, namely whether aesthetic experiences can be quantified. If they can, it will satisfy my Floridian statistician. If not, a reader might get a double dose of endorphins. I still don’t know, MRI data or not.