Brain finds true beauty in maths

From BBC: Brain finds true beauty in maths. A quote:

Brain scans show a complex string of numbers and letters in mathematical formulae can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers.

Mathematicians were shown “ugly” and “beautiful” equations while in a brain scanner at University College London.

The same emotional brain centres used to appreciate art were being activated by “beautiful” maths.

The researchers suggest there may be a neurobiological basis to beauty.

The study in the journal Frontiers in Human Neuroscience says,in partucular, that

The formula most consistently rated as beautiful (average rating of 0.8667), both before and during the scans, was Leonhard Euler’s identity


which links 5 fundamental mathematical constants with three basic arithmetic operations, each occurring once; the one most consistently rated as ugly (average rating of −0.7333) was Srinivasa Ramanujan’s infinite series for 1/π,

\(\frac{1}{π}=\frac{2\sqrt{2}}{9801}\sum_{k=0}^\infty  \frac{(4k)!(1103+26390k)}{(k!)^4\cdot 396^{4k}}\)

which expresses the reciprocal of π as an infinite sum.

Other highly rated equations included the Pythagorean identity, the identity between exponential and trigonometric functions derivable from Euler’s formula for complex analysis, and the Cauchy-Riemann equations. Formulae commonly rated as neutral included Euler’s formula for polyhedral triangulation, the Gauss Bonnet theorem and a formulation of the Spectral theorem. Low rated equations included Riemann’s functional equation, the smallest number expressible as the sum of two cubes in two different ways, and an example of an exact sequence where the image of one morphism equals the kernel of the next .

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