Many proofs that ${\sum }_{n=1}^{\infty }\frac{1}{n^2}=\frac{{\pi }^2}{6}$ can be found in the conformal invariance of planar Brownian motion

Abstract

A number of recent new proofs of Euler's celebrated identity are presented, all of which are probabilistic in nature and depend on the conformal invariance of planar Brownian motion.